%% 14.461 Problem Set 1 Fall 2009 % Question 1 clear all close all clc %% Parameters b = 0.99; d = 0.025; e =1; sg = 1; a = 0.36; ro = 0.95; A = 1; p1 = ((1/b -1 + d) / (A*a)) ^ (1/ (1-a)); p2 = A * (p1) ^ (-a) - d * (p1)^(-1); %% Steady State N = ((1-a)*A * (p2) ^(-sg) * (p1) ^ (-a) ) ^ (1 / (e+sg)); C = p2 * N; K = N / p1; Y = A * K ^ a * N ^ (1-a); %% Define more parameters p3 = (1/b * K / C + (1-a) * Y /C * (e+a)^ (-1) * a )/ (1 + (1-a) * Y / C * (e+a)^ (-1) * sg ) ; p4 = (K / C) / ( 1 + (1-a) * Y / C * (e+a)^ (-1) * sg ); p5 = ( (1-a) * Y / C * (e+a)^ (-1) + Y / C ) / ( 1 + (1-a) * Y / C * (e+a)^ (-1) * sg ); p6 = (K / C) / ( 1 + (1-a) * Y / C * (e+a)^ (-1) * sg ); %% Main quadratic equation aa = p4 * (1 + (1 - (1 - d )*b )*(1-a) * sg / (e+a) ); bb = -p3 - sg*p4 + (1 - (1 - d )*b )*(1-a) * ( (a - sg * p3) / (e+a) - 1) ; cc = sg * p3; vkk = (-bb - sqrt (bb^2 - 4 * aa * cc)) / (2 * aa); vck = p3 - p4 * vkk; vnk = a / (a + e) - sg / (a + e) * p3 + (sg / (a + e)) * p4 * vkk; vka = - ( (1 - (1 - d )*b )*ro + (1 - (1 - d )*b )*(1-a)*ro / (e+a) *(1 - sg*p5 ) + sg * (1-ro) * p5 ) / ( (1 - (1 - d )*b )*(1-a) * ( ro * p6 * sg /(e+a) - 1 ) - sg * (1 - ro) * p6 - vck + vnk * (1 - (1 - d )*b )*(1-a) ); vca = p5 - p6 * vka; vna = 1 / (e+a) - sg / (e+a) * p5 + sg / (e+a )*p6 *vka; %% IR functions eps(1) = 1; eps(2:50) = zeros(49,1); aaa(1) = 0; kkk(1) = 0; ccc(1) = 0; nnn(1) = 0; yyy(1) = 0; iii(1) = 0 for i=1:50 aaa(i+1) = ro * aaa(i) + eps(i); kkk(i+1) = vkk * kkk(i) + vka * aaa(i+1); nnn(i+1) = vnk * kkk(i) + vna * aaa(i+1); ccc(i+1) = vck * kkk(i) + vca * aaa(i+1); yyy(i+1) = aaa(i+1) + a * kkk(i) + (1-a) * nnn(i+1); end plot(ccc)