Hello Mari,
I understand that the code you provided is attempting to find the optimal initial consumption value for a neoclassical growth model, but is encountering some issues. Here are a few suggestions:
- Check your model equations: Make sure that your model equations are correct and that you're using the right parameter values. If your model equations are incorrect, then your optimization algorithm won't be able to find the right solution.
- Check convergence criteria: Make sure that your convergence criteria are appropriate for your problem. If your criteria are too strict, then your algorithm may never converge. If they're too loose, then your algorithm may converge to a suboptimal solution.
Here's an example code to find a particular initial consumption value that will lead to the steady state for a neoclassical growth model:
% Define the model parameters
alpha = 0.3; % capital share of output
beta = 0.95; % discount factor
delta = 0.1; % depreciation rate
sigma = 2; % intertemporal elasticity of substitution
% Define the steady-state values
k_ss = (alpha / (1/beta - (1-delta)))^(1/(1-alpha));
c_ss = (1-alpha)*k_ss^alpha;
% Define the tolerance level
tol = 1e-6;
% Define the lower and upper bounds for initial consumption
c0_lb = 0;
c0_ub = c_ss;
% Define the initial consumption value
c0 = c_ss/2;
% Define the time step and simulation horizon
Delta = 0.01;
T = 100;
% Simulate the model dynamics
for t = 1:T
% Compute the new values of k and c
k_dot = k_ss^alpha - c0 + (1-delta)*k_ss;
c_dot = c0*(beta*(alpha*k_ss^(alpha-1) + 1 - delta))^(1/sigma);
k_ss_new = k_ss + Delta*k_dot;
c_ss_new = c0 + Delta*c_dot;
% Check if we've reached the steady state
if abs(k_ss_new - k_ss) < tol && abs(c_ss_new - c_ss) < tol
break;
end
% Update the values of k and c
k_ss = k_ss_new;
c_ss = c_ss_new;
end
% Print the results
fprintf('Initial consumption value: %f', c0);
fprintf('Steady-state capital stock: %f', k_ss);
fprintf('Steady-state consumption: %f', c_ss);
In this example, we first define the model parameters and the steady-state values of capital and consumption. We then define the tolerance level, lower and upper bounds for initial consumption, and the initial consumption value. We simulate the model dynamics using a for loop and check if we've reached the steady state at each time step. Finally, we print the results.
Hope this helps!
