Please help to correct my code

% Parameters

alpha = 0.3;

epsilon = 0.4;

K_bar = 1;

R = 1.05;

z_bar = 2;

z_min = 0;

z_max = 2;

% Number of points for simulation

num_points = 100; % Adjust as needed

% Array to store results

z_underline = linspace(0.1, 1, num_points);

z_ast = zeros(1, num_points);

% Simulation

for i = 1:num_points

% Calculate P_i

z_vals = linspace(z_min, z_max, num_points);

P_i = (R / (epsilon * alpha * z_underline(i) * z_vals.^alpha)) .* ...

((R / (epsilon * alpha * z_underline(i))).^((1 - alpha) / alpha));

% Calculate Hat(P)

hat_P = (trapz(z_vals(z_vals > z_ast(i)), P_i(z_vals > z_ast(i)).^(epsilon / (epsilon - 1))))^((epsilon - 1) / epsilon);

% Calculate z_ast

z_ast(i) = (R^(1 + alpha * epsilon - epsilon) * hat_P^((1 - epsilon * alpha) / (alpha * epsilon)) * ...

(1 / (epsilon * alpha))^((1 / (alpha * epsilon))) * K_bar^((epsilon - 1) / (alpha * epsilon)) * ...

(1 / z_underline(i))^(1 / alpha) * (alpha / (1 - alpha))^((epsilon - alpha * epsilon) / (alpha * epsilon)) * ...

(1 / (epsilon * alpha) - 1 / alpha)^((epsilon - 1) / (alpha * epsilon)) * (1 / K_bar)^((epsilon - 1) / (alpha * epsilon)));

end

% Plotting

plot(z_underline, z_ast);

xlabel('\underline{z}');

ylabel('z^*');

title('Relation between \underline{z} and z^*');

My price function is determined by z_i, which is the only variable. And \hat_P is the aggregator function. It aggregates the firms' prices with z_i greater than z*. I want to simulate z* and its relation with underline_z

[Dyuman Joshi]

"And z_ or underline z is also a value between [0,2]. How to adjust it?"

You have define z_ between 0.1 and 1. Just change the values.

%Adjust the values
z_underline = linspace(0, 2, num_points);

"How do I simulate z*."

I do not understand what you mean by this. Please clarify.

[Jiiim Wu]

I mean z* is the value betwwen [0,2] and is the threshold for firm to produce. I want to express the value between z* and underline z. Both should be in the range of [0,2]. I want to plot when shock different range of firms, the z* will increase. Each firm is characterized by specific productivity. So the continnum of firms are following a uniform distribution. Can you help me to look at the screenshot as well? I have trouble to code

[Dyuman Joshi]

"I want to express the value between z* and underline z."

Do you want to calculate the integratal shown in the first image you have attached?

[Jiiim Wu]

Yes. I want to calculate P_i and then \Hat{P}. And then compute z*. Since Z* is a function of \underline{z}. I want to express the relationship between them. the only random variable is z_i

Answer 1

[Dyuman Joshi]

You need to use element-wise operators for the variable P_i

% Parameters
alpha = 0.3;
epsilon = 0.4;
K_bar = 1;
R = 1.05;
z_bar = 2;
z_min = 0;
z_max = 2;
% Number of points for simulation
num_points = 100; % Adjust as needed
% Array to store results
z_underline = linspace(0.1, 1, num_points);
z_ast = zeros(1, num_points);
% Simulation
for i = 1:num_points
    % Calculate P_i
    z_vals = linspace(z_min, z_max, num_points);
    %%%      v element-wise division
    P_i = (R ./ (epsilon * alpha * z_underline(i) * z_vals.^alpha)) .* ...
        ((R ./ (epsilon * alpha * z_underline(i))).^((1 - alpha) / alpha));
    
    % Calculate Hat(P)
    hat_P = (trapz(z_vals(z_vals > z_ast(i)), P_i(z_vals > z_ast(i)).^(epsilon / (epsilon - 1))))^((epsilon - 1) / epsilon);
    
    % Calculate z_ast
    z_ast(i) = (R^(1 + alpha * epsilon - epsilon) * hat_P^((1 - epsilon * alpha) / (alpha * epsilon)) * ...
        (1 / (epsilon * alpha))^((1 / (alpha * epsilon))) * K_bar^((epsilon - 1) / (alpha * epsilon)) * ...
        (1 / z_underline(i))^(1 / alpha) * (alpha / (1 - alpha))^((epsilon - alpha * epsilon) / (alpha * epsilon)) * ...
        (1 / (epsilon * alpha) - 1 / alpha)^((epsilon - 1) / (alpha * epsilon)) * (1 / K_bar)^((epsilon - 1) / (alpha * epsilon)));
end

% Plotting
plot(z_underline, z_ast);

Some symbols (underscore ( _ ) for subscript and caret ( ^ ) for superscript, etc) in have a predefined meaning (TeX characters) while dealing the text in MATLAB. Use the backslash character with these symbols to bypass the interpeter.

xlabel('z\_underline');
ylabel('z^*');
title('Relation between z\_underline and z^*');

Answer 2

[Jiiim Wu]

Hi, thank you for your answer. The code is an economics code. If I want to express z_i follows the uniform distribution from [0,2] and z* is a threshold above which the firm is going to produce. So the z* value is too large. And z_ or underline z is also a value between [0,2]. How to adjust it? So the only random variable is z_i. How do I simulate z*. The price P_i is the price of firm when its productivity is z_i. In other words, there is a continnum of firms in my model. So I have to make sure z* also lies in the range of [0,2] since it is a threshold. Maybe I assume the wrong parameter values.

Moreover, I want to assume that at some range of z aove z*, z_i'=0.7*z_i.For exampe, at the range of [1.2,1.4].z_i' =0.7z_i.

If I assume z_i'=0.7 z_i at the range [1.6,1.8], it has different z*.

Can you help me to put these three curves in one diagram. More than appreciative if you could help me. The attachment are my equations. Thank you so so much.