Question

1. Given the production function Y = zK^1/3N^2/3, complete the below table by including the values corresponding to the Golden Rule of Capital Accumulation capital per worker, output per worker, and consumption per worker.   Assume that d = 0.075 across all countries.

	z	n	k	y	c
Argentina	045	0.014
Thailand	0.23	0.015
Cameroon	0.05	0.028

Answer 1

Per-capita production function: Y/N = z x (K/N)^1/3

y = z x k^1/3

The Golden Rule condition states:

MPK = d + n

Using production function:

MPK = Y/K = (1/3) x z x (N/K)^2/3 = (z/3) / k^2/3 = 0.075 + n

c = y - [(d + n) x k]

(A) Argentina

(0.45/3) / k^2/3 = 0.075 + 0.014

0.15 / k^2/3 = 0.089

k^2/3 = 0.15 / 0.089 = 1.69

k = (1.69)^(3/2) = 2.19

y = 0.45 x (2.19)^(1/3) = 0.58

c = 0.58 - (0.089 x 2.19) = 0.58 - 0.19 = 0.39

(B) Thailand

(0.23/3) / k^2/3 = 0.075 + 0.015

(0.23/3) / k^2/3 = 0.09

k^2/3 = (0.23/3) / 0.09 = 0.85

k = (0.85)^(3/2) = 0.79

y = 0.23 x (0.79)^(1/3) = 0.21

c = 0.21 - (0.09 x 0.79) = 0.21 - 0.07 = 0.14

(C) Cameroon

(0.05/3) / k^2/3 = 0.075 + 0.028

(0.05/3) / k^2/3 = 0.103

k^2/3 = (0.05/3) / 0.103 = 0.16

k = (0.16)^(3/2) = 0.07

y = 0.05 x (0.07)^(1/3) = 0.02

c = 0.02 - (0.103 x 0.07) = 0.02 - 0.007 = 0.01