Question

Problem Set on Growth and the Solow Model KIN 1. Suppose that the production function for Serbia is given by Y (a) If you double the amount of capital and double the amount of labor available, does output always double? Show mathematically (b) Rewrite the production function in intensive form. (c) Suppose the savings rate is r and the depreciation rate is m. Derive an expression for the steady state capital per worker and the steady state output per worker. (d) By how much would have to rise (assuming all else remains the same) for the steady state output per worker in Serbia to double? Show all steps. 2. Country A and B cach have a production function Y KiN, Assume 8 0.05 in each country but s 0.1 in country A and 0.2 in country B. Each country starts off with an initial k of 2. (a) Rewrite the production function in intensive form. (b) Track c, i, k and y in each country for the next three periods. Track each coun- try's growth rate of output per worker, g. (c) What happens to output per worker in each country in the long run? (d) Does country B overtake country A? when? (e) Suppose an earthquake hits country A so its initial k (instead of being 2) is now reduced to 1. There is no effect on country B. Track the growth rate of output per worker in each country. How do these compare with your answers in (a) above?

Answer 1

(0) Y = 34 14 314 K L If (tk, ti) = (tk). (AL) y tf(,1) - { ****] 1 tl 14 3147 t-t Hence, Constant returns to scale. VA 314 (b) y = ДК - iz st) 12 І. К. МК a y = ( 2 ) R = ( 2 steady state output capital per worker. x Reklama na Mkan