% MATLAB HEAD
clc, clear,
randn('seed', 5678)  % reset normal random number generator
global N
N = 1000;           % # of Observations
a=40; b=2;
%%%%%%%%%%%%%%%%%%%%%
% SIMULATE DATA
%%%%%%%%%%%%%%%%%%%%%
Q  =a+b*randn(N,1);    % Quantity
%%%%%%%%%%%%%%%%%%%%%%%%%%
% COMPUTING FOR ANALYSIS %
%%%%%%%%%%%%%%%%%%%%%%%%%%
%Let's create a couple of dummies
ud1 = randn(N,1);
% Brand 1 and 2
BRAND= 1+(ud1>0.15);
% Eleven Weeks! 
% R = unidrnd(T) generates random numbers for the discrete uniform distribution with maximum T.
T=11;
WEEK= unidrnd( T*ones(N,1));
% Construct the Market Shares of X1
mean([ WEEK, BRAND]);
hist(WEEK)
hist(BRAND)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Compute a Matrix to Show how many observations you have per brand and per
% week with total column and row, i.e., (T+1 times 3) matrix 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

data1=zeros(T+1,3);
for n=1:N
    for j=1:2
        for t=1:T;
            if BRAND(n,1)==j && WEEK(n,1)==t
                    data1(t,j)=data1(t,j)+1;
            end
        end
    end
end
data1(1:T,3)= data1(1:T,1)+data1(1:T,2);
data1(T+1,:)= sum(data1(1:T,:));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
data2=zeros(T+1,3);
for j=1:2
    for i=1:T;
        index= (((WEEK==i).*(BRAND==j)) ==1);
        data2(i,j)= sum(index);
        clear index
    end
end
data2(:,3)= sum( data2(:,1:2),2);
data2(T+1,:)= sum( data2(1:T,:) ,1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       From Quantities to Market Shares 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Q_T=sum(Q);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       Market Shares per Brand
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Q_B1=sum(Q.*(BRAND==1));
Q_B2=sum(Q.*(BRAND==2));
MKS_1= Q_B1/Q_T;
MKS_2= Q_B2/Q_T;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       Market Shares per Week
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Q_B1=sum(Q.*(BRAND==1));
Q_B2=sum(Q.*(BRAND==2));

MKS_1_weekly=zeros(T,1);
MKS_2_weekly=zeros(T,1);
for t=1:T
    i1=(WEEK==t).*(BRAND==1);
    i2=(WEEK==t).*(BRAND==2);
    MKS_1_weekly(t,1)= sum(Q((i1==1)))./sum(Q((WEEK==t)));
    MKS_2_weekly(t,1)= sum(Q((i2==1)))./sum(Q((WEEK==t)));
end

plot(MKS_1_weekly, '-diamond');
hold on;
plot(MKS_2_weekly ,'--o');
hold on;
h = legend('Market Share Brand 1','Market Share Brand 2',2);
set(gca,'XTick',1:5:T);
set(gca,'XTickLabel',{'Week1','Mid Week','Final Week'})
ylabel('[%]');   
xlabel('Weeks from 1 to T');
title('Weekly Market Share by Brands.','FontSize',12);
hold off
filename = 'MKS_Weekly';
print('-deps', filename);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%     WEIGHTED PRICES
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Suppose Liner Demand
P=100-Q;
hist(P)
%%% CONSTRUCT WEEKLY PRICE INDEX USING WEEKLY MARKET SHARES AS WEIGHTS
P_Weekly = zeros(T,1);
for t=1:T
    i     =(WEEK==t);
    weight=Q(i)/sum(Q(i));
    Pwei  = P(i).*weight;
    P_Weekly(t,1)= sum( Pwei);
    clear weight
end
% CONSTRUCT WEEKLY PRICE INDEX PER BRAND
% USING WEEKLY MARKET SHARES AS WEIGHTS
P_Weekly_byBrand = zeros(T,2);
for j=1:2
    for t=1:T
        k     =( (WEEK==t).*(BRAND==j) )==1;
        weight=Q(k)/sum(Q(k));
    Pwei_bybrand  = P(k).*weight;
    P_Weekly_byBrand(t,j)= sum( Pwei_bybrand);
    clear weight k Pwei_bybrand  
    end
end

plot(P_Weekly ,'-square');
hold on;
plot(P_Weekly_byBrand(:,1),'--diamond');
hold on;
plot(P_Weekly_byBrand(:,2) ,'--o');
hold on;

h = legend('Weekly weighted Price','Weekly weighted Price for Brand 1','Weekly weighted Price for Brand 2' ,4);
set(gca,'XTick',1:5:T);
set(gca,'XTickLabel',{'Week1','Mid Week','Final Week'})
ylabel('Price [$]');   
xlabel('Weeks from 1 to T');
title('Weekly Weighted Price per Week and Brand','FontSize',12);
hold off
filename = 'Weighted_Price_Weekly';
print('-deps', filename);