# Returning multiple values in fminbnd

조회 수: 5(최근 30일)
Prerna Mishra 2023년 2월 25일
댓글: Torsten 2023년 2월 25일
I am trying to solve a dynamic optimization problem in which I solve for optimxal capital and debt. The problem is structured such that for each period I have to find the value of debt, variable d, that maximizes the firm value, given the value of k and k0. And then in the next step I have to find the value of k that maximizes the firm value over time, given k0. My main looks as follows:
disc = 0.96; %discount rate for the expected next period value function
alpha = 0.45; %capital elasticity, Cobb-Douglas *
beta = 0.34; %labor elasticity, Cobb-Douglas *
R = 719.0615; %Market Size
f = 4.02; %fixed cost of production
sigma = 5.23; %elasticity of substitution
W = 0.3; %wage *
theta = 0.7; %cost of bankruptcy *
chi = 0.8; %level of debt at which bankruptcy happens *
c = 0.2; %parameters of capital adjustment *
kappa = 0.3; %managerial rent *
mu_b = 0.1; %mean of the firm level shock *
sigma_b = 0.12; %standard deviation of the firm level shock
omega = (beta*(sigma-1))/(beta*(sigma-1) - sigma);%an itermediary parameter
na = 3;%TFP shock grid size
nk = 11; %capital grid size
%setting up the capital grid
kmin = 1;
kmax = 10000000000;
kvec = linspace(log(kmin),log(kmax),nk)';
kvec = exp(kvec);
%setting up the TFP grid
multiple = 3;
mu_a = 0;
rho_a = 0.7;
sigma_a = 0.05;
[avec,pi]=tauchen(0.0,sigma_a,rho_a,multiple,na);
Unrecognized function or variable 'tauchen'.
avec = exp(avec)';
tol = 1e-5;
diff = 1;
its = 0;
maxits = 500;
v0 = zeros(nk,na);
while diff>tol && its <maxits
for j = 1:na
for i = 1:nk
P0 = 0.001;
a0 = avec(j);
k0 = kvec(i);
k1 = fminbnd(@(k)ValueFunctionCapital(k,v0,k0,a0,j,P0),kmin,kmax);
[val,d] = -ValueFunctionCapital(k1,v0,k0,a0,j,P0);
P = fixedPointP(P0,k1);
v1(i,j) = val;
k11(i,j) = k1;
d11(i,j) = d;
p11(i,j) = P;
end
end
diff = norm(v0-v1)
v0 = v1;
its = its+1
end
My ValueFuntionFunctionCapital looks as follows:
function [val,d] = ValueFunctionCapital(k,v0,k0,a0,j,P)
global disc alpha beta R f sigma W theta chi c kappa mu_b sigma_b omega pi mu_a sigma_a kvec avec maxits
g1 = interp1(kvec,v0,k,'linear'); %smooth out previous value function
%some constants
prof_brac = (sigma/(beta*(sigma-1)))^omega - (sigma/(beta*(sigma-1)))...
^(sigma/(beta*(sigma-1)-sigma));
function val_inner = ValueFunctionDebtInner(d,k0,k,a0,P)
g_inner = @(b) lognpdf(b, mu_b, sigma_b); % define PDF of lognormal distribution
fun_inner = @(b) (1./b).^omega .* g_inner(b);
Q11_inner = integral(fun_inner, 0, Inf);
pdf_inner = @(x) lognpdf(x, mu_b, sigma_b);
V_term1_1_inner = (1-kappa)*(R*P^(sigma-1))^(-1/(beta*(sigma-1)))*(a0*k^alpha)^...
(-(sigma-1)/(beta*(sigma-1)-sigma))*W^omega*prof_brac*Q11_inner;
V_term1_inner = V_term1_1_inner + V_term1_2_inner;
b_th_inner = bankruptcy(a0,k0,k,d,P,prof_brac,W,chi,kappa,f,sigma,beta,c,R);
V_term2_cdf_inner = logncdf(b_th_inner, mu_b, sigma_b); % compute CDF at x ;
V_term2_inner = kappa*d*(1-V_term2_cdf_inner);
Q31_inner = integral(fun_inner, 0, b_th_inner);
% define PDF function using lognpdf
Q32_inner = integral(pdf_inner, 0, b_th_inner);
V_term3_1_inner = (1-kappa)*theta*(R*P^(sigma-1))^(-1/(beta*(sigma-1)-sigma))*...
(a0*k^alpha)^ (-(sigma-1)/(beta*(sigma-1)-sigma))*W^omega*...
prof_brac*Q31_inner;
V_term3_inner = V_term3_1_inner + V_term3_2_inner;
V_final_inner = V_term1_inner + V_term2_inner - V_term3_inner ;
val_inner = V_final_inner;
val_inner = -val_inner;
end
dmin = 1;
dmax = k;
d = fminbnd(@(d)ValueFunctionDebtInner(d,k0,k,a0,P),dmin,dmax);
g = @(b) lognpdf(b, mu_b, sigma_b); % define PDF of lognormal distribution
fun = @(b) (1./b).^omega .* g(b);
Q11 = integral(fun, 0, Inf);
pdf = @(x) lognpdf(x, mu_b, sigma_b);
V_term1_1 = (1-kappa)*(R*P^(sigma-1))^(-1/(beta*(sigma-1)))*(a0*k^alpha)^...
(-(sigma-1)/(beta*(sigma-1)-sigma))*W^omega*prof_brac*Q11;
V_term1 = V_term1_1 + V_term1_2;
b_th = bankruptcy(a0,k0,k,d,P,prof_brac,W,chi,kappa,f,sigma,beta,c,R);
V_term2_cdf = logncdf(b_th, mu_b, sigma_b); % compute CDF at x ;
V_term2 = kappa*d*(1-V_term2_cdf);
Q31 = integral(fun, 0, b_th);
% define PDF function using lognpdf
Q32 = integral(pdf, 0, b_th);
V_term3_1 = (1-kappa)*theta*(R*P^(sigma-1))^(-1/(beta*(sigma-1)-sigma))*...
(a0*k^alpha)^ (-(sigma-1)/(beta*(sigma-1)-sigma))*W^omega*...
prof_brac*Q31;
V_term3 = V_term3_1 + V_term3_2;
%V_term3 = -V_term3;
V_final = V_term1 + V_term2 - V_term3 ;
val = V_final + disc * (g1*pi(j,:)');
val = -val;
end
I understand that there is a lot of repetition of code here. But for now what I want is that I can store k, the value of capital that maximizes the value and the corresponding d. I am having troubles storing that since with fminbnd I am not able to retrieve both the values when I call the function. Is there anyway I can get both k and corresponding d in main?
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Torsten 2023년 2월 25일
You can get d only by calling "ValueFunctionCapital" again with the optimal k1 as you do in the next line of your code. Doesn't that work ? I cannot run your code since at least "tauchen" is missing.

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