%%    solow.m %    Economics 303:%    Solow Model Graphs%%    George J Hall%    Brandeis University%    September 2006%clearclose all%%  set initial values for K, N and Y%K_1959 = 411.7;   % starting point for the capital stock                  % net stock of nonresidential fixed private capital (in billions 1959 dollars)                  % BEA Survey of Current Business, August 1994                  % Fixed Reproducible Tangible Wealth in the United States                    N_1959 = 115.3;   % starting point for the labor force                    % 16+ population from Economic Report of the President Y_1959 = 506.6;   % starting point for output                  % GDP (in billions of 1959 dollars)                  % Economic Report of the President   %%  set values for parameters of the model%alpha = 1/3;   % capital share of incomedelta = 0.08;  % depreciation rate of capitals = 0.10;      % saving rate n = 0.015;     % population growth rate gamma = 0.0;   % growth rate in TFPT = 100;       % number of periods to simulate %%  back out initial level of A%A_1959 = Y_1959/( K_1959^(alpha)*N_1959^(1-alpha));A_1959%%  initialize time series and %  compute initial capital-to-labor ratio%k = zeros(T,1);N = zeros(T,1);A = zeros(T,1);k(1) = K_1959/N_1959;N(1) = N_1959;A(1) = A_1959; %%  simulate model%for time = 1:T-1    A(time+1,1) = (1+gamma)*A(time,1);    N(time+1,1) = (1+n)*N(time,1);    k(time+1,1) = (1-delta)*k(time,1)/(1+n) + s*A(time,1)*k(time,1)^(alpha)/(1+n);end;%%  compute output per worker, total capital, total output,%  wages and rental rate of capital%y = A.*k.^(alpha)*1000;K = k.*N;Y = A.*(K.^(alpha)).*(N.^(1-alpha));rental_rate = alpha*A.*(K.^(alpha-1)).*(N.^(1-alpha));wages = (1-alpha)*A.*(K.^(alpha)).*(N.^(-alpha));%%  plot a bunch of stuff%figure(1)plot((1959:(1959+T-1)),k)xlabel('year');ylabel('capital-to-labor');title('Simulated time path of the Capital-to-Labor Ratio');print litk.psdisp('pausing: hit the enter key');pausefigure(2)plot((1959:(1959+T-1)),y)xlabel('year');ylabel('output (1959 dollars)');title('Simulated time path of real GDP per worker');print lity.psdisp('pausing: hit the enter key');pausefigure(3)plot((1959:(1959+T-1)),wages)xlabel('year');ylabel('wages (1959 dollars)');title('Simulated time path of real wages');print wages.psdisp('pausing: hit the enter key');pausefigure(4)plot((1959:(1959+T-1)),rental_rate)xlabel('year');ylabel('rental rate of capital (1959 dollars)');title('Simulated time path of real rental rate');print rental_rate.psdisp('pausing: hit the enter key');pausefigure(5)plot((1959:(1959+T-1)),Y)xlabel('year');ylabel('output (Billions of 1959 dollars)');title('Simulated time path of real GDP');print bigY.psdisp('pausing: hit the enter key');pausefigure(6)plot((1959:(1959+T-1)),log(Y))xlabel('year');ylabel('log output');title('Simulated time path of log real GDP');print logbigY.psdisp('pausing: hit the enter key');pause%%  load in real GDP %load GDPC1.DATT1 = length(GDPC1);year = GDPC1(49:4:T1,1);mth  = GDPC1(49:4:T1,2);day  = GDPC1(49:4:T1,3);RGDP = GDPC1(49:4:T1,4)*Y_1959/GDPC1(49,4); % Scale GDP to 1959 dollars. T2 = length(RGDP);figure(7)plot((1959:(1959+T2-1)),log(Y(1:T2)),year,log(RGDP),'r')xlabel('year');ylabel('log output');title('Simulated and actual time path of log real GDP');legend('simulated data','Scaled U.S. GDP',0); print logbigY.ps