Problem Set 1 (Growth Models) Part 3 of 3: New Growth Theory ECON 6002, Semester 1 2017 (Lect: Denny Lie) Due date: Wed, 12 April, 6pm Problem 1...

sR)L, and (d is the depreciation rate)

K_ =sKY dK (3)

(i) Find the expression for k_ as a function of k = K=AL (capital per unit of e§ective labor), A_=A, and the parameters.

(ii) Find the steady-state value of k (assuming that A_=A is constant in the steady state). Compare this to the expression in the Solow model, why are they somewhat di§erent?

(iii) Find the expression for the steady-state growth rate of A (itís supposed to be constant and Önite!). Hint: you should Örst eliminate KA in (1) and use k instead.

(iv) Compare the result in (iii) to that in the lecture (with no capital input). Which one is higher? Why?

(v) Suppose there is a one-time permanent increase in the exogenous saving rate sK. Does this a§ect gA (growth rate of A) in the long run?