Question

Q.2 Consider the Solow growth model. Suppose that F(K,N)=RºS No5 with d=0.1, s=0.2, n=0.01, and z=1 and take a period to be one year. (15 marks) a. Determine capital per worker, income per capita, and consumption per capita in the steady state. Show the theoretical derivation and numerical solution. (7 marks) b. Now suppose that the economy is initially in the steady state that you calculated in part a, and savings increases to s=0.4. Determine capital per worker, income per capita, and consumption per capita in the new steady state. (4 marks) C. Suppose that the depreciation rate d increases, what is the effect of this change on the quantity of capital per worker and output per worker from the steady state in a? (4 marks)

Answer 1

KISNIS pose 0.2 F(k,n) = y = kosNos oy=Y - a. k = k » n 시의 k - alt, zla -n k 1.82 = - k E By-dk -n -_BY d-n = Bf(k)-d-n k k's Bf (R) – (d+n) at steady state, k = 0 sy-(d+n)k=0 → 0.2k•5 = (0.1 +0,01) k ko5 6* = 3,3) income per Capita, y = (3.31)•5 -1.82 Consumption per-capita, c = (1-P) y=( -0.2)x 1.12 = 1.4 56 6. At new steady state, s'y-d thk=0 0.48.5 = 0.01) k → k:5+ 3.64 k*- 13.25 yt = 3.64 K*- (1-0.4) 3.64 = 2.184 828, 18tak $,+n) ke Y FAIR) C, 18 is ef() >k Rz k, k→ both k* & * declines due to rise in depreciation rate.