Entry 953

%% find the cost minimizing input
x0 = [1,1,1]
[xstar,fval,exitflag,output] = fminsearch(objfn,x0)
%disp('optimal input'), disp(xstar)

%% verify with theoretical results
fprintf('\nCompare numerical and Theoretical results\n')
fprintf(  '-----------------------------------------\n')
%disp('cost shares'), xstar.*w/fval
disp('numerical and analytic cost shares')
wc=w.^(eta+1)./(theta.^eta);
sharesv = wc/sum(wc)
disp([xstar.*w/fval;wc/sum(wc)])

lambda = (sum(wc)/fval).^(1/eta); % formula for lambda with numerical unitcost
lambda_r = sum(wc)^(1/(eta+1));  % formula for lambda without endogenous variables
disp('fval lambda lambda_r'), disp([fval; lambda; lambda_r])

disp('numerical and theoretical demand')
xd=(w./theta/lambda).^eta;
disp([xstar;xd])