Plot inaction/action state space

I'm trying to plot the inaction/action state space for (A,K). The problem is that of a firm that chooses to invest or not to invest every period, based on the expected discounted profits. I solve the problem with brute-force grid search. The code is as follows.

The idea would be to plot (A,K) based on the decision of the firm to invest or not.

Any help would be much appreciated!

%% PS 4

%Housekeeping
tic
clear 
close all
clc

%global A0 theta beta p gamma F_cost k0 valueFunction prob j kgrid %valueFunction_a valueFunction_i

%% 1 Calibration
tic
theta=0.592;
p=1;
beta=0.90;
gamma=0.049;
F=0.039;

prob=[0.997 0.003 0; 
    0.0003 0.9994 0.0003; 
    0 0.003 0.997];

A=[0.8134 1 1.2293]';
expectedprod=A'*prob;
expectedprod=expectedprod';
%k1=0.01;
%k2=100;
nGridCapital=500;
A_ss=sum(A)/(length(A));

tol=1*10^(-10);
%% Steady State
capitalSS=(F/A_ss)^(1/(1-theta));
kmin= 0.01; %0.1*capitalSS;
kmax=100; % 1.1*capitalSS; 


%% Grid construction
vGridCapital=linspace(kmin, kmax, nGridCapital);
%vGridCapital=vGridCapital';

%% Matrices
mValueFunction=zeros(3,nGridCapital);
mValueFunctionnew=zeros(3,nGridCapital);

mValueFunctionnew_i=zeros(3,nGridCapital);

mValueFunctionnew_a=zeros(3,nGridCapital);

mPolicyFunction=zeros(3,nGridCapital);
mPolicyFunction_i=zeros(3,nGridCapital);
mPolicyFunction_a=zeros(3,nGridCapital);

valueProvisional_i=zeros(3,nGridCapital);

valueProvisional_a=zeros(3,nGridCapital);
adjcost=zeros(3,nGridCapital);
invest=zeros(3,nGridCapital);
revenue=zeros(3,nGridCapital);

vIter=mValueFunction;
%% Revenue
Pi=A*(vGridCapital.^theta); %pre-build revenue for each point in the capital grid and the different productivity levels

%% Iterations
diff_i=10;
diff_a=10;
iteration=0;
diff=max(diff_i, diff_a);
while (diff>tol)
    
    %loop for capital values
    for nCapital =1:nGridCapital
        %loop for A values
    for prod= 1:size(A,1)
        %loop for capital in the next period
        for nCapitalNext =1:nGridCapital 
        %loop for productivity in the next period
        for prodnext =1:size(expectedprod,1) 
            
            adjcost(nCapital,nCapitalNext)=(gamma/2)*(vGridCapital(nCapitalNext)-vGridCapital(nCapital)/vGridCapital(nCapital))^2 * vGridCapital(nCapital);
            invest(nCapital,nCapitalNext)=p*(vGridCapital(nCapitalNext)-vGridCapital(nCapital));
            revenue(nCapital)=prod*vGridCapital(nCapital).^theta;
            valueProvisional_i(prodnext,nCapitalNext)=(1-beta)*(revenue(nCapital))+beta*(mValueFunction(prodnext,nCapitalNext));
            valueProvisional_a(prodnext,nCapitalNext)=(1-beta)*(revenue(nCapital)- F*vGridCapital(nCapital)-adjcost(nCapital,nCapitalNext)-invest(nCapital,nCapitalNext))+beta*(mValueFunction(prodnext,nCapitalNext));
            
        end
            
            
        end
           
      %find capital prime and A prime that maximize the function for each,
      %adjustment and inactivity, given this period's productivity
      mValueFunctionnew_i(prod,nCapital)=max(valueProvisional_i(prod,nCapital));
      mPolicyFunction_i(prod,nCapital)=max(valueProvisional_i(prod,nCapital));
      mValueFunctionnew_a(prod,nCapital)=max(valueProvisional_a(prod,nCapital));
      mPolicyFunction_a(prod,nCapital)=max(valueProvisional_a(prod,nCapital));
      %chose the max between the two new value functions and policy
      %functions
       mValueFunctionnew=max(mValueFunctionnew_a, mValueFunctionnew_i); 
       mPolicyFunction=max(mPolicyFunction_i,mPolicyFunction_a);
       
    end
        
    end
    %mPolicyFunction=vGridCapital(1,mPolicyFunction); %convert the policy function back to capital units
    
    % find the differences
    diff=norm(mValueFunctionnew-mValueFunction);
    
    % set the new value function
    mValueFunction=mValueFunctionnew;
    
    iteration=iteration+1
    
    fprintf('Iteration=%d, Sup=%2.8f\n', iteration, diff)
    fprintf('\n')
  
end

%% plots


figure(2)
plot(vGridCapital, mPolicyFunction(1,:), 'red')
hold on
plot(vGridCapital, mPolicyFunction(2,:), 'blue')
hold on
plot(vGridCapital, mPolicyFunction(3,:), 'green')
legend('Low A', 'Medium A', 'High A')



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Answer 1

[Sugandhi]

Hi Carlos Fellmann,

I understand that you want to make plot (A, K) based on the decision of the firm to invest or not.

>> plot(X,Y)

The above command creates a 2-D line plot of the data in Y versus the corresponding values in X.

• To plot a set of coordinates connected by line segments, specify X and Y as vectors of the same length.
• To plot multiple sets of coordinates on the same set of axes, specify at least one of X or Y as a matrix.

In order to better assist you, please share more details of the issue you are facing.

For more understanding kindly go through the following link –

• Plot - https://www.mathworks.com/help/matlab/ref/plot.html?searchHighlight=plot&s_tid=srchtitle_plot_1