Find maximum of a function

Hi,

I am new to Matlab. I was using Mathematica before. I am writing a code for a research paper (in economics. I attach it below. It probably is not written in the best possible way, but it works until the last line.

I would like to evaluate totaltax(t1,t2) for each (t1,t2) with t1 in 0:step:1 and t2 in 0:step:1. My objective is then to find the (t1,t2) combination which maximizes totaltax.

I tried to use meshgrid, but did not manage to get what I wanted. So I am presently stuck. Your help would be much appreciated! Best,

Laurent

kmax = 5; % I will increase it later
mu1 = 10.19357; % mean of log wages omega
sigma1 =0.3022616; % standard deviation of log wages
mu2 = 11.795; % mean of shifting cost gamma
sigma2 = 0.1*11.795;  % 10% of the mean cost
rho=-0.2;
elastmean=0.2;
elastsd=1/2*elastmean;
step=0.1;
%%%%%%%%%%%%%%%%%%%%%%%%
mu=[mu1 mu2];
sigma=[sigma1 sigma2];    
corr=[1 rho*sigma1*sigma2; rho*sigma1*sigma2 1];
data=MvLogNRand(mu,sigma,kmax,corr);
omega=data(:,1); %column vector with skills
gamma=data(:,2); %column vector with shifting costs
plot(omega,gamma,'+');
ppd=makedist('Normal','mu',elastmean,'sigma',elastsd);
tt=truncate(ppd,0,1);
elasticity=random(tt,kmax,1); % elasticities defined from normal draw
threshold=@(t1,t2,elast,g) (((1.+elast).*g)./((1-t2).^(1.+elast)-(1-t1).^(1.+elast))).^(1./(1.+elast));
omegatilde=@(t1,t2) threshold(t1,t2,elasticity,gamma); % shifting if omega > omegatilde
shift=@(t1,t2) omega>omegatilde(t1,t2); % vector with 1 for shifters and 0 for non-shiftersshift(1,0)
noshift=@(t1,t2) omega<=omegatilde(t1,t2); % vector with 0 for shifters and 1 for non-shiftersshift(1,0)
tax1=@(t1,t2) t1.*(1.-t1).^elasticity.*omega.^(1.+elasticity);
tax2=@(t1,t2) t2.*(1.-t2).^elasticity.*omega.^(1.+elasticity);
indtax=@(t1,t2) tax1(t1,t2).*noshift(t1,t2)+tax2(t1,t2).*shift(t1,t2);
totaltax=@(t1,t2) sum(indtax(t1,t2));

[Stephen23]

If the functions are fully vectorized then ndgrid or meshgrid to get the values, call the function with those values, and then find the minimum. Otherwise you will have to use a loop or arrayfun.

[Laurent Simula]

Thanks a lot! I managed to get what I wanted with a loop.