%Econ 202C Macro. Homework#2. Problem1 Anton Cheremukhin close all; clear all; clc; % Parameters % T=70; %number of periods for transition% teta=7/20; %capital share% fi=65/41; %elasticity of disutility of labor 1.5853 delta=123/680; %depreciation rate% 0.1810=123/680 beta=203/240; %discount rate% 0.845=203/240 gamma0=203/200; %scale parameter in production function% gamma=gamma0; %old steady-state u=teta/(gamma/beta-1+delta); v=gamma-1+delta; kk1=(u^(1/(1-teta)))/((fi/(1-teta))*(1/(u*v)-1)+1/(u*v)); kc1=kk1*(1/(u*v)-1); %new s-s gamma=212/200; %scale parameter in production function% u=teta/(gamma/beta-1+delta); v=gamma-1+delta; kkT=(u^(1/(1-teta)))/((fi/(1-teta))*(1/(u*v)-1)+1/(u*v)); kcT=kkT*(1/(u*v)-1); %initial guess %kguess=ones(T,1)*[kcT, kkT]; kguess=[kc1+(kcT-kc1)*[0:1:T-1]'/(T-1), kk1+(kkT-kk1)*[0:1:T-1]'/(T-1)]; a=1+fi/(1-teta); b=1-delta; %solve options = optimset('Display','iter','LargeScale','on','Jacobian','off','MaxFunEvals',100000000,'TolX',0.0000000000001,'TolFun',0.0000000000001,'MaxIter',1000); [kpath,G]=fsolve(@optpath2,kguess,options,a,b,gamma,beta,teta,kc1,kk1,kcT,kkT,T); %results %T=70; kc=kpath(1:T,1); kk=kpath(1:T,2); lc=1./(a+kk./kc); lk=kk.*lc./kc; c=(kc.^teta).*(lc.^(1-teta)); ic=gamma*kc(2:T)-b*kc(1:T-1); ic(T)=ic(T-1); ik=gamma*kk(2:T)-b*kk(1:T-1); ik(T)=ik(T-1); p=(c.*kk)./(kc.*(ik+ic)); figure(1) plot(1:T,kc,1:T,kk,1:T,kc1,1:T,kcT,1:T,kk1,1:T,kkT,... 'LineWidth',2); title('capital'); legend('kc','kk'); xlabel('periods'); figure(2) plot(1:T,lc,1:T,lk,... 'LineWidth',2); title('labor'); legend('lc','lk'); xlabel('periods'); figure(3) plot(1:T,ic,1:T,ik,1:T,c,... 'LineWidth',2); title('investment and consumption'); legend('ic','ik','c'); xlabel('periods'); figure(4) plot(1:T,p,... 'LineWidth',2); title('price'); legend('p'); xlabel('periods'); %intuition L=7; kc=[ones(L,1)*kc(1); kc(1:T)]; kk=[ones(L,1)*kk(1); kk(1:T)]; lk=[ones(L,1)*lk(1); lk(1:T)]; lc=[ones(L,1)*lc(1); lc(1:T)]; c=[ones(L,1)*c(1); c(1:T)]; ik=[ones(L,1)*ik(1); ik(1:T)]; ic=[ones(L,1)*ic(1); ic(1:T)]; trend=[gamma0.^[1-L:0] gamma.^[1:T]]; gamma1=(gamma0^(1-teta))*(gamma^teta); trendc=[gamma0.^[1-L:0] gamma1.^[1:T]]; kc1=log(kc.*trend'); kk1=log(kk.*trend'); lk1=lk; lc1=lc; c1=log(c.*trendc'); ik1=log(ik.*trend'); ic1=log(ic.*trend'); T=20; figure(5) plot(1:T,kc1(1:T),1:T,kk1(1:T),... 'LineWidth',2); title('log undetrended capital'); legend('kc','kk'); xlabel('periods'); figure(6) plot(1:T,ic1(1:T),1:T,ik1(1:T),1:T,c1(1:T),... 'LineWidth',2); title('log undetrended investment and consumption'); legend('ic','ik','c'); xlabel('periods');