create a script which find the minimum of a cobb douglas function in matlab

To create a script that finds the minimum of a Cobb-Douglas function in Matlab, you can use the built-in optimization functions available in the Optimization Toolbox. Here's an example script that demonstrates how to do it:

main.m
% Define the Cobb-Douglas function
f = @(x) x(1)^a * x(2)^b;

% Define the constraint function
constraint = @(x) x(1) + x(2) - 1;

% Define the initial guess
x0 = [0.5, 0.5];

% Define the exponents for the Cobb-Douglas function
a = 0.5;
b = 0.5;

% Set the options for the optimization algorithm
options = optimoptions('fmincon', 'Display', 'iter');

% Call the optimization function to find the minimum
[x, fval] = fmincon(f, x0, [], [], [], [], [], [], constraint, options);

% Display the result
disp(['Minimum value: ' num2str(fval)]);
disp(['Optimal x: ' num2str(x)]);
575 chars
23 lines

In this script, f represents the Cobb-Douglas function to be minimized. constraint is an equality constraint that ensures the variables sum up to 1. x0 is the initial guess for the optimization algorithm. a and b represent the exponents of the Cobb-Douglas function.

The fmincon function is used to find the minimum of the objective function subject to the given constraints. The result of the optimization is returned in the x and fval variables.

Note that you need to have the Optimization Toolbox installed in your Matlab in order to use the fmincon function.