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<!DOCTYPE TEI.2 SYSTEM "base.dtd">





<publicationStmt><distributor>BASE and Oxford Text Archive</distributor>


<availability><p>The British Academic Spoken English (BASE) corpus was developed at the

Universities of Warwick and Reading, under the directorship of Hilary Nesi

(Centre for English Language Teacher Education, Warwick) and Paul Thompson

(Department of Applied Linguistics, Reading), with funding from BALEAP,

EURALEX, the British Academy and the Arts and Humanities Research Board. The

original recordings are held at the Universities of Warwick and Reading, and

at the Oxford Text Archive and may be consulted by bona fide researchers

upon written application to any of the holding bodies.

The BASE corpus is freely available to researchers who agree to the

following conditions:</p>

<p>1. The recordings and transcriptions should not be modified in any


<p>2. The recordings and transcriptions should be used for research purposes

only; they should not be reproduced in teaching materials</p>

<p>3. The recordings and transcriptions should not be reproduced in full for

a wider audience/readership, although researchers are free to quote short

passages of text (up to 200 running words from any given speech event)</p>

<p>4. The corpus developers should be informed of all presentations or

publications arising from analysis of the corpus</p><p>

Researchers should acknowledge their use of the corpus using the following

form of words:

The recordings and transcriptions used in this study come from the British

Academic Spoken English (BASE) corpus, which was developed at the

Universities of Warwick and Reading under the directorship of Hilary Nesi

(Warwick) and Paul Thompson (Reading). Corpus development was assisted by

funding from the Universities of Warwick and Reading, BALEAP, EURALEX, the

British Academy and the Arts and Humanities Research Board. </p></availability>




<recording dur="01:25:42" n="11809">


<respStmt><name>BASE team</name>



<langUsage><language id="en">English</language>



<person id="nm0757" role="main speaker" n="n" sex="m"><p>nm0757, main speaker, non-student, male</p></person>

<person id="sm0758" role="participant" n="s" sex="m"><p>sm0758, participant, student, male</p></person>

<person id="sf0759" role="participant" n="s" sex="f"><p>sf0759, participant, student, female</p></person>

<person id="sf0760" role="participant" n="s" sex="f"><p>sf0760, participant, student, female</p></person>

<person id="sm0761" role="participant" n="s" sex="m"><p>sm0761, participant, student, male</p></person>

<person id="sf0762" role="participant" n="s" sex="f"><p>sf0762, participant, student, female</p></person>

<personGrp id="ss" role="audience" size="m"><p>ss, audience, medium group </p></personGrp>

<personGrp id="sl" role="all" size="m"><p>sl, all, medium group</p></personGrp>

<personGrp role="speakers" size="8"><p>number of speakers: 8</p></personGrp>





<item n="speechevent">Lecture</item>

<item n="acaddept">Agricultural and Food Economics</item>

<item n="acaddiv">ps</item>

<item n="partlevel">UG3</item>

<item n="module">unknown</item>




<u who="nm0757"> # two three weeks is to <pause dur="0.4"/> # <pause dur="3.8"/> is to try and build up a framework a a model that will allow us to understand how <pause dur="0.3"/> consumers make choices and <pause dur="0.8"/> we've almost got to the end of <pause dur="0.2"/> the <pause dur="0.2"/> # what people would like to buy <pause dur="0.3"/> element # of the framework <pause dur="0.3"/> and then what we're going to try and do today when we've finished that off is to actually put it together <pause dur="0.3"/> to try and <pause dur="0.2"/> # create a framework a model that will allow us to understand the choices that actually made so we going to put together that <pause dur="0.3"/> availability set the things that people can choose <pause dur="0.5"/> and the part that looks at what they actually want to choose <pause dur="0.3"/> to actually <pause dur="0.3"/> look at the choices that are actually made <pause dur="0.8"/> and what we want to try and do is to put that framework together in such a way that we can use it <pause dur="0.3"/> not just in an academic sense to <pause dur="0.2"/> have some nice diagrams but to actually <pause dur="0.2"/> predict what people will choose <pause dur="0.4"/> # and <pause dur="0.2"/> to look at what happens when things change so if we can build this framework up <pause dur="0.2"/> we can try and understand well if prices change <pause dur="0.5"/>

what's going to happen to the demand for a good is it going to go up is it going to go down <pause dur="0.3"/> and by how much <trunc>likew</trunc> wise with income <pause dur="0.2"/> for example <pause dur="0.3"/> if income changes how will demand change <pause dur="0.3"/> # and by how much so <pause dur="0.6"/> that's where we want to <pause dur="0.3"/> to end up <pause dur="1.0"/> now if you remember <pause dur="0.4"/> where we got to # <pause dur="1.1"/> at the end of <pause dur="0.3"/> last week <pause dur="4.7"/> was we we started at the end of <pause dur="0.4"/> last week hang on <pause dur="0.2"/> try and remember which of these light switches it is again <pause dur="3.2"/><event desc="changes lights" iterated="y" dur="3"/><gap reason="inaudible" extent="2 words"/><pause dur="3.3"/><kinesic desc="writes on board" iterated="y" dur="3"/> where <pause dur="1.4"/> we have all of this this space these combinations of two goods X-one and X-two <pause dur="0.3"/> okay <pause dur="0.3"/> and if you remember we said well we can represent it in two dimensions but really <pause dur="0.3"/> we're looking at the choices between all the goods and services that <pause dur="0.2"/> consumers have available to them <pause dur="1.5"/> and we started saying well what the consumer can do <pause dur="0.2"/> we assume <pause dur="0.4"/> is <pause dur="1.1"/> compare <pause dur="0.2"/> any <pause dur="0.2"/><kinesic desc="writes on board" iterated="y" dur="2"/> combination of these goods <pause dur="0.7"/> wherever it is <pause dur="0.7"/> and can say <pause dur="0.3"/> i prefer this point that combination of the two goods over this point <pause dur="0.3"/> and so on <pause dur="0.2"/> and that they can <pause dur="0.4"/> compare all the possible combinations of the things <pause dur="0.3"/> that are available

to them <pause dur="0.6"/> okay <pause dur="0.6"/> and say i prefer this combination to that combination <pause dur="0.9"/> and they do that <pause dur="0.4"/> # they have these preferences they can say that they have strong preference i prefer A over B <pause dur="0.4"/> i'm indifferent i don't care which i have <pause dur="0.5"/> or weak preference i prefer A to B or i'm indifferent between the two <pause dur="1.7"/> and then what we we did was <pause dur="0.3"/> we said okay that's fine but what we want to try and do is to build up the model that will allow us to predict choices <pause dur="0.4"/> and to do that we have to make certain assumptions about the preferences that consumers have <pause dur="1.0"/> and we we had all these assumptions of completeness there are no black holes there are no <pause dur="0.5"/> # <pause dur="0.3"/> combinations of the goods that the consumer can't express a preference over <pause dur="1.0"/> transitivity <pause dur="0.4"/> that is that we have this rule that if you say <pause dur="0.3"/> i prefer A to B <pause dur="0.2"/> and i prefer B to C we can assume that they prefer <pause dur="0.4"/> A over C <pause dur="0.5"/> and we've we we said that <pause dur="0.3"/> often that doesn't hold but <pause dur="0.6"/> # <pause dur="0.2"/> at least logically it seems that a rational consumer might have transitive preferences <pause dur="0.6"/>

we then had the idea of reflexivity that if a if a consumer couldn't compare a good <pause dur="0.3"/> or combination of goods to any other <pause dur="0.4"/> they could compare them to themselves <pause dur="1.8"/> and using that <pause dur="0.4"/> okay <pause dur="0.6"/> we said okay <pause dur="1.0"/> every single one of these points <pause dur="0.6"/> # we can express a preference over <pause dur="0.2"/> but there won't be any inconsistencies <pause dur="1.0"/> we then went on to say okay <pause dur="0.4"/> can we make any general rules about the direction of the consumer's preference and we had the idea of non-satiation <pause dur="0.6"/><kinesic desc="writes on board" iterated="y" dur="1"/> which means that preferences go out in that direction I-E <pause dur="0.4"/> that <pause dur="0.7"/> within the realms of most of the choices that consumers make with lots and lots of goods and services available to them <pause dur="0.3"/> they will prefer more to less they prefer more of the goods to less of the goods <pause dur="0.4"/> and if that is the case <pause dur="0.4"/> their preferences will go out in that direction <pause dur="0.2"/> and hence we automatically can say for example <pause dur="0.2"/> that this point here <pause dur="0.5"/> is preferred to that point there <pause dur="0.7"/> simply because it has more of # both of <pause dur="0.3"/> # <pause dur="0.2"/> the goods <pause dur="0.4"/> # and therefore <pause dur="0.2"/> automatically the

consumer will prefer more <pause dur="2.4"/> we then said okay if that's the case then we can start talking about indifference lines <pause dur="0.7"/> and because that is the case an indifference line or indifference curve must <pause dur="0.3"/> have a negative slope <pause dur="1.3"/> okay <pause dur="0.2"/> that is if we <trunc>combi</trunc> if we we <pause dur="0.3"/> draw a line that combines all of the combinations of these goods <pause dur="0.4"/> between which <pause dur="0.2"/> the consumer is indifferent <pause dur="0.9"/> it must be the case that if you get more of one good you have less of another <pause dur="0.8"/> and <trunc>w</trunc> the measure of that <pause dur="0.2"/><kinesic desc="writes on board" iterated="n"/> is the marginal rate of substitution <pause dur="0.4"/> okay the slope <pause dur="0.2"/> of <pause dur="0.6"/> the line <pause dur="1.9"/> so that's negative and it's a measure of the trade off between these two goods which reflects <pause dur="0.2"/> the relative preference that the consumer has <pause dur="0.3"/> for one good over another <pause dur="0.3"/> so if a consumer really likes X-one <pause dur="0.6"/> if they give up one unit of X-one they're going to require a lot of X-two to take its place <pause dur="0.6"/> okay <pause dur="0.4"/> for example <pause dur="1.5"/> then we said okay <pause dur="0.8"/> that's fine <pause dur="0.3"/> but <pause dur="0.4"/> looking at the way <trunc>c</trunc> they're looking at the sorts of preferences that consumers have <pause dur="0.6"/> what we tend to

find is that this rate of trade off this marginal rate of substitution <pause dur="0.3"/> isn't constant <pause dur="0.9"/> okay <pause dur="0.6"/> and we said in fact <pause dur="1.4"/> that <pause dur="0.5"/> we would expect the indifference curve <pause dur="0.3"/> to be <pause dur="0.3"/> convex to the origin <pause dur="0.8"/> which means that <pause dur="0.5"/> the rate of trade off <pause dur="0.8"/><kinesic desc="writes on board" iterated="n"/> at this point here <pause dur="0.2"/> when you have a lot of X-two and not much X-one <pause dur="0.2"/> will be different <pause dur="0.4"/> to the rate of trade off here <pause dur="0.5"/> where you have a lot of X-one and not much X-two <pause dur="0.6"/> because we know that as <pause dur="0.3"/> you get more of a good its marginal utility declines <pause dur="0.7"/> and and vice versa <pause dur="1.3"/> so where we ended up <pause dur="0.2"/> last time <pause dur="0.4"/> was <pause dur="0.2"/> with <pause dur="1.2"/> basically the ability <pause dur="1.5"/> to <pause dur="3.8"/> represent <gap reason="inaudible" extent="1 sec"/> sort of <pause dur="0.2"/> colour <pause dur="4.5"/> to represent the consumer's preferences <pause dur="0.6"/> between these two goods <pause dur="1.5"/> okay <kinesic desc="writes on board" iterated="y" dur="3"/><pause dur="0.6"/> as a series <pause dur="0.3"/> of indifference curves <pause dur="0.4"/> like this <pause dur="0.3"/> that are <pause dur="0.3"/> negatively sloped <pause dur="0.4"/> convex to the origin <pause dur="1.3"/> the direction of the consumer's preferences <pause dur="1.6"/> is out here <pause dur="0.5"/><kinesic desc="writes on board" iterated="y" dur="8"/> so we automatically know <pause dur="0.2"/> that <pause dur="3.0"/> indifference curve <pause dur="0.3"/> two <pause dur="0.7"/> is preferred to indifference curve one <pause dur="0.3"/> every single combination of the two goods on <pause dur="0.2"/> this indifference curve <pause dur="0.9"/>

<trunc>des</trunc> is preferred to every single combination <pause dur="0.4"/> on indifference curve one <pause dur="1.1"/> and likewise indifference curve three <pause dur="0.3"/> every combination on that indifference curve is preferred <pause dur="0.2"/> to indifference curve two <pause dur="0.8"/> okay and so on <pause dur="0.3"/> so the least preferred point is this point here zero consumption <pause dur="0.5"/> 'cause the consumer gets no utility because they only get utility from consumption from the goods <pause dur="0.7"/> and the maximum is some infinite point up here <pause dur="0.9"/> okay <pause dur="0.5"/> # <pause dur="0.4"/> <trunc>whoo</trunc> <pause dur="0.2"/> whoops where <pause dur="1.0"/> they consume however much <pause dur="0.6"/> because at the moment they have no constraints <pause dur="0.5"/> okay because we haven't brought the availability set in <pause dur="0.6"/> # <pause dur="0.2"/> so this is what they would like to do <pause dur="1.3"/> okay <pause dur="0.5"/> now <pause dur="0.6"/> you may say okay that's totally unrealistic because eventually the consumer will grow satiated <pause dur="0.6"/> okay <pause dur="0.3"/> now that may be true with <pause dur="0.2"/> # <pause dur="0.2"/> two goods <pause dur="0.4"/> but remember <pause dur="0.5"/> if we try and represent this with all the goods available <pause dur="0.2"/> then we can have very small substitutions between all the different goods that are available <pause dur="1.0"/> and we would assume that normally within the realms of <pause dur="0.3"/> of <pause dur="0.8"/> balanced consumption <pause dur="0.9"/> of <pause dur="0.4"/> consuming a large number of different goods <pause dur="0.4"/> that <pause dur="0.3"/> the consumer

will operate within the context of not having great satiation <pause dur="0.2"/> in most circumstances <pause dur="0.7"/> okay <pause dur="1.5"/> so that's where <pause dur="0.2"/> where we got to <pause dur="1.5"/> and <pause dur="0.5"/> that's fine we can <pause dur="0.2"/> so far <trunc>wh</trunc> if i could draw it <pause dur="0.3"/> do it in three dimensions we could do three goods <pause dur="0.5"/> okay <pause dur="0.9"/> but <pause dur="0.9"/> that is just a diagram it is it's just a representation a a theoretical <pause dur="0.3"/> model <pause dur="0.2"/> of <pause dur="0.5"/> # the consumer's preferences <pause dur="0.5"/> we can't use it at the moment to do anything <pause dur="0.2"/> except <pause dur="0.3"/> # to to try and think about the way in which choices are made <pause dur="0.8"/> what we need to do is to be able to represent this <pause dur="0.2"/> numerically <pause dur="0.2"/> we need to be able to represent <pause dur="0.4"/> these indifference curves <pause dur="0.3"/> in a numerical form <pause dur="0.7"/> 'cause if we can do that <pause dur="0.8"/> if you remember the availability set can be represented # <pause dur="0.3"/> # mathematically because you have the budget line <pause dur="1.4"/> what we need to be able to do is to represent these <pause dur="0.5"/> algebraically mathematically <pause dur="0.4"/> # and then we can combine the two together and use that to actually predict the <trunc>ch</trunc> the <trunc>co</trunc> the choices the consumer would actually make <pause dur="1.5"/> if we can <trunc>al</trunc> also

if we can represent it algebraically of course we're not constrained to three goods which is what we are in a three-dimensional diagram <pause dur="0.3"/> we can have however many goods <pause dur="0.2"/> that the consumer has available to them <pause dur="0.9"/> okay <pause dur="0.3"/> so we need to <pause dur="0.2"/> represent this in some other way <pause dur="0.5"/> and so the final assumption <pause dur="0.2"/> is that we can represent <pause dur="1.1"/> these indifference curves algebraically <pause dur="0.3"/> and that they are differentiable <pause dur="1.1"/> okay <pause dur="0.4"/> that is that if <pause dur="0.2"/> we we we can differentiate them so that we can derive an optimum <pause dur="0.8"/> okay we can derive a point <pause dur="0.4"/> # a choice that the consumer will make <pause dur="0.2"/> when we put all of all all of the information together <pause dur="0.2"/> the two sides <pause dur="0.6"/> so that's the final assumption <pause dur="0.5"/> that <pause dur="0.2"/> that we are we are going to make <pause dur="1.2"/> now we're not going to go into <pause dur="0.3"/> # a lot of the <trunc>m</trunc> of the mathematics <pause dur="0.4"/> okay <pause dur="0.3"/> it's it's <pause dur="0.3"/> the basic principle that really <pause dur="0.3"/> matters here <pause dur="1.0"/> okay <pause dur="0.8"/> now <pause dur="1.0"/> the complication we have <pause dur="1.5"/> is that we have said that utility is not <pause dur="0.3"/> measurable <pause dur="0.3"/> in a cardinal sense that is <pause dur="0.3"/> we cannot say <pause dur="0.3"/> for example that if a consumer <pause dur="0.3"/> # has a certain consumes a

certain combination of goods their utility is level X <pause dur="0.6"/> and then if they consume another combination it's level Y <pause dur="1.0"/> okay <pause dur="0.2"/> we can't say there's a <trunc>l</trunc> level utility ten <pause dur="0.4"/> and another combination of goods gives you level of utility twenty <pause dur="0.4"/> we've said we can't do that we can't measure utility <pause dur="0.5"/> # and even if we could we couldn't combine it across individuals because it's totally individual <pause dur="0.4"/> # to that consumer <pause dur="2.3"/> that seems to fly in the face of saying well we want to represent those indifference curves <pause dur="0.4"/> mathematically algebraically <pause dur="0.2"/> and we want to be able to predict the choice they make <pause dur="1.1"/> that's because the reason for that conflict is that all of the mathematical functions that you will have seen to date <pause dur="0.5"/> are what called <trunc>a</trunc> are are are called cardinal functions that is functions where <pause dur="0.2"/> the numbers are measuring things so if we have a value of ten <pause dur="0.3"/> we can say that is half of a value of twenty <pause dur="1.1"/> okay <pause dur="0.8"/> now what we are going to do <pause dur="0.9"/> is to use a type of function that is called an ordinal

function <pause dur="1.0"/> and an ordinal function <pause dur="0.4"/> is a function where the numbers <pause dur="0.5"/> only matter in terms of their relative position <pause dur="0.5"/> so if you have values of one and two <pause dur="0.9"/> the two is greater than one <pause dur="0.6"/> okay it doesn't matter how much <pause dur="0.2"/> but it's just greater <pause dur="0.6"/> okay so that all that matters in an ordinal function <pause dur="0.2"/> is order <pause dur="0.5"/> not relative position <pause dur="0.8"/>

okay <pause dur="0.7"/> so <pause dur="0.2"/> what we want to do <pause dur="0.6"/> is <pause dur="1.2"/> we have our indifference curves <pause dur="4.0"/><kinesic desc="writes on board" iterated="y" dur="6"/> like this <pause dur="2.5"/> and we want to be able to represent those indifference curves <pause dur="2.0"/> with a number <pause dur="0.5"/> okay algebraically <pause dur="1.6"/> and <pause dur="0.2"/> presume that we can represent that <pause dur="1.8"/><kinesic desc="writes on board" iterated="y" dur="2"/> utility function as # U-X-one-X-two <pause dur="0.6"/> that is <pause dur="0.3"/> utility <pause dur="1.2"/> the satisfaction they get <pause dur="0.5"/> is a function of the amounts of these goods which is what we've said and don't get they don't get satisfaction from anything else they just get it from consumption <pause dur="0.3"/> in <pause dur="0.6"/> in the context of the market <pause dur="1.9"/> and clearly the amount of the utility depends on the quantities of those two goods and that's exactly what this diagram says <pause dur="0.9"/> okay it says that <pause dur="0.3"/> # <pause dur="1.6"/><vocal desc="cough" iterated="n"/><pause dur="0.4"/> if we have this combination <pause dur="0.9"/><kinesic desc="writes on board" iterated="y" dur="2"/> and this

combination <pause dur="0.2"/> these two points here <pause dur="0.7"/> the level of utility's exactly the same <pause dur="0.2"/> although the quantities of these two goods is actually different <pause dur="0.2"/> because <pause dur="0.3"/> the consumer is indifferent between those two combinations <pause dur="0.6"/> and we've said that if we have a combination here <pause dur="3.3"/><kinesic desc="writes on board" iterated="y" dur="3"/> the the level of utility is greater <pause dur="0.8"/> again the quantities of the two goods are different <pause dur="0.5"/> but the level of utility that the consumer gets is is greater because it's on a higher indifference curve <pause dur="1.6"/> and so what we want to do is to represent these <pause dur="0.2"/> these indifference curves <pause dur="0.2"/><vocal desc="cough" iterated="n"/><pause dur="0.3"/> as <pause dur="0.4"/> what is called a utility function <pause dur="0.4"/> a function that simply says the utility the consumer gets <pause dur="0.5"/> is a function mathematically of <pause dur="0.4"/> the <pause dur="0.2"/> quantity of X-one <pause dur="0.5"/> and the quantity of X-two <pause dur="0.9"/> okay the quantity the amount of the two goods <pause dur="2.1"/> one of these could be zero <pause dur="0.2"/><vocal desc="cough" iterated="n"/> so if the consumer got no utility at all from <pause dur="0.3"/> the consumption of that good <pause dur="0.3"/> then simply <pause dur="0.3"/> the <pause dur="0.4"/> the expression relating to say X-one this good here would just be zero <pause dur="1.0"/> okay so that's possible <pause dur="0.6"/> # <pause dur="0.5"/> and if the consumer <trunc>go</trunc> got

no utility at all from these two <pause dur="0.3"/> then <pause dur="0.5"/> it <unclear>would</unclear> be zero for both <pause dur="1.2"/> okay so we can represent that no no problem at all <pause dur="1.7"/> but we don't we're not going to represent <pause dur="0.2"/> these indifference curves with a function <pause dur="1.6"/> which assumes that we're measuring utility <pause dur="0.2"/> so we're going to use <pause dur="0.5"/> # what is termed a a an ordinal function <pause dur="2.3"/><vocal desc="cough" iterated="n"/><pause dur="0.2"/> okay <pause dur="2.8"/> so <pause dur="0.7"/> we're not going back to a world where <pause dur="1.5"/> yeah we can measure marginal utility et cetera <pause dur="0.4"/> we're still in a world of of indifference curves <pause dur="0.2"/> okay that's so that's <pause dur="0.2"/> that's fine <pause dur="1.6"/> okay <vocal desc="cough" iterated="n"/><pause dur="0.9"/> the type of function we want is as is as follows <pause dur="0.5"/> if we assume that we have two <pause dur="0.5"/> consumption bundles <kinesic desc="writes on board" iterated="y" dur="3"/> X-one <pause dur="1.2"/> # and X-two <pause dur="0.6"/> okay and these are the utility functions that represent those two consumption bundles <pause dur="0.3"/> so X-<pause dur="0.6"/>one here is a combination of these two goods <pause dur="0.5"/> and X-two here is a combination of these two goods <pause dur="0.5"/> a different combination <pause dur="1.8"/><vocal desc="cough" iterated="n"/><pause dur="0.8"/> and <pause dur="1.0"/> what we want to do <pause dur="0.4"/> is to effectively so U-X-one <pause dur="0.8"/> okay could be associated with this indifference curve here and U-X-two could be associated with this indifference <pause dur="0.2"/>

curve here <pause dur="0.8"/> okay for example <pause dur="2.0"/> what we want is to put numbers on these things <pause dur="0.3"/> so hence any combination of goods that lay on indifference curve <pause dur="0.3"/> two <pause dur="0.2"/> would have a greater number <pause dur="0.2"/> than any combination <pause dur="0.4"/> on indifference curve one <pause dur="0.9"/> okay <pause dur="3.2"/> now <pause dur="0.7"/> let's assume that we give we have a <trunc>lar</trunc> a larger <pause dur="0.2"/> value <pause dur="0.4"/> for U-X-one this combination <pause dur="0.3"/> than U-X-two <pause dur="0.3"/> what that would mean of course is that the consumer preferred <pause dur="0.3"/> this combination <pause dur="0.2"/> to that combination that is <pause dur="1.5"/> that <pause dur="0.4"/><kinesic desc="writes on board" iterated="y" dur="5"/> X-one <pause dur="0.2"/> was preferred <pause dur="1.0"/> to X-two <pause dur="1.6"/> okay and that's what that would imply <pause dur="0.5"/> is that the consumer strictly preferred X-one over X-two <pause dur="2.9"/> the other possible scenario <pause dur="1.0"/> is that <kinesic desc="writes on board" iterated="y" dur="4"/> U<pause dur="0.7"/>-X-one is equal to U<pause dur="0.3"/>-X-two like if two goods were on the same indifference curve <pause dur="0.8"/> and that would assume <pause dur="1.3"/> that the consumer was <pause dur="0.3"/> indifferent <pause dur="1.6"/> okay <pause dur="3.2"/> so <pause dur="0.2"/> we want <pause dur="0.3"/> to represent these indifference curves in such a way <pause dur="0.5"/> that either <pause dur="0.7"/> if the consumer is indifferent <pause dur="0.9"/> the value we give the number we give is exactly the same <pause dur="1.8"/> okay <pause dur="1.1"/> if the consumer prefers one bundle of goods over another we will give

a bigger number <pause dur="0.4"/> to <pause dur="0.6"/> the # <pause dur="0.8"/> bundle the consumer prefers <pause dur="2.3"/> what <trunc>th</trunc> <trunc>th</trunc> the the very important thing to get clear in your mind is it doesn't matter what the number is <pause dur="1.1"/> okay <pause dur="1.0"/> all that matters is that we give the same number <pause dur="0.7"/> to bundles of goods between which the consumer is indifferent <pause dur="1.1"/> and we give a bigger number <pause dur="0.7"/> to combinations of goods <pause dur="0.2"/> that the consumer prefers <pause dur="0.9"/> it doesn't matter how much bigger <pause dur="1.6"/> okay <pause dur="0.5"/> and that is the crucial difference <pause dur="0.2"/> if it mattered how much <pause dur="0.2"/> bigger the number was <pause dur="0.2"/> we would be using it as a real measure of utility we'd be saying that <pause dur="0.3"/> if it was a value of ten <pause dur="0.6"/> that would be half a value of twenty <pause dur="1.5"/> all we're saying is that if we give a value of ten <pause dur="0.4"/> that is less <pause dur="0.2"/> than twenty <pause dur="0.4"/> doesn't matter how much because we're not measuring utility <pause dur="0.3"/> we're just measuring order <pause dur="0.4"/> hence it is called an ordinal function <pause dur="1.3"/> okay <pause dur="0.5"/> so <pause dur="0.3"/> any combinations on one indifference curve will have the same number <pause dur="1.2"/> any higher indifference curve any combinations that are on a higher <trunc>diss</trunc> <pause dur="0.2"/> indifference

curve will have a bigger number it doesn't matter how much bigger the number is <pause dur="1.5"/> okay <pause dur="0.8"/> so <pause dur="0.7"/> let's <kinesic desc="changes transparency" iterated="y" dur="3"/> assume for example that we have <pause dur="0.3"/> # three <pause dur="0.4"/> no sorry four <pause dur="0.2"/> # <pause dur="2.3"/> consumption bundles <pause dur="0.9"/> okay these are four different combinations of those goods <pause dur="0.9"/> and we have a utility function <pause dur="1.5"/> U-X <pause dur="6.8"/> okay <pause dur="2.0"/> now <pause dur="1.5"/> if we assume that X-one that that this combination X-one and this combination X-two the consumer is totally indifferent between them <pause dur="0.3"/> they will have exactly the same number <pause dur="0.2"/> say five and five <pause dur="3.5"/> okay <pause dur="1.9"/> and let's assume that they prefer X-three over those two <pause dur="0.8"/> and it may then have a number of <pause dur="0.2"/> ten <pause dur="1.9"/> and they like X-four even more <pause dur="1.5"/> and that could have a number which is say twenty <pause dur="1.6"/> okay <pause dur="0.9"/> so <pause dur="0.2"/> X-one and X-two are indifferent <pause dur="1.0"/> they <trunc>pref</trunc> <trunc>thi</trunc> this consumer prefers X-three over two and one <pause dur="0.6"/> and prefers four over three two and one <pause dur="7.4"/> let's assume that we have let's think say another function <pause dur="0.3"/> that we <trunc>rec</trunc> we could we and we give another numerical representation <pause dur="0.4"/> to <pause dur="0.6"/> # <pause dur="0.3"/> to this consumer's preferences <pause dur="1.1"/> and let's say

we have a value of # a thousand <pause dur="0.7"/> here <pause dur="3.9"/> again the numbers are the same hence the consumer's indifferent <pause dur="4.9"/> let's assume the number given to X-three is ten-thousand <pause dur="2.4"/> that indicates the consumer prefers X-three over two and one <pause dur="1.7"/> it does not say <pause dur="0.2"/> that they prefer the <trunc>consu</trunc> <pause dur="0.2"/> X-two more <pause dur="0.6"/> than when <pause dur="0.2"/> we had a value of ten <pause dur="1.0"/> okay <pause dur="0.8"/> all that matters <pause dur="0.3"/> is that that number <pause dur="0.3"/> is bigger <pause dur="0.4"/> than the numbers given to X-one and X-two <pause dur="0.4"/> it doesn't matter how much because we're not measuring utility <pause dur="0.5"/> all that matters is relative <pause dur="0.7"/> # positioning <pause dur="0.6"/> and so we could have a value of say a million <pause dur="1.2"/><kinesic desc="writes on board" iterated="y" dur="1"/> given to X-four <pause dur="0.6"/> and again that doesn't tell us anything more <pause dur="0.7"/> than the values here <pause dur="1.0"/> it's exactly the same <pause dur="1.2"/> because all that matters is relative ordering <pause dur="0.6"/> hence it's an ordinal function <pause dur="0.7"/> the higher the number <pause dur="0.8"/> the greater the consumer's preference <pause dur="1.0"/> okay that's true <pause dur="1.6"/> but it doesn't say <pause dur="0.2"/> how much higher it is <pause dur="0.2"/> it just says it is higher <pause dur="1.9"/> so whenever a number is bigger than another number it means the consumer has greater

preference they will go for that combination of goods <pause dur="0.3"/> rather than one to which we've allocated <pause dur="0.2"/> a lower number <pause dur="3.5"/> how much the number differs <pause dur="0.3"/> is irrelevant <pause dur="0.9"/> it could differ by <pause dur="0.2"/> you know <pause dur="0.3"/> one decimal point <pause dur="0.4"/> or it could differ by <pause dur="0.8"/> a million <pause dur="1.3"/> the information is exactly the same because <pause dur="0.2"/> what we're well what we're not saying is that this how the consumer <pause dur="0.4"/> chooses <pause dur="0.3"/> you know they they think in their head what is my utility function <pause dur="0.7"/> how much utility do i get from these combinations <pause dur="0.3"/> what we're saying is that we want to represent <pause dur="2.1"/><kinesic desc="changes transparency" iterated="y" dur="1"/> # these <pause dur="0.3"/> these ideas that we have about their preferences <pause dur="0.5"/> in a numerical way <pause dur="1.1"/> okay <pause dur="0.8"/> we don't want to measure utility because we assumed that we can't do that <pause dur="1.8"/> but what we do want to do is to say <pause dur="0.2"/> we want to give a bigger number <pause dur="0.4"/> to <pause dur="0.2"/> a higher indifference curve because of course what we want to do <pause dur="0.2"/> is to produce a model that says <pause dur="0.4"/> the consumer <pause dur="0.2"/> aims for the highest indifference curve <pause dur="1.1"/> okay they aim for the one <pause dur="0.2"/> which is <pause dur="0.6"/> furthest up <pause dur="1.1"/> okay <pause dur="1.7"/> we're not saying <pause dur="0.3"/> that <pause dur="0.7"/> we can

measure their utility we're saying is that all they will do is to strive for the highest indifference curve <pause dur="1.0"/> okay and <pause dur="0.7"/> that is # that is all <pause dur="0.9"/> these are termed ordinal functions and they are <pause dur="1.4"/> very different <pause dur="0.3"/> to <pause dur="0.4"/> the sorts of functions that you see we can treat them in exactly the same way as any other <pause dur="0.2"/> mathematical function <pause dur="0.5"/> we can do everything to them that we can do to another <pause dur="0.2"/> mathematical function <pause dur="0.5"/> the only difference is the interpretation we give to these numbers <pause dur="0.6"/> all that matters <pause dur="0.2"/> is their relative position <pause dur="0.8"/> okay <pause dur="0.3"/> how much they are different <pause dur="0.4"/> does not matter <pause dur="0.2"/> simply because <pause dur="0.5"/> # <pause dur="0.5"/> we're not measuring their utility <pause dur="0.2"/> we're just measuring <pause dur="0.2"/> order <pause dur="0.9"/> okay <pause dur="1.6"/>

do you do you understand <pause dur="0.2"/> that distinction <pause dur="0.2"/> between the two types of functions and and what <pause dur="0.5"/> those functions are representing <pause dur="0.2"/> yeah <pause dur="1.1"/> simply they're saying <pause dur="1.0"/> if we get more preference we have a bigger number <pause dur="0.3"/> doesn't matter how much <pause dur="0.2"/> that's irrelevant <pause dur="0.4"/> okay <pause dur="0.4"/> and it does take you know given you've been used to using other the other functions in in other ways <pause dur="0.2"/> it does take some sort of <pause dur="0.2"/> getting your head round but # <pause dur="1.3"/> okay that's <trunc>th</trunc> basically what what we want to do <pause dur="2.8"/> once we once we've said we can do that we can give a number to the preferences <pause dur="0.2"/> then we just have to decide what is the mathematical form <pause dur="1.7"/> okay what is the mathematical form <pause dur="1.4"/> and i'm just going to quickly give you some <pause dur="0.5"/> # examples <vocal desc="cough" iterated="n"/><pause dur="0.4"/> okay <pause dur="0.5"/> # <pause dur="3.1"/> some some extreme <pause dur="0.3"/> examples <pause dur="0.2"/> okay <trunc>th</trunc> the normal case that we'd tend to find and then just some extreme examples so that you <pause dur="0.5"/> # <pause dur="0.8"/> you understand <pause dur="0.3"/><vocal desc="cough" iterated="n"/><pause dur="1.3"/><kinesic desc="changes transparency" iterated="y" dur="10"/> now you've been used to seeing <pause dur="1.0"/> # <pause dur="0.4"/> indifference curves like this <pause dur="2.4"/> okay <pause dur="8.1"/>

fine <pause dur="0.9"/> they represent the sorts of things <trunc>th</trunc> the sort of assumptions that we've built up the sort of assumptions we built up last week <pause dur="1.1"/> and which is <pause dur="0.3"/> a convex marginal rate of substitution changes <pause dur="0.3"/> as the combinations of the good change <pause dur="0.3"/> <trunc>tha</trunc> <trunc>tha</trunc> it's negative <pause dur="0.6"/> okay so there's a trade off between the goods <pause dur="0.3"/> the consumer prefers a higher indifference curve to a lower one and so on <pause dur="0.7"/> okay <pause dur="1.4"/> if they're the assumptions we make <pause dur="0.8"/> then we want to be able to represent <pause dur="0.3"/> those types of preferences between the goods in some <pause dur="0.4"/> mathematical form <pause dur="1.6"/> and the normal form that is used there <pause dur="3.0"/> okay <pause dur="0.2"/> is <pause dur="0.7"/> # <pause dur="4.4"/> is a quadratic form of some kind <pause dur="1.6"/> okay <pause dur="0.3"/> that simply says that <pause dur="0.4"/> # and these here are your marginal rates of substitution alpha and beta <pause dur="1.1"/> okay <pause dur="1.3"/> so these are the marginal utilities of the goods the ratio of those will be the marginal rate of substitution <pause dur="0.7"/> okay <pause dur="0.2"/> so alpha is the marginal utility associated with X-one <pause dur="1.0"/> # <pause dur="0.2"/> and beta is the marginal rate of substitution <pause dur="0.3"/> associated with X-two <pause dur="0.5"/> and of course the

ratio of those which is the slope of the <pause dur="0.2"/> indifference curve <pause dur="0.5"/> will give you the marginal rate of substitution <pause dur="0.8"/> okay <pause dur="2.3"/> and all we've said is okay <pause dur="0.3"/> this mathematical function <pause dur="1.8"/> okay will <trunc>dem</trunc> will will display mathematical properties <pause dur="1.2"/> like <pause dur="0.2"/> we have here <pause dur="1.4"/> okay <pause dur="1.0"/> I-E <pause dur="0.2"/> that represents that will allow us algebraically to represent that <pause dur="0.8"/> okay <pause dur="1.2"/> the alpha <pause dur="0.4"/> marginal utility of of X-one<pause dur="0.2"/>-beta marginal utility of X-two <pause dur="0.6"/> the ratio between alpha and beta marginal rate of substitution which is a piece of information we may want <pause dur="0.4"/> and directly we can represent this algebraically <pause dur="0.2"/> we can get that marginal rate of substitution <pause dur="0.8"/> okay <pause dur="0.9"/> of course it may change <pause dur="1.5"/> according to which point on the indifference curve we are because we've said that's what happens <pause dur="0.8"/> so it will change according to the absolute amounts of X-one and X-two <pause dur="1.2"/> okay <pause dur="0.8"/> # <pause dur="0.4"/> but <pause dur="0.9"/> that <pause dur="0.8"/> would represent <pause dur="0.2"/> that <pause dur="0.5"/> and so that is the normal form that is used <pause dur="1.7"/> okay <pause dur="0.4"/> okay it's a bit <pause dur="0.2"/> # more difficult <pause dur="0.2"/> # mathematically <pause dur="0.4"/> to deal with <pause dur="1.0"/> because it's not linear <pause dur="0.4"/>

but <pause dur="0.2"/> in fact if you take the logs of that it becomes linear anyway <pause dur="0.2"/> so so it's relatively easy to use <pause dur="0.3"/> but that is the sort of thing that we might use to represent the normal types of preferences <pause dur="0.3"/> that we assume consumers have <pause dur="1.6"/> okay <pause dur="0.6"/> so that's <pause dur="0.5"/> one form <pause dur="0.6"/> that we might use <pause dur="0.3"/> and then what we would do <pause dur="0.3"/> okay <pause dur="0.4"/> is <pause dur="0.4"/> X-one and X-two will be the quantities of the goods <pause dur="1.5"/> and of course if there are ten goods there will be ten <pause dur="0.5"/> of these X-one X-two X-three up to X-ten <pause dur="0.3"/> and there'll be ten of these <pause dur="0.2"/> marginal utilities <pause dur="1.3"/> okay <pause dur="0.4"/> and then again there will be a marginal rate of substitution between <pause dur="0.4"/> all of the pairs of goods that the consumer has available to them <pause dur="0.5"/> so X-one and X-two there'll be a marginal rate of substitution between X<pause dur="0.3"/>-one and X-three <pause dur="0.4"/> and so on <pause dur="1.3"/> okay <pause dur="1.0"/> and that will simply be these ratios the ratios between these <pause dur="3.3"/> but all we're saying is that that mathematical form <pause dur="2.4"/> can represent that <pause dur="0.6"/> we're not saying that the consumer goes in the shop <pause dur="0.5"/> and gets out a calculator <pause dur="0.2"/> with that sort of

mathematical function imprinted in it we're saying that <pause dur="0.2"/> that is a mathematical way of representing the preferences that we've said <pause dur="0.2"/> the consumer might have the model that we've we've actually built up <pause dur="4.1"/><kinesic desc="changes transparency" iterated="y" dur="12"/> okay <pause dur="0.2"/><vocal desc="cough" iterated="n"/><pause dur="5.5"/> an alternative form <pause dur="3.9"/> might be as follows <pause dur="12.1"/> these are linear <pause dur="0.7"/> indifference curves straight lines <pause dur="7.3"/> okay <pause dur="4.7"/> they're different to the previous ones because the other ones are convex <pause dur="1.1"/> they're curved <pause dur="0.6"/> these ones are straight lines <pause dur="0.4"/> how much <pause dur="0.2"/> or to what extent does the marginal rate of substitution change as you go up and down on the indifference curve like this <pause dur="2.8"/> go up go down </u><pause dur="0.2"/><u who="sm0758" trans="pause"> constant </u><u who="sf0759" trans="latching"> constant </u><u who="nm0757" trans="latching"> it's constant yeah <pause dur="0.2"/> so the marginal rate of substitution <pause dur="0.2"/> doesn't change <pause dur="1.0"/> it's constant <pause dur="2.2"/> okay <pause dur="0.6"/> it's still going to be <pause dur="0.5"/> that ratio <trunc>al</trunc> A alpha over beta <pause dur="1.6"/> okay because the alpha the coefficient <unclear>of X-four</unclear> <pause dur="0.2"/> represented marginal utility of X-one <pause dur="0.3"/> and the beta represented marginal utility of X-two <pause dur="0.2"/> so the marginal rate of substitution is still exactly the same and in every one of these it's exactly the same <pause dur="0.4"/>

mathematically <pause dur="0.5"/> but in this case it doesn't change <pause dur="0.6"/> it's it's going to remain exactly constant <pause dur="0.3"/> what sort of goods demonstrate would have that sort of <pause dur="0.7"/> of # <pause dur="0.2"/> indifference curve <pause dur="3.3"/> what we're saying is <pause dur="0.3"/> that <pause dur="1.0"/> your margin utility <pause dur="0.8"/> okay <pause dur="0.2"/> doesn't change according to how much you have <pause dur="0.9"/> and <pause dur="0.2"/> the rate at which you substitute between the two goods remains exactly the same <pause dur="0.6"/> so if you <trunc>alwa</trunc> you will always require for example <pause dur="0.3"/> two units of X-one to replace one unit of X-two <pause dur="2.8"/> have you got any idea of the sorts of goods we might <pause dur="0.3"/> see that with <pause dur="4.0"/> how substitutable are these goods <pause dur="4.3"/> do you think <pause dur="1.7"/> very substitutable or <pause dur="0.2"/> not very substitutable <pause dur="2.5"/> very <pause dur="0.3"/> yeah <pause dur="0.5"/> these are perfect substitutes <pause dur="2.1"/> okay <pause dur="0.5"/> that doesn't mean that the marginal rate of substitution is one I-E <pause dur="0.4"/> one unit for one unit one unit of X-one for one unit of X-two <pause dur="0.2"/> but it does mean <pause dur="0.2"/> that the rate of substitution doesn't change at all <pause dur="1.4"/> it remains exactly the same <pause dur="0.3"/> hence they are perfect substitutes for one another <pause dur="0.6"/> and that remains exactly the <pause dur="0.3"/> the same

however much you have <pause dur="2.2"/> and a function <pause dur="0.8"/> that would represent that <pause dur="0.9"/> is simply alpha-X-one plus beta-X-two <pause dur="2.3"/> okay <pause dur="2.3"/> the marginal rate of substitution is again alpha over beta <pause dur="0.6"/> it's the ratio <pause dur="0.3"/> okay <pause dur="0.2"/> of of the two <pause dur="1.8"/> because alpha's the marginal utility of X-one beta's <trunc>u</trunc> marginal utility of X-two <pause dur="0.2"/> but in this case it remains it's <pause dur="0.2"/> it's a constant <pause dur="1.7"/> okay <pause dur="0.6"/> # however much X-one or X-two the consumer has these are perfect substitutes for one another <pause dur="2.2"/> okay <pause dur="2.2"/> these of course are easy to handle 'cause they're linear <pause dur="0.7"/> it's a very <trunc>s</trunc> simple function <pause dur="0.4"/> but again all we're saying is that if that was <pause dur="0.8"/> if we had two goods <pause dur="0.6"/> for which the consumer <pause dur="0.4"/> you know <pause dur="0.4"/> # regarded them as perfectly <pause dur="0.3"/> # substitutable <pause dur="0.5"/> then that that would represent that <pause dur="1.9"/> okay <pause dur="0.6"/> alpha-X-one plus beta-X-two <pause dur="2.3"/> and <pause dur="0.7"/> so that is the perfect substitute case which is one extreme <pause dur="0.8"/> away from <pause dur="0.4"/> the convex <pause dur="0.2"/> # <pause dur="0.2"/> indifference curves that we <pause dur="0.8"/> we saw before <pause dur="2.8"/> the other extreme <pause dur="1.0"/> <trunc>i</trunc> is as follows <pause dur="19.2"/><kinesic desc="changes transparency" iterated="y" dur="17"/> right-angled indifference curves <pause dur="3.8"/> have you any idea what sort of grid this

might be <pause dur="5.5"/> because you may have seen demand curves that look exactly like this in the past </u><pause dur="0.6"/> <u who="sf0760" trans="pause"> right and left shoe <gap desc="inaudible" extent="1 word"/></u><pause dur="0.5"/> <u who="nm0757" trans="pause"> sorry </u> <u who="sf0760" trans="latching"> <vocal desc="cough" iterated="n"/> left shoe and right shoe </u><pause dur="1.1"/> <u who="nm0757" trans="pause"> left shift and right shift </u><u who="sf0760" trans="overlap"> left left left shoe and right shoe </u><u who="nm0757" trans="overlap"> oh left shoe and right shoe <pause dur="0.4"/> # <pause dur="1.0"/> not necessarily no <pause dur="3.8"/> mm <pause dur="0.2"/> maybe <pause dur="1.0"/> maybe <pause dur="0.2"/> what <pause dur="0.3"/> what do you mean by that </u><pause dur="1.3"/> <u who="sf0760" trans="pause"> <gap reason="inaudible" extent="2 secs"/></u><pause dur="2.5"/> <u who="nm0757" trans="pause"> okay yeah <trunc>mayb</trunc> yeah okay <pause dur="0.3"/> so <pause dur="0.2"/> what are you saying about the two goods </u><pause dur="1.3"/><u who="sf0760" trans="pause"> <gap reason="inaudible" extent="1 sec"/> <pause dur="0.9"/> </u><u who="nm0757" trans="latching"> mm </u><u who="sf0760" trans="overlap"> you mean like one or the other </u><pause dur="0.3"/> <u who="nm0757" trans="pause"> okay <pause dur="0.4"/> in which case yeah <pause dur="1.0"/> can you think of any other examples <pause dur="5.9"/> these these goods are perfect complements <pause dur="0.5"/> yeah <pause dur="1.4"/> that is <pause dur="0.2"/> that they are consumed <pause dur="0.6"/> in <pause dur="0.2"/> certain combinations so in fact you're right left shoes right shoes <pause dur="0.4"/> # exactly the same <pause dur="0.5"/> # if someone likes # <pause dur="0.5"/> black coffee <pause dur="0.8"/> then they don't have any milk if they like very milky coffee then they they <pause dur="0.2"/> they consume a certain amount of milk in their coffee <pause dur="0.4"/> but the two <pause dur="0.5"/> cannot compensate for one another <pause dur="0.9"/> okay they can't compensate for one another <pause dur="1.8"/> so <pause dur="0.3"/> if you have so you're right if you have a left shoe then you have then have a right shoe <pause dur="1.0"/> that's fine but if you then have one extra right shoe that doesn't

actually give you any more satisfaction because you need another left shoe presumably to consume with it <pause dur="0.6"/> or <pause dur="0.2"/> if you like <pause dur="0.2"/> a certain combination of of milk and and coffee in a drink <pause dur="1.1"/> if you add more milk <pause dur="0.6"/> then you don't get any extra satisfaction <pause dur="0.6"/> and that combination <pause dur="1.1"/> is that point there <pause dur="1.9"/>

okay that combination says well in this case you require equal amounts of X-one and X-two so it could be left and right shoes for example <pause dur="1.8"/> okay <pause dur="0.3"/> # <pause dur="0.6"/> you have to consume them in that combination if you have more X-one <pause dur="0.8"/> okay which is going out along here <pause dur="0.9"/> you don't get any more satisfaction at all <pause dur="0.9"/> it remains exactly the same 'cause you don't go to another indifference curve <pause dur="0.6"/> and likewise if you have more X-two <pause dur="0.3"/> you don't get any more satisfaction <pause dur="0.2"/> you remain on the same indifference curve <pause dur="1.2"/> okay <pause dur="0.6"/> so <pause dur="1.7"/> the only way you get more satisfaction <pause dur="0.5"/> is <pause dur="0.7"/> to <pause dur="1.1"/> move up <pause dur="0.9"/> here <pause dur="1.1"/> on a line <pause dur="5.6"/> with the same combinations of X-one and X-two <pause dur="0.2"/> I-E <pause dur="0.7"/> you need more <pause dur="0.5"/> of both goods in exactly the same ratio <pause dur="0.2"/> to get more satisfaction <pause dur="2.1"/> if you get more

of one and no more of the other <pause dur="0.4"/> you don't get any more satisfaction at all because you <trunc>m</trunc> you need to consume the two goods together <pause dur="2.2"/> okay <pause dur="0.9"/> now <pause dur="1.9"/> this <pause dur="1.1"/> is the other extreme of course perfect complements perfect substitutes <pause dur="1.0"/> it is however slightly <pause dur="1.0"/> # unrealistic <pause dur="0.9"/> <trunc>i</trunc> in in some senses because <pause dur="1.2"/> what we're saying is that if the consumer has this amount of the two goods so <pause dur="0.5"/> like milk and coffee <pause dur="0.8"/> so in this case the consumer would have white very milky coffee in the sense that they require <pause dur="0.3"/> the same quantities of both <pause dur="0.7"/> okay half and half <pause dur="1.9"/> what we're then saying is okay if this consumer was given <pause dur="0.3"/> coffee <pause dur="0.2"/> with more and more milk <pause dur="1.2"/> the amount of satisfaction they get <pause dur="0.7"/> doesn't go up it doesn't go down <pause dur="1.6"/> okay <pause dur="0.9"/> so they don't get any extra satisfaction <pause dur="0.5"/> but they don't get disutility either <pause dur="1.7"/> now <pause dur="0.2"/> that is probably unrealistic <pause dur="0.3"/> because what probably happens actually is that they require in this case same amount of milk the same amount of coffee <pause dur="0.4"/> but if they get more or less of one <pause dur="0.3"/> their actual utility

goes down <pause dur="0.4"/> okay because the coffee gets more and more milk they don't like it <pause dur="0.2"/> hence their level of satisfaction goes down <pause dur="1.3"/> okay <pause dur="1.4"/> and we're assuming having the green lines here that that doesn't happen <pause dur="1.3"/> okay so they're perfect complements but if they get out of synch with one another <pause dur="1.0"/> they # you don't get disutility <pause dur="1.1"/> if you get disutility <pause dur="0.7"/> then in fact the indifference curve would simply be <pause dur="2.3"/> the points <pause dur="1.4"/> okay <pause dur="3.5"/> up here <pause dur="0.5"/> because <pause dur="0.3"/> the goods would have to be consumed in absolutely those quantities <pause dur="0.8"/> any other <pause dur="0.2"/> spoils everything <pause dur="1.7"/> okay <pause dur="2.4"/> so in certain cases extreme cases it could be that <pause dur="0.2"/> you have to consume them in <pause dur="0.2"/> absolute quantities <pause dur="0.7"/> in the same ratio <pause dur="0.2"/> or <pause dur="0.5"/> you got no utility at all <pause dur="1.5"/> okay <pause dur="0.2"/><vocal desc="cough" iterated="n"/><pause dur="0.2"/> and we're assuming here that that's <pause dur="0.9"/> not quite <pause dur="0.3"/> the extreme <pause dur="0.6"/> okay there is <pause dur="0.9"/> there are these combinations you have to consume them in <pause dur="0.4"/> but <pause dur="0.4"/> if you don't <pause dur="0.9"/> then <pause dur="0.4"/> # you don't get disutility but you don't get any more utility <pause dur="1.5"/> okay <pause dur="1.8"/> how we represent this <pause dur="1.1"/> algebraically is with a very strange <pause dur="2.0"/> function which is minimum <pause dur="0.7"/> alpha-X-one <pause dur="0.4"/>

comma <pause dur="0.3"/> beta-X-two <pause dur="3.9"/> that is the <pause dur="0.4"/> again alpha is the marginal utility of X-one beta is the marginal utility of X-two <pause dur="1.7"/> the ratio between them will give you the marginal rate of substitution <pause dur="0.8"/> # <pause dur="0.2"/> but <pause dur="1.0"/> imagine utility is entirely determined by <pause dur="0.9"/> the <pause dur="0.4"/> good <pause dur="1.4"/> okay which <pause dur="0.4"/> is in the lowest amount <pause dur="1.7"/> okay <pause dur="0.2"/> so there may be excess amounts of one good <pause dur="1.7"/> so you might have say <pause dur="0.2"/> ten units of coffee <pause dur="0.5"/> and thirty units of milk <pause dur="1.4"/> but clearly you'd only use <pause dur="0.3"/> # <pause dur="0.8"/> ten units of milk because you'd need it to go in the coffee <pause dur="1.0"/> okay you'd you could use them in <pause dur="0.2"/> in equal amounts <pause dur="1.4"/> the excess amount of milk doesn't give any <trunc>diss</trunc> dissatisfaction but it doesn't give any satisfaction and so <pause dur="0.2"/> the amount of utility the consumer gets is entirely <trunc>con</trunc> # constrained by the amount of coffee <pause dur="0.3"/> the thing that's in short supply <pause dur="0.9"/> okay <pause dur="0.3"/> and that's the sort of function that would <pause dur="0.3"/> would represent that <pause dur="1.3"/> okay <pause dur="1.9"/> so what we're saying <pause dur="1.7"/><kinesic desc="changes transparency" iterated="y" dur="4"/> is that <pause dur="0.6"/> we can represent all types of <pause dur="0.2"/> of preference <pause dur="0.6"/> # <pause dur="2.1"/> perfect substitutes <pause dur="0.6"/> like that <pause dur="4.4"/> # perfect complements <pause dur="0.2"/> like that <pause dur="1.0"/>

and the normal case <pause dur="0.3"/> with convex indifference curves like that <pause dur="0.9"/> and what we do is to represent these <pause dur="0.3"/> # <pause dur="0.5"/> types of preference <pause dur="7.8"/> okay <pause dur="0.2"/> mathematically <pause dur="1.7"/> and all we're saying is that <pause dur="0.6"/> if we look at <pause dur="0.8"/> the preferences that consumers have <pause dur="0.7"/> the way in which they trade off <pause dur="0.3"/> between the goods that are available to them <pause dur="0.6"/> and we observe that <pause dur="0.2"/> for some goods <pause dur="0.2"/> that have <trunc>o</trunc> # substitutes that is the consumer <pause dur="0.5"/> # <pause dur="0.2"/> doesn't really care which they have <pause dur="0.3"/> and will trade off between them at a rate that doesn't change <pause dur="2.2"/> or if we observe their perfect complements the other extreme <pause dur="0.2"/> these goods are always consumed in exactly the same quantities <pause dur="1.0"/> okay <pause dur="0.2"/> in a particular combination because that's how the two go together <pause dur="0.2"/> to produce something else and on their own they don't give any utillity <pause dur="0.9"/> or <pause dur="0.5"/> the middle case which is <trunc>w</trunc> <trunc>w</trunc> what we would normally # observe <pause dur="0.3"/> we think <pause dur="0.4"/> that in fact <pause dur="0.6"/> the goods <pause dur="0.8"/> are not perfect complements or <trunc>per</trunc> perfect substitutes there is substitutability <pause dur="0.6"/> between the two goods the amount

of substitutability <pause dur="0.4"/> will depend on the slope <pause dur="0.7"/> so <pause dur="0.2"/> the flatter <pause dur="0.3"/> this indifference curve is <pause dur="0.7"/> this board's getting worse <pause dur="0.3"/> so if it was like <kinesic desc="writes on board" iterated="y" dur="1"/> that <pause dur="1.8"/> that would mean <trunc>act</trunc> actually there's not that much <trunc>s</trunc> # # <pause dur="0.2"/> sorry there's a lot of substitutability between those goods <pause dur="0.8"/> okay <pause dur="0.2"/> 'cause it's it's getting towards flat it does change <pause dur="0.4"/> but not that much <pause dur="1.9"/> so we'd be erring in this direction here <pause dur="1.4"/> okay <pause dur="4.2"/> and maybe if we had indifference curves that were like that <pause dur="0.9"/> we'd now erring in this direction here towards perfect complements <pause dur="1.3"/> so the <pause dur="0.2"/> the slope of the indifference curve of course <pause dur="0.2"/> differs <pause dur="0.6"/> but we do have these two extremes perfect substitutes and perfect complements <pause dur="1.2"/> okay <pause dur="1.1"/> # <pause dur="2.8"/> we can represent <pause dur="0.2"/> these so if we observe these types of preference <pause dur="0.7"/> we can represent them <pause dur="0.7"/> in an algebraic way <pause dur="0.2"/> using functions that we've just looked at <pause dur="1.1"/> okay <pause dur="0.3"/> they're ordinal functions which means that all that matters is the higher the number <pause dur="0.2"/> the higher the indifference curve <pause dur="0.4"/> it means that <pause dur="0.5"/> if we have a number <pause dur="0.3"/> # which is higher <pause dur="0.4"/> for example

we'd be on this indifference curve rather than that one <pause dur="0.4"/> perhaps <pause dur="1.8"/> we're not saying how much <pause dur="0.2"/> they differ <pause dur="1.7"/> we're not saying we can measure utility we are not saying that if the number is higher that means the consumer gets <pause dur="0.2"/> twice the amount of utility <pause dur="1.7"/> we're not doing that because we <pause dur="0.3"/> know we can't measure utility <pause dur="0.3"/> but also we don't need to <pause dur="1.1"/> if all we're interested in <pause dur="0.2"/> is how much of the goods the consumer consumes <pause dur="0.3"/> 'cause that's what we're interested in <pause dur="0.2"/> the choice the consumer makes <pause dur="0.3"/> which we assume is <trunc>meas</trunc> is driven by utility <pause dur="0.7"/> okay they want to maximize then the the degree to which they meet their needs and wants <pause dur="0.4"/> we measure that as this idea of utility or preference whatever <pause dur="0.9"/> we don't actually need to measure <pause dur="0.2"/> preference or utility <pause dur="1.3"/> in a <trunc>c</trunc> in a cardinal sense <pause dur="0.3"/> all we need to know <pause dur="0.7"/> is that the consumer does get the highest level of utility they possibly can <pause dur="1.0"/> okay <pause dur="0.5"/> and to do that we represent these preferences <pause dur="0.5"/> using these mathematical forms <pause dur="1.3"/> okay <pause dur="2.1"/> the mathematical form we use

depends on the type of preferences we see if they're perfect substitutes <pause dur="0.4"/> then we use the type of function <pause dur="0.3"/> that we've just looked at <pause dur="0.5"/> okay <pause dur="0.3"/> # <pause dur="0.9"/> alpha-X-one plus alpha # plus beta-X-two <pause dur="1.1"/> if <pause dur="0.2"/> we observe they're perfect complements we use minimum <pause dur="0.3"/> alpha-X-one <pause dur="0.8"/> beta-X-two <pause dur="1.7"/> more normally we would <pause dur="0.4"/> # we would have preferences like in in the middle case <pause dur="1.1"/> they would differ in the amount of substitutability complementarity <pause dur="0.4"/> and that would be represented in <pause dur="0.2"/> the alpha and beta values <pause dur="0.2"/> but we would use a function which was <pause dur="0.3"/> # X-one<pause dur="0.3"/>-to-the-alpha <pause dur="0.3"/> X-two-to-the-beta <pause dur="0.3"/> which is the normal <pause dur="0.2"/> form we would use those <trunc>am</trunc> those the values of alpha and beta <pause dur="0.2"/> represent the marginal utilities <pause dur="0.4"/> and therefore the ratio represents the marginal rate of substitution and that will differ according to all the goods that the consumer has <pause dur="0.4"/> and will differ between every consumer according to their preferences <pause dur="1.2"/> okay <pause dur="1.1"/> but all we're saying is that we can represent now <pause dur="0.6"/> these ideas that we've built up <pause dur="0.3"/> the ideas on preference <pause dur="0.3"/>

and the the the <pause dur="0.2"/> properties that preferences have <pause dur="0.5"/> in a in a mathematical sense <pause dur="0.8"/> which means we can do it for any number of goods we want we're not constrained to three <pause dur="0.2"/> which we are here <pause dur="0.7"/><kinesic desc="indicates point on board" iterated="n"/> and we can now put it together <pause dur="0.2"/> and we can actually produce something that will allow us to measure <pause dur="0.2"/> the marginal rate of substitution <pause dur="0.6"/> which is a useful piece of information <pause dur="1.0"/> to <pause dur="0.2"/> predict <pause dur="0.2"/> the choices that a consumer will make <pause dur="0.4"/> in particular circumstances <pause dur="0.8"/> which is vaguely interesting <pause dur="1.2"/> most interesting <pause dur="0.3"/> we can <pause dur="0.2"/> put it together to <trunc>u</trunc> to build up a model that allows us to predict <pause dur="0.3"/> what happens if things change <pause dur="0.3"/> if this is what the consumer chooses now <pause dur="1.3"/> what happens if <pause dur="0.6"/> something a factor that influences their choices <pause dur="0.2"/>

changes <pause dur="0.7"/> prices go up <pause dur="0.2"/> income goes down whatever <pause dur="0.4"/> that is very useful <pause dur="0.4"/> 'cause it allows us to derive elasticities <pause dur="0.2"/> for example <pause dur="1.0"/> and that is useful information <pause dur="0.4"/> somebody who wants to market a product wants to know <pause dur="0.3"/> if i increase my price ten per cent <pause dur="0.3"/> how much does demand change will my revenue go up or will my revenue go down <pause dur="0.4"/> what happens if my competitor <pause dur="0.3"/> changes their price <pause dur="0.2"/> reduces their price by five per cent <pause dur="0.3"/> how much is the demand for my product going to change <pause dur="2.1"/> so being able to represent all of this these notions <pause dur="0.3"/> in an algebraic sense allows us to <pause dur="0.2"/> to produce that sort of model <pause dur="0.9"/> okay and that's what we want to do <pause dur="0.5"/> okay let's take a a break there and then when we come back what we're going to do is to put the two sides together <pause dur="0.5"/> okay </u><gap reason="break in recording" extent="uncertain"/> <u who="nm0757" trans="pause">

this <pause dur="0.4"/> choice process can be <pause dur="0.2"/> broken down into two parts <pause dur="1.2"/> the things the the combinations of the goods that the consumer is able to buy <pause dur="1.2"/> and if you remember we said that that <pause dur="0.3"/> the first of all the availability part <pause dur="12.7"/> is determined by <pause dur="1.5"/><kinesic desc="writes on board" iterated="y" dur="35"/> their <pause dur="0.9"/> budget line <pause dur="1.5"/> which is equal to P-one-X-one <pause dur="0.3"/> plus <pause dur="0.2"/> P-two<pause dur="0.6"/>-X-two <pause dur="0.9"/> # is smaller or equal to M <pause dur="5.1"/> so they cannot consume any combination of these goods <pause dur="1.3"/> which they can't afford <pause dur="2.1"/> the slope of that line <pause dur="0.5"/> is is equal to <pause dur="0.8"/> p-one over p-two <pause dur="1.2"/> the ratio of the prices <pause dur="0.5"/> the price of X-one over the price of X-two <pause dur="2.7"/> this <pause dur="0.2"/> is the same for every consumer <pause dur="0.3"/> the consumer is a minor part of the total market they <pause dur="0.3"/> double their consumption demand doesn't change price doesn't change <pause dur="0.7"/> that is the same for everyone <pause dur="1.6"/> the position of this line is determined by their income <pause dur="1.7"/> okay the higher their income <pause dur="0.5"/> the further out it is <pause dur="0.6"/> the lower their income <pause dur="0.7"/> the further in it is <pause dur="0.4"/> if there's zero income then the clearly they <pause dur="0.4"/> will be at that point there <pause dur="0.2"/> presuming there are no free goods <pause dur="0.2"/> there are no

goods that don't cost anything <pause dur="1.4"/><kinesic desc="writes on board" iterated="y" dur="30"/> okay <pause dur="2.9"/> we also had these non-negativities <pause dur="0.9"/> here <pause dur="0.2"/> and here it's not possible to consume negative amounts of <pause dur="0.3"/> goods <pause dur="1.6"/> and this one here we said X-two must be greater or equal to nought <pause dur="0.8"/> and here X-one must be greater or equal to normal so you can't consume anything less than zero which is <pause dur="1.3"/> at the origin <pause dur="3.1"/> that is <pause dur="0.6"/> the availability set what they can consume <pause dur="0.3"/> given the prices of the goods <pause dur="0.8"/> given their income <pause dur="1.3"/> prices change <pause dur="0.6"/> this changes <pause dur="0.5"/> and the slope of the budget line changes <pause dur="0.2"/> their income changes <pause dur="0.5"/> the slope remains the same <pause dur="0.6"/> and we just move in in and out <pause dur="1.5"/> that's what we looked at <pause dur="0.3"/> # a while ago now <pause dur="0.2"/> their availability set <pause dur="2.2"/> then the other part <pause dur="2.6"/> their preferences <pause dur="4.0"/><kinesic desc="writes on board" iterated="y" dur="3"/> what do they want <pause dur="0.7"/> to consume <pause dur="1.4"/> okay <pause dur="1.7"/> and <pause dur="0.4"/> just like here <pause dur="0.2"/> we looked at what was available to them <pause dur="0.2"/> regardless of what they wanted to do <pause dur="0.7"/> what we've just done is to look at what they want to do regardless of what they can do <pause dur="1.0"/> okay regardless of what they <pause dur="0.3"/> they have available to them <pause dur="0.9"/> and we've said that <pause dur="0.8"/> that is

driven <pause dur="0.3"/> consumption behaviour is <pause dur="0.2"/> induced motivated by your needs and wants consumers' needs and wants <pause dur="0.5"/> and <pause dur="0.3"/> we have the it's driven by the idea of preferences that is a <trunc>c</trunc> the consumer prefers a good <pause dur="0.2"/> that meets more of their needs and wants <pause dur="0.2"/> than one that <trunc>pref</trunc> that that meets less of their needs and wants so it's totally motivated behaviour <pause dur="1.8"/> and we can represent <pause dur="0.2"/> that <pause dur="0.2"/><gap reason="inaudible" extent="1 sec"/><pause dur="5.0"/> through <pause dur="0.7"/> indifference curves <pause dur="5.1"/><kinesic desc="writes on board" iterated="y" dur="5"/> and the direction of the consumer's preferences given non-satiation is out in this direction <pause dur="0.2"/> so they want to get out as far as possible out here <pause dur="0.2"/> as they can <pause dur="4.2"/> these <pause dur="0.2"/> these preferences exhibit things like transitivity <pause dur="0.4"/> we have a convex <pause dur="0.4"/> # indifference curve which means that <pause dur="0.5"/> we have a rate of trade off between the good and the marginal rate of substitution <pause dur="0.2"/> which changes according to the amount of the goods that they consume so these are in this case <pause dur="0.3"/> some substitutability between the goods but they're not <pause dur="0.2"/> they're not perfect <pause dur="0.2"/> # complements <pause dur="0.8"/> okay but they're not perfect substitutes <pause dur="1.5"/> and that

we can represent that <pause dur="0.7"/> these these preferences <pause dur="0.3"/> <trunc>u</trunc> using a utility function an ordinal function <pause dur="0.5"/> which is U<pause dur="0.8"/>-X-one-X-two <pause dur="3.4"/> and we can <pause dur="0.6"/> the mathematical form of that function will depend on <pause dur="0.8"/> what the preferences look like <pause dur="0.5"/> whether they're perfect substitutes perfect complements <pause dur="0.6"/> or like this <pause dur="0.5"/> in the normal type <pause dur="0.8"/> and we'll use the mathematical form <pause dur="0.2"/> which <pause dur="0.4"/> satisfies that <pause dur="0.2"/> which which has that that has those properties <pause dur="3.4"/> given that the consumer <pause dur="0.6"/> aims to <pause dur="0.4"/> consume as much of these goods as possible they're non-satiating <pause dur="0.5"/> we said the consumer <pause dur="0.3"/> and the idea of rationality we came up with in the first week <pause dur="0.5"/> is that the consumer aims to maximize their satisfaction <pause dur="0.9"/> okay <pause dur="0.3"/> aims to maximize the degree to which their needs and wants are satisfied <pause dur="2.4"/> and so <pause dur="0.4"/> what we're saying is on this diagram <pause dur="0.2"/> they've aimed for the highest indifference curve <pause dur="1.4"/> they want the one that's as high as possible because that's the one that gives them <pause dur="0.2"/> the highest level of utility <pause dur="0.8"/> or <pause dur="0.8"/> we want to maximize the value of their utility

function <pause dur="1.2"/> 'cause the higher that is <pause dur="0.9"/> the higher the indifference curve they're on <pause dur="1.2"/> okay <pause dur="2.4"/> putting it together <pause dur="1.7"/> then <pause dur="3.4"/> we have <pause dur="1.1"/> what they want to do they want to aim to get that <pause dur="0.2"/> the the <trunc>con</trunc> <trunc>th</trunc> they want to consume as much X-one and X-two as possible <pause dur="0.6"/> and in the realm of all the goods as much of those goods as possible however many are available to them <pause dur="0.8"/> they want to maximize their utility <pause dur="0.6"/> they want to consume that combination of goods and services <pause dur="0.3"/> that gives them <pause dur="0.2"/> the greatest satisfaction meets as much of their needs and wants as possible <pause dur="2.1"/> but they're constrained in doing so <pause dur="0.8"/> because these goods are not free <pause dur="0.7"/> they have to pay for them <pause dur="1.3"/> and their ability to pay for them is constrained by their income <pause dur="2.2"/> okay <pause dur="0.4"/> the extent to which they're constrained depends on what their income is <pause dur="0.5"/> and how much the goods are <pause dur="0.2"/> but they are constrained <pause dur="0.5"/> in doing this <pause dur="2.7"/> and if we put <pause dur="1.0"/><kinesic desc="changes transparency" iterated="y" dur="12"/> those two together <pause dur="12.4"/> okay <pause dur="0.3"/> that's a consumer's budget line <pause dur="0.2"/> <trunc>f</trunc> for for an individual consumer <pause dur="0.8"/> okay <pause dur="0.6"/> and it will be the

same slope for all consumers but the position will depend on <pause dur="0.3"/> how much income they have so all the consumers have the same level of income <pause dur="0.2"/> it'll be in the same position <pause dur="0.4"/> those that have more income <pause dur="0.2"/> it'll be further out those that have low income <pause dur="0.2"/> will be further in <pause dur="1.4"/> okay <pause dur="0.4"/> that's their availability set <pause dur="1.6"/> and we have <pause dur="0.3"/> these indifference curves <pause dur="0.3"/> which represent their <pause dur="0.3"/> preferences <pause dur="6.3"/><kinesic desc="writes on board" iterated="y" dur="5"/> okay <pause dur="5.6"/><kinesic desc="writes on board" iterated="y" dur="2"/> let's just call them U-one to U-three <pause dur="2.7"/> and what they will do is to choose <pause dur="0.6"/> that combination of goods <pause dur="1.4"/> that gives them the highest level of utility <pause dur="0.6"/> gives the maximum preferences <pause dur="0.5"/> given the resources that are available to them <pause dur="0.5"/> and that will occur <pause dur="0.5"/> at the point <pause dur="1.7"/> where <pause dur="1.2"/><kinesic desc="writes on board" iterated="y" dur="2"/> the budget line just touches the highest <pause dur="0.2"/> indifference curve <pause dur="2.5"/> and that is the choice that the consumer <pause dur="0.6"/> will make <pause dur="2.6"/> so that's the quantity of X-one <pause dur="1.0"/> and that's the quantity of X-two that the consumer will <pause dur="0.9"/> be able <pause dur="0.2"/> to consume <pause dur="1.7"/> okay <pause dur="0.7"/> so what we're saying is that <pause dur="2.1"/> given the the constraints on the choice choices that the consumer can make which is

<trunc>t</trunc> <trunc>t</trunc> which are totally outside of their control <pause dur="0.5"/> they are <pause dur="0.2"/> economic constraints <pause dur="0.4"/> okay <pause dur="0.4"/> on <pause dur="0.5"/> # <pause dur="0.3"/> basically how much of these goods they can consume <pause dur="0.4"/> determined by the market prices and by their income <pause dur="1.4"/> and at any point in time <pause dur="0.9"/> those things are fixed <pause dur="0.7"/> of course someone can have influenced their income in the longer term <pause dur="0.3"/> work longer hours for example <pause dur="0.3"/> # can save at one point in time <pause dur="0.2"/> so they have more resources in the future and so on <pause dur="0.3"/> but at any point in time <pause dur="0.3"/> when the consumer <pause dur="0.2"/> chooses so when they're in the supermarket whatever <pause dur="0.7"/> then those are are fixed things the prices are fixed <pause dur="0.2"/> and <pause dur="0.2"/> their income is fixed <pause dur="1.2"/> and what we're saying is that how they <pause dur="1.0"/> decide <pause dur="0.5"/> between all the combinations of goods they can buy <pause dur="0.4"/> within those constraints <pause dur="1.2"/> is by <pause dur="0.5"/> thinking about <pause dur="0.3"/> how much all the different combinations will meet their needs and wants and they will be driven to choose <pause dur="0.3"/> that combination <pause dur="0.3"/> that provides <pause dur="0.2"/> the greatest utility <pause dur="0.6"/> that combination that meets their needs and wants <pause dur="0.2"/> most

effectively <pause dur="1.4"/> we've represented <pause dur="0.2"/> that <pause dur="0.7"/> through a series of indifference curves and they're i i <trunc>o</trunc> <pause dur="0.7"/> we emphasize again <pause dur="0.3"/> we're not saying that the consumer goes into the supermarket with indifference curves or utility functions whatever <pause dur="1.0"/> what we're saying is we can represent <pause dur="0.5"/> how they make their choices in this way <pause dur="0.8"/> okay in this <trunc>s</trunc> sort of <pause dur="0.8"/> abstract model <pause dur="1.5"/> and putting the two sides together <pause dur="0.2"/> it will be the point at which <pause dur="0.7"/> the budget line <pause dur="0.3"/> just touches their highest indifference curve <pause dur="1.2"/> okay <pause dur="0.3"/> and that will be the choice they make <pause dur="0.6"/> that amount of X-one <pause dur="0.3"/> that amount of X-two <pause dur="1.1"/> okay <pause dur="2.4"/> if <pause dur="0.5"/> their income changes <pause dur="0.3"/> the choice will change <pause dur="0.9"/> if the price of any of the goods changes <pause dur="0.5"/> their choice will change <pause dur="0.7"/> if their preferences change <pause dur="1.1"/> then the choice may change <pause dur="0.5"/> okay so if <pause dur="0.3"/> there's an advertising campaign <pause dur="0.2"/> about one of the goods say X-one <pause dur="0.3"/> that shifts their preferences so they like X-one more then their choice may change <pause dur="0.7"/> okay <pause dur="0.5"/> and we're going to look at those sorts of changes <pause dur="0.3"/> # <pause dur="0.6"/> next week <pause dur="1.1"/> # <pause dur="0.3"/> but <pause dur="0.6"/> those

are the sorts of <pause dur="0.4"/> # <pause dur="0.8"/> changes <pause dur="0.3"/> that might go on <pause dur="0.4"/> and that would be reflected <pause dur="0.4"/> in a shift in <pause dur="0.4"/> the position of that point the choice that the consumer actually makes <pause dur="0.9"/> okay <pause dur="3.2"/> now <pause dur="0.8"/> we can represent that also <pause dur="0.8"/> # algebraically <pause dur="1.3"/> by just putting together <pause dur="3.1"/><kinesic desc="changes transparency" iterated="y" dur="3"/> these elements here <pause dur="1.0"/> okay <pause dur="0.4"/> because we've been able <pause dur="0.4"/> we've said to represent <pause dur="0.5"/> mathematically <pause dur="0.2"/> these the indifference curves through this utility function <pause dur="1.0"/> and the availability set through <pause dur="0.4"/> this budget constraint <pause dur="0.7"/> and through these non-negativities <pause dur="0.3"/> so you can't consume negative amounts <pause dur="1.8"/> and <pause dur="1.0"/> so we can represent this <pause dur="1.1"/><kinesic desc="indicates point on board" iterated="y" dur="1"/> mathematically it is simply that we want to <pause dur="3.1"/> maximize <pause dur="0.9"/> that utility function <pause dur="1.9"/>

okay we want to be on the highest indifference curve possible <pause dur="0.5"/> that's how you want to think about it <pause dur="0.3"/> we want to maximize <pause dur="0.4"/> the utility the consumer gets and what we've done is to represent that <pause dur="0.2"/> through this utility function <pause dur="1.2"/> whatever its mathematical form <pause dur="0.5"/> and all that mathematical form does is to represent <pause dur="0.4"/> the way in which the consumer <pause dur="0.3"/> thinks about the goods the preferences the consumer has <pause dur="0.3"/> perfect complements <pause dur="0.2"/> perfect substitutes <pause dur="0.4"/> anything in between <pause dur="0.3"/> and that will depend on the individual <pause dur="0.4"/> one individual may regard <pause dur="0.2"/> products as <pause dur="0.3"/> perfect substitutes and another individual may not <pause dur="1.1"/> okay <pause dur="0.4"/> but all we're doing is representing how they see <pause dur="0.3"/> those goods <pause dur="0.4"/> in some mathematical sense <pause dur="1.9"/> and we'll maximize that <pause dur="0.9"/> okay <pause dur="0.4"/> and that would go to infinity if they weren't constrained but they are <pause dur="5.0"/> they're subject to <pause dur="0.3"/> two <pause dur="1.0"/> basic constraints <pause dur="0.3"/> the first <pause dur="1.7"/> is the budget line <pause dur="6.4"/> so they can maximize this <pause dur="1.3"/> freely <pause dur="0.4"/> until they hit this <pause dur="1.5"/> they can't spend more than they earn <pause dur="1.6"/> okay <pause dur="2.4"/> so

they hit this budget line <pause dur="1.4"/> and secondly <pause dur="1.3"/> the non-negativities <pause dur="5.6"/> you can't consume <pause dur="0.3"/> less than zero of a good however much you hate it <pause dur="0.3"/><vocal desc="cough" iterated="n"/><pause dur="1.5"/> now that is obvious in real life but mathematically we have to <pause dur="0.3"/> allow for all eventualities because <pause dur="0.2"/> what we've now done <pause dur="0.5"/> is to say okay <pause dur="0.4"/> we can represent all these things that we can see go on and the assumptions we've made <pause dur="0.3"/> and what we can do <pause dur="0.3"/> is we can <pause dur="0.4"/> # <pause dur="0.8"/> now represent that this in this way because it's now mathematical <pause dur="0.2"/> we of course have to stop it doing stupid things <pause dur="0.6"/> okay <pause dur="0.3"/> when we run this <pause dur="0.5"/> and so we have to include those <pause dur="2.4"/> and that is the basic model <pause dur="0.8"/> that says <pause dur="0.3"/> what the consumer will do <pause dur="0.6"/> when faced with all of the goods and services that are available to them <pause dur="1.2"/> is they will select between those goods and services on the basis of their own personal preferences <pause dur="1.6"/> and we can represent those preferences <pause dur="1.1"/> in <pause dur="0.4"/> the mathematical sense <pause dur="0.9"/> okay <pause dur="0.2"/> and that mathematical representation <pause dur="0.2"/> will encapsulate will include <pause dur="0.3"/> all of the properties <pause dur="0.3"/> that we <pause dur="0.3"/> have observed <pause dur="0.6"/> okay in

consumer preferences things like transitivity <pause dur="0.2"/> things like non-satiation <pause dur="0.5"/> things like the fact that the marginal rate of substitution diminishes <pause dur="0.5"/> # as or changes as the amount of the goods change because the marginal utility's changed <pause dur="0.3"/> all of those things that we can see <pause dur="1.4"/> okay <pause dur="1.1"/> # and which <pause dur="0.3"/> we know we think <pause dur="0.6"/> influence the way in which <trunc>pe</trunc> # people trade off the goods that they <unclear>based</unclear> <pause dur="0.6"/> we can represent that in within this <pause dur="0.6"/> and <pause dur="0.3"/> the mathematical form we use <pause dur="0.4"/> okay will depend on what we observed <pause dur="0.5"/> okay perfect substitutes we've one form <pause dur="0.6"/> perfect complements another form <pause dur="0.3"/> any other <pause dur="0.3"/> # type <pause dur="0.2"/> we use another form <pause dur="1.3"/> relative values of alpha and beta will again reflect those trade offs how much they like the two goods <pause dur="0.3"/> and how that <pause dur="0.2"/> rate of trade off changes <pause dur="0.2"/> as you get more and less of the goods <pause dur="0.4"/> okay so all of that can be represented <pause dur="1.2"/> and that's all that is doing <pause dur="0.5"/> is representing the way in which the consumer makes those choices <pause dur="1.1"/> again we're not saying that's how they make them we're

saying that we can represent it in that way <pause dur="2.1"/> and they can <pause dur="0.5"/> do that they <trunc>c</trunc> <pause dur="0.2"/> they make their choices but they're constrained <pause dur="0.8"/> in so doing <pause dur="0.9"/> because well first of all the non-negativities which are fairly obvious <pause dur="0.9"/> but they're constrained by <pause dur="0.4"/> just economic facts of life <pause dur="0.7"/> the fact that they <pause dur="0.4"/> face these prices which are non-zero so they have to pay for the goods <pause dur="0.3"/> and that's out of their control as an individual consumer <pause dur="1.5"/> okay <pause dur="0.7"/> and they also face their income which at any point in time when they make a choice is fixed <pause dur="0.8"/> okay <pause dur="0.3"/> it will depend on <pause dur="0.4"/> their <pause dur="1.3"/> money income from employment from other sources it will depend on their savings decisions in the past <pause dur="0.5"/> # access to credit and and all that <pause dur="0.4"/> but <trunc>th</trunc> at the point they make their choice will be fixed <pause dur="0.9"/> okay <pause dur="0.6"/> and so <pause dur="1.0"/> what we've done is to break down <pause dur="0.6"/> # <pause dur="1.1"/> the choices into these two parts <pause dur="0.5"/> and <pause dur="0.4"/> <trunc>pu</trunc> pulled together <pause dur="0.4"/> # <pause dur="0.3"/> the parts that we consider most important <pause dur="0.8"/> okay <pause dur="1.4"/> now of course <pause dur="0.4"/> this model <pause dur="1.5"/> # <pause dur="0.3"/> includes and there are certain elements of it include an awful lot of

factors <pause dur="1.5"/> like utility preferences will include an awful lot of things that influence preferences like advertising access to information <pause dur="0.3"/> your own attitudes and beliefs about # the product about the world whatever <pause dur="0.6"/> and those will change over time <pause dur="1.0"/> and they will be different between individuals every individual will be different <pause dur="0.8"/> and hence <pause dur="0.2"/> this will change <pause dur="0.9"/> but at the point where the consumer <pause dur="0.2"/> stands in the supermarket or or whatever <pause dur="0.7"/> that is fixed <pause dur="0.3"/> okay at the point at which they make the choice <pause dur="0.7"/> the next time they make the choice <pause dur="0.3"/> that may be different <pause dur="0.4"/> that's okay <pause dur="0.5"/> but at the point that they make the choice <pause dur="0.5"/> that will be fixed <pause dur="0.5"/> just like this is fixed <pause dur="1.6"/> and we might be interested in knowing <pause dur="0.2"/> how this differs <pause dur="0.4"/> and the impact of changes in this <pause dur="1.0"/> okay and that's fine so we might <pause dur="0.2"/> be interested in looking at <pause dur="0.2"/> well if a consumer makes a choice now and then they make it next week after there's been an advertising campaign whatever <pause dur="0.3"/> we might be interested in knowing how that has

changed <pause dur="1.1"/> okay that may be one of the variables that we want to consider <pause dur="0.8"/> but at the point they make the choice standing there <pause dur="0.2"/> that is fixed <pause dur="0.9"/> okay <pause dur="1.2"/> likewise these may change from week to week month to month or whatever <pause dur="0.2"/> but at the point <pause dur="0.4"/> where they're facing a choice at any point in time <pause dur="0.2"/> those are fixed <pause dur="2.1"/> and so what we've done is represent the choices that the consumer makes <pause dur="0.4"/> in this this algebraic sense <pause dur="1.5"/> what that allows us to do <pause dur="0.9"/> is to <pause dur="0.4"/> mathematically <pause dur="0.9"/> # <pause dur="1.5"/> look at the choices people make <pause dur="0.4"/> we can look at <pause dur="0.2"/> the prices people face <pause dur="0.2"/> the incomes they face <pause dur="0.3"/> we can represent their preferences through some utility function <pause dur="0.2"/> and we look at choice <pause dur="1.6"/> okay <pause dur="0.3"/> that combination of the two goods in this case <pause dur="0.5"/> that the consumer's likely to choose <pause dur="0.4"/> and we can then use that model <pause dur="0.8"/> to look at <pause dur="0.2"/> what happens if things change if the price of X-one <pause dur="0.2"/> doubles what's going to happen <pause dur="0.2"/> are they going to stop consuming X-one altogether <pause dur="0.2"/> or do they like X-one so much <pause dur="0.3"/> that they only reduce their consumption by a little

bit <pause dur="0.4"/> and so on <pause dur="0.8"/> okay so that's what we can <pause dur="0.3"/> we can do with this <pause dur="1.5"/> we can also represent <pause dur="0.6"/> # <pause dur="0.6"/> the optimal point <pause dur="0.6"/> okay we can consider <pause dur="1.0"/> what happens at the point where they actually <pause dur="1.8"/> made their choices <pause dur="12.5"/> let me # <pause dur="0.7"/> quickly <pause dur="0.3"/> put this down again <pause dur="9.4"/><kinesic desc="changes transparency" iterated="y" dur="5"/> okay so that's the point at which they make their <pause dur="0.2"/> that's the optimal point <pause dur="1.4"/> okay <pause dur="1.4"/> and we can consider <pause dur="1.7"/> what are what <pause dur="0.4"/> what are the conditions <pause dur="0.5"/> # which must be satisfied <pause dur="0.7"/> for <pause dur="0.6"/> for the consumer to be at an optimum <pause dur="0.2"/> for them to actually be <trunc>ma</trunc> <pause dur="0.4"/> achieving <pause dur="0.3"/> the maximum level of satisfaction they can <pause dur="2.5"/> and there are two <pause dur="0.6"/> basic conditions <pause dur="2.7"/> first of all <pause dur="0.5"/> they must be using all of their income <pause dur="2.6"/> okay <pause dur="1.1"/> because <pause dur="0.6"/> we're assuming that we've included within <pause dur="0.3"/> our framework all of the things that give utility and remember this is a world where <pause dur="0.4"/> people get utility from consumption <pause dur="1.7"/> we can include if people like lots of money in the bank we can include that as well because we can include savings <pause dur="0.4"/> as a source of utility that's that's okay <pause dur="0.7"/> but what we have done is we've included <pause dur="0.3"/>

within their utility function <pause dur="0.2"/> within the idea of our indifference curves everything that gives them satisfaction <pause dur="0.2"/> and hence <pause dur="0.6"/> at the end of the day <pause dur="0.3"/> they must allocate all of their incomings to to those things that give them satisfaction <pause dur="0.5"/> including maybe savings <pause dur="1.3"/> so first of all that must be the case their expenditure <pause dur="0.6"/> which is this <pause dur="1.3"/><kinesic desc="indicates point on board" iterated="n"/> that's their total expenditure <pause dur="6.1"/> must equal <pause dur="0.9"/> their money income <pause dur="4.5"/><kinesic desc="writes on board" iterated="y" dur="5"/> okay <pause dur="2.4"/> that's the first thing that must be <pause dur="0.6"/> # must occur <pause dur="9.5"/> so that means they're going to be on their budget line <pause dur="1.9"/> okay <pause dur="1.3"/> providing we've included everything in the in here that gives them utility they must be on their budget line because they don't get any utility from not allocating their income <pause dur="1.4"/> that's the first # <pause dur="0.5"/> # <pause dur="0.4"/> thing we would we would see <pause dur="3.1"/> so their expenditure's not going to be less than their income it's going to be exactly equal to it of course it can't be more <pause dur="1.5"/> the second <pause dur="0.5"/> is that they are at this point here <pause dur="1.2"/> okay they're at that point there <pause dur="7.0"/> okay that means that the slope of the budget line <pause dur="1.2"/> is

equal to the slope of the indifference curve <pause dur="1.0"/> okay 'cause at that point there <pause dur="0.2"/> they're going to be exactly the same <pause dur="0.9"/> the slope of their <pause dur="0.2"/> budget line <pause dur="0.9"/> and the slope of their indifference curve <pause dur="0.2"/> are going to be exactly the same <pause dur="2.3"/> and that's the second condition <pause dur="0.9"/> okay <pause dur="1.7"/> what is the slope of the budget line <pause dur="0.9"/> equal to </u><pause dur="1.9"/> <u who="sm0761" trans="pause"> inverse price ratio </u><pause dur="0.2"/> <u who="nm0757" trans="pause"> sorry </u><pause dur="0.5"/> <u who="sm0761" trans="pause"> inverse price ratio </u><pause dur="0.2"/> <u who="nm0757" trans="pause"> okay <pause dur="0.2"/> so it's the ratio of the prices yeah <pause dur="8.0"/> so the slope of that at any point is equal to p-one over p-two <pause dur="0.3"/> and it's exactly constant of course it's a straight line the prices do not depend on how much the <pause dur="0.2"/> the # consumer chooses <pause dur="0.3"/> so that one's linear that's a straight line <pause dur="1.8"/> what's the slope of the indifference curve <pause dur="0.3"/> what's the marginal rate of substitution </u><pause dur="7.9"/> <u who="sf0762" trans="pause"> it's the ratio of marginal utility </u><u who="nm0757" trans="latching"> okay <pause dur="0.4"/> it's the ratio of the marginal utility so the the slope of this <pause dur="1.6"/><kinesic desc="writes on board" iterated="y" dur="5"/> is equal to marg utility of X-one <pause dur="1.0"/> over marg utility of X-two <pause dur="2.2"/> and at the optimum <pause dur="4.3"/> they must be equal <pause dur="1.8"/> okay <pause dur="0.3"/> the ratio of prices must be equal to the ratio of the marginal utility <pause dur="2.6"/>

okay <pause dur="8.7"/> now <pause dur="0.5"/> you you know that that is equal to the marginal rate of substitution <pause dur="0.5"/> okay <pause dur="0.6"/> but in fact that is what is termed <pause dur="0.2"/> the marginal rate for substitution <pause dur="1.0"/> in consumption what it is <pause dur="0.3"/> is the rate at which the consumer <pause dur="0.3"/> wants to substitute <pause dur="0.2"/> between the goods <pause dur="1.2"/> given their preferences how they feel about the goods <pause dur="1.1"/> that is the rate at which they <pause dur="0.2"/> are willing to trade off between them <pause dur="1.5"/> okay or willing to trade off X-one and X-two or whatever goods we're dealing with <pause dur="1.4"/> okay <pause dur="3.3"/> so given their preferences that is the rate at which they are willing to trade them off <pause dur="0.5"/> and at this and it this is at that point there <pause dur="0.3"/> it depends on how much of the two goods because <pause dur="0.3"/> we this is convex to the origin <pause dur="0.5"/> so this differs this changes <pause dur="0.3"/> when diminishes as we move from the top to the bottom <pause dur="2.1"/> this <pause dur="0.8"/> is also the marginal rate of substitution <pause dur="1.3"/> this is the marginal rate of substitution in exchange <pause dur="0.2"/> it is the rate at which they are able <pause dur="0.2"/> to trade off the two goods <pause dur="1.6"/> and that is <pause dur="0.2"/> totally determined by their relative prices <pause dur="1.4"/> so the rate at

which you are able <pause dur="0.2"/> to trade off <pause dur="0.3"/> one good for another <pause dur="0.2"/> depends on their relative price if one good <pause dur="0.3"/> is <pause dur="0.2"/> # <pause dur="0.3"/> costs you know a pound <pause dur="0.9"/> and another good costs fifty pence clearly then <pause dur="0.3"/> you can have you know two of the goods that cost fifty pence or one of the goods that cost a pound <pause dur="0.3"/> and that is totally determined by the prices out of your control <pause dur="0.9"/> okay <pause dur="0.2"/> but that is your your marginal rate of substitution <pause dur="0.2"/> all consumers' marginal rate of substitution in exchange <pause dur="0.2"/> is determined by the market place <pause dur="0.2"/> determined by the collective decisions of the suppliers <pause dur="0.2"/> and of all consumers <pause dur="0.8"/> but for you as an individual it's fixed because you are irrelevant within the market <pause dur="0.5"/> as a consumer <pause dur="1.2"/> and so at the optimal point <pause dur="0.5"/> we're saying <pause dur="0.3"/> that <pause dur="0.9"/> the rate at which the consumer is able to substitute between the goods <pause dur="0.4"/> determined by market prices <pause dur="0.4"/> is exactly equal to the rate at which they want to <trunc>consu</trunc> to to substitute between them <pause dur="0.5"/> which is determined by their ratio of marginal utilities <pause dur="1.1"/> okay <pause dur="0.2"/> so at the

optimum <pause dur="0.6"/> it is the case that the marginal rate of substitution in exchange <pause dur="0.4"/> is exactly equal to the marginal rate of substitution in consumption <pause dur="0.4"/> the rate at which the consumers <pause dur="0.2"/> are able to substitute between the goods through market transactions <pause dur="0.3"/> is exactly equal to the rate at which they <pause dur="0.3"/> wish <pause dur="0.2"/> to substitute between them <pause dur="0.3"/> given their preferences <pause dur="1.6"/> okay <pause dur="4.7"/> the implication of that <pause dur="0.2"/> is that <pause dur="1.3"/> if we <pause dur="2.7"/> we order this we change this around <pause dur="1.1"/> okay <pause dur="1.2"/> what we find is that <pause dur="14.5"/><kinesic desc="writes on board" iterated="y" dur="10"/> just rejigging this around we find that in fact that is equal to this expression here <pause dur="1.4"/> that at the optimum <pause dur="1.0"/> the ratio of the marginal utilities <pause dur="0.2"/> to the unit prices of the goods is exactly equal for every good that is <pause dur="0.4"/> the amount of utility you get <pause dur="0.9"/> for every unit of money spent <pause dur="0.7"/> is exactly the same for all of the goods <pause dur="1.4"/> okay <pause dur="0.4"/> so <pause dur="2.1"/> the marginal utility the amount of utility you get from consuming <pause dur="0.2"/> one extra unit of the good <pause dur="2.3"/><kinesic desc="writes on board" iterated="y" dur="2"/> the ratio of that to the price that is how much it costs you <pause dur="0.4"/> to consume <pause dur="0.2"/> one extra unit of the good <pause dur="0.7"/> at the optimum <pause dur="0.6"/> is

exactly equal <pause dur="0.5"/> for all of the goods you consume so the amount of utility <pause dur="0.4"/> for one unit of money <pause dur="0.6"/> is the same <pause dur="0.2"/> for X-one and for X-two <pause dur="1.1"/> can anyone remember what that is called <pause dur="1.9"/> you've done this in part one <pause dur="5.6"/> anyone remember <pause dur="3.5"/> this is termed the equimarginal principle <pause dur="0.8"/> okay <pause dur="0.7"/> if you remember you did it in part one with # looking at cardinal theory <trunc>wi</trunc> of consumer choice <pause dur="1.3"/> you said that what the <trunc>d</trunc> consumer does is they allocate <pause dur="0.3"/> their <pause dur="0.2"/> the goods and we assumed then we could measure it <pause dur="0.3"/> but what they did was they do it in such a way that <pause dur="0.2"/> the amount of income sorry the amount of utility they get for each of the <pause dur="0.3"/> for for the # <pause dur="0.2"/> unit amount of money they spend is the same for all the goods <pause dur="0.5"/> so it's not possible to allocate your money <pause dur="0.3"/> between the goods <pause dur="0.5"/> and get any extra utility <pause dur="1.1"/> so therefore you must be at the optimum <pause dur="0.3"/> okay you cannot reallocate your income <pause dur="0.3"/> in any way <pause dur="0.7"/> given the price of the goods <pause dur="0.2"/> and given the your preferences for those goods <pause dur="0.2"/> and achieve any <pause dur="0.6"/> extra utility <pause dur="0.4"/> this is called the

equimarginal principle <pause dur="9.0"/><kinesic desc="writes on board" iterated="y" dur="6"/> which you'll have met before <pause dur="0.7"/> so we end up in the <trunc>s</trunc> <trunc>t</trunc> in the same position <pause dur="0.9"/> okay as with other ideas <pause dur="0.6"/> but we're not measuring utility now <pause dur="0.4"/> we've represented it in a far more sophisticated model that we can actually <trunc>applo</trunc> employ <pause dur="0.4"/> to <pause dur="0.4"/> estimate things like elasticities to predict demand change in demand whatever <pause dur="0.4"/> but <pause dur="0.5"/> fundamentally it's based on the principle that consumers <pause dur="0.2"/> given their choices are driven by preferences that are individual to them <pause dur="0.4"/> and given they're constrained by their economic circumstances <pause dur="1.1"/> they will allocate their income in such a way <pause dur="0.3"/> given their preferences <pause dur="0.3"/> that <pause dur="0.2"/> they cannot achieve any extra utility they can't meet any more of their needs and wants <pause dur="0.3"/> by jigging around <pause dur="0.3"/> their <pause dur="0.9"/> # <pause dur="0.4"/> their their allocation of their income between the goods <pause dur="3.7"/><kinesic desc="writes on board" iterated="y" dur="2"/> this <pause dur="0.5"/> is also equal <pause dur="0.3"/> to <pause dur="0.2"/> U-M <pause dur="1.5"/> the marginal utility of their money income <pause dur="0.7"/> if the consumer was given <pause dur="0.2"/> a <pause dur="0.7"/> fractional increase in their money income <pause dur="1.5"/> okay <pause dur="1.2"/> at the optimum <pause dur="1.3"/> it wouldn't matter which good <pause dur="0.5"/>

they bought more of <pause dur="0.8"/> their extra marginal utility would be exactly the same because it has been equated <pause dur="0.9"/> across <pause dur="0.2"/> the groups <pause dur="0.2"/> ratio of the marginal utilities to their money their money to their prices <pause dur="0.2"/> it's exactly the same so if they were given <pause dur="0.3"/> a fractional increase in income it wouldn't matter which good they allocated it to <pause dur="0.4"/> simply because the ratio of marginal utility to prices is the same for every one of them <pause dur="0.8"/> and so that <pause dur="0.3"/> is at the margin <pause dur="0.5"/> the marginal utility of their money income <pause dur="0.2"/> of money <pause dur="1.6"/> okay <pause dur="3.5"/> so <pause dur="0.6"/> what we've done <pause dur="0.5"/> is to build up <pause dur="0.2"/> a model <pause dur="0.9"/> which we can represent <pause dur="1.0"/> okay <pause dur="0.3"/> diagrammatically for up to three goods <pause dur="0.2"/> but we've built it up <pause dur="0.2"/> taking account of <pause dur="0.4"/> all of the characteristics of consumer preferences <pause dur="0.4"/> and of their economic constraints okay that that <pause dur="0.3"/> you know really matter <pause dur="0.9"/> yes sure we have <pause dur="0.5"/> put a lot of things together like <pause dur="0.5"/> the indifference curve represents all of those things <pause dur="0.2"/> well includes all those things that influence the consumer's preferences every

one of those <pause dur="0.3"/> is included within that <pause dur="0.4"/> and any one of those <pause dur="0.3"/> if it changes will change <pause dur="0.2"/> that indifference curve <pause dur="0.8"/> okay <pause dur="0.2"/> that's fine <pause dur="1.4"/> we've equally included the economic constraints <pause dur="0.2"/> okay and <pause dur="0.3"/> what we've now done is put them together <pause dur="0.5"/> to produce a model which we hope will allow us to <pause dur="0.4"/> okay on the <trunc>f</trunc> on the one hand predict the choice this consumer will make in this circumstance which <pause dur="0.5"/> is vaguely interesting <pause dur="0.3"/> what is more interesting is if we then use this to say <pause dur="0.3"/> okay <pause dur="0.3"/> what happens if things change can we use this <pause dur="0.2"/> given that we can now <pause dur="0.2"/> represent it <pause dur="0.4"/> # mathematically <pause dur="0.8"/><kinesic desc="changes transparency" iterated="y" dur="5"/> so we can actually represent it like this <pause dur="0.9"/> so we could <pause dur="0.4"/> given we can represent this mathematically we could apply this <pause dur="0.4"/> to <pause dur="0.8"/> data from the real world price data <pause dur="0.2"/> income data et cetera we so we can actually <pause dur="0.3"/> put <pause dur="0.3"/> real data into this when we've put it in an empirical model <pause dur="0.4"/> <trunc>a</trunc> and predict what will happen and what will happen if things change <pause dur="0.4"/> so now we can do that <pause dur="1.6"/> and to prove that this model <pause dur="1.5"/> # <pause dur="0.6"/> really does

sort of encapsulate the way in which at least economists <pause dur="0.2"/> see the choices consumer makes <pause dur="0.3"/> the consumer makes <pause dur="0.2"/> again <pause dur="0.2"/> we're not saying this is how the consumer does make it <pause dur="0.2"/> we're sort of <pause dur="0.2"/> abstracting from the real world and trying to encapsulate <pause dur="0.2"/> how they make choices in a model that we can <pause dur="0.2"/> we can use <pause dur="1.2"/> that at that point they will spend all their income 'cause <unclear>of</unclear> another <pause dur="0.4"/> black holes that give utility <pause dur="0.3"/> and <pause dur="0.2"/> at that point <pause dur="3.0"/> they will maximize <pause dur="0.2"/> their utility <pause dur="0.3"/> they will <pause dur="0.6"/> not be able <pause dur="0.2"/> to reallocate their income in such a way <pause dur="0.3"/> that they can <pause dur="0.7"/> meet more of their needs and wants and so <pause dur="0.7"/> the rate at which they are able <pause dur="0.6"/> to substitute between the goods <pause dur="0.3"/> within the marketplace through <pause dur="0.2"/> through their market transactions <pause dur="0.4"/> is just equal to <pause dur="0.3"/> the rate at which they <pause dur="0.3"/> wish <pause dur="0.3"/> <trunc>t</trunc> to substitute between those goods <pause dur="0.9"/> and <pause dur="0.4"/> that gives us <pause dur="0.7"/> the principle <trunc>the</trunc> the marginal principle which <pause dur="0.3"/> says that <pause dur="0.4"/> the ratio of the marginal utility to price is the same for all of the goods <pause dur="0.5"/> so if the consumer's given a fractional

increase in income <pause dur="0.3"/> it wouldn't matter <pause dur="0.3"/> which of the goods they allocated it to 'cause it would be exactly the same <pause dur="1.4"/> okay <pause dur="2.8"/> so that is the basic <pause dur="0.4"/> the basic model <pause dur="0.7"/> that we've built up and it encapsulates <pause dur="0.6"/> all of the things that we <pause dur="0.2"/> we have said <pause dur="0.7"/> we think we observe in the real world <pause dur="0.4"/> so <pause dur="0.2"/> the ideas of diminishing marginal rate of substitution because of changes in <pause dur="0.3"/> # marginal utilities <pause dur="0.6"/> okay <pause dur="0.4"/> # the ideas of non-satiation transitivity all of those are encapsulated here <pause dur="0.8"/> 'cause we've built up the indifference curves <pause dur="0.5"/> and therefore are encapsulated here <pause dur="0.3"/> 'cause we can now represent them in a mathematical sense <pause dur="1.2"/> and the availability set <pause dur="0.3"/> which we we've said <pause dur="0.3"/> applies to the consumer <pause dur="0.6"/> the economic constraints they face <pause dur="1.0"/> so we've put all that together and we've produced this <pause dur="0.6"/> rather simple model <pause dur="1.1"/> the complication with it <pause dur="0.3"/> comes when you want to actually employ it in practice and we're not going to look at that in great detail <pause dur="0.2"/> because there <pause dur="0.2"/> you're getting into complex statistical

procedures econometric procedures <pause dur="0.4"/> relating to the mathematical form that this takes okay and <pause dur="0.2"/> how we can <pause dur="0.3"/> put it together into something we can estimate <pause dur="1.3"/> what we're now going to do <pause dur="0.4"/> next week <pause dur="0.3"/> is to look at how we can use this <pause dur="1.2"/> okay <pause dur="0.2"/> we've said this is how we can model the choice they make <pause dur="1.1"/> okay <pause dur="0.3"/> I-E <pause dur="0.3"/> remember what we're saying is <pause dur="0.2"/> what we can observe in the real world is the prices <pause dur="0.6"/> the income <pause dur="0.3"/> and what people choose <pause dur="0.2"/> okay they're the things we can see <pause dur="0.3"/> we can see what people buy <pause dur="1.4"/> because we can actually collect that information we could do it on an individual basis 'cause we could ask people <pause dur="0.3"/> we could # <pause dur="0.3"/> ask them to give us their till receipts from the supermarket <pause dur="0.2"/> we could follow them around the shop we can gather that information in many ways <pause dur="0.3"/> we can do it on a collective basis <pause dur="0.5"/> of all consumers by looking at how much <pause dur="0.4"/> # how many bananas Sainsbury's and Tesco et cetera sell <pause dur="0.4"/> or <pause dur="0.3"/> at a national account level we can gather that information <pause dur="0.8"/> so we can look at what people choose <pause dur="0.3"/> I-E the X-one

and X-two <pause dur="1.6"/> we can look at prices because again we can gather that information <pause dur="0.9"/> what the prices are in the shops <pause dur="0.5"/> and we can gather information on income <pause dur="1.1"/> so we can get all the variables income prices and choice we can get all of those <pause dur="0.3"/> and what we are <trunc>go</trunc> what we do <pause dur="0.2"/> is to use this model <pause dur="0.3"/> to make sense of those choices <pause dur="1.1"/> and when we've used this model to make sense of those choices I-E we use this model <pause dur="0.3"/> to understand why they've made the choices they have <pause dur="1.2"/> for example to discover what their preferences are <pause dur="1.0"/> we can then use that <pause dur="0.2"/> to say okay <pause dur="0.8"/> how much do we what do we think the consumption of bananas is going to be next year <pause dur="1.0"/> if we expect the prices to go up ten per cent and we expect people's incomes to go up say three four per cent <pause dur="0.8"/> what's the demand for bananas likely to be <pause dur="0.2"/> is it going to be higher is it going to be lower <pause dur="0.2"/> and by how much <pause dur="0.4"/> and that's useful <pause dur="0.7"/> so we're going to look at <pause dur="0.2"/> what happens if things change <pause dur="0.7"/> okay <pause dur="0.2"/> and what measures can we produce of <pause dur="0.4"/> those changes <pause dur="0.2"/> so things like elasticities <pause dur="0.4"/> # for example <pause dur="0.9"/> okay let's leave it there