Question

2. A country has the following production function: Y = 0.3L0.5p0.2 where Y is total output, K is capital stock, L is population size and P is land size (P is a fixed number). The depreciation rate (8) is 0.05. The population growth rate (n) is 0. The saving rate is 0.2. We define: y = Y/L, K = K/L and p = P/L. Use: Ak = sy - (n + )k. a) Find out the steady state values of k and y in terms of p, the per capita land size. b) If p → 0, what will happen to the steady state values of k and y in terms of p you find in part a) ? c) Find out the golden rule steady state values of k and y in terms of p, the per capita land size. d) What saving rate can be used to support the golden rule steady state ?

Answer 1

0 5 0:3 0.2 2. a) : x= k production function Per capita form: y. Steady stare : Ale=0 ... sy =(n+d) k 1?? 02 nt BJ S.p°.3. nis :iks spo-2707 :: h4 = 7.246 224 :: y* = 1.812p27 0.2 [n. % 217 to o b) If psos in het and y* ; but to and y c) Golden rule steady state: Mekanto ::0.3. 202 het : nuo $ av, te ik 03per? 5 0-3po2 70:t: 12.931874 nao nge med Í 93.77777 2'155p?

Now 0:2 Then for her to the gr ; s=03. savings rate of 0.3 supports golden rule.