Question

Consider an economy with the following production function zf(k ∗ ) = z (k ∗ )^0.5

1. Solve for golden rule capital per worker and optimal savings rate using the equation characterizing the best steady state. Then, you can back out optimal saving rate given that the best capital per worker.

2. Assume that we are at the steady state with a saving rate s1 < sgold. If the government increases the saving rate up to sgold through policies, what happens to capital, output and consumption during the transition to the Golden Rule?

3. Assume that we are at the steady state with a saving rate s2 > sgold. If the government decreases the saving rate up to sgold through policies, what happens to capital, output and consumption during the transition to the Golden Rule

Answer 1

0.5 Z f(K) = 2(K) s.2.0 t _ Sk K= (32) Z.15.2 S.K s= (SK ) Z.go.5 OS E8.k 2) Here, we have to increase taning initially rife in saning would reduce Consumption but over the long run consumption output and capital per worker would rise. 3 S > Sg , thus, there would be fall in Danny, there will rise consumption but capital per worker and output per worker will decrease.