Question

Consider two countries: Frugalia (denoted by F) and Prodigalia (denoted by P). In both countries the production function is Cobb-Douglas: Y = A ⋅ K 1 3 N 2 3. The population growth rate (n) is 0.1, physical capital depreciates at the rate of 0.1; δ = 0.1, and A = 1. In F the saving rate is s F = 0.2 and in P it is s P = 0.4.

a) (5pts) Write the production function in terms of output per capita (Y/N).

b) (10 pts) Find the steady-state values of the capital-labor ratio (K/N) in both countries.

c) (10 pts) Find the steady-state values of the output per capita (Y/N) in both countries.

d) (10 pts) In which of the countries is consumption per capita (C/N) higher in the steady-state?

e) (10 pts) In which of the countries is the marginal product of labor (MPN) higher in the steady-state? You can relate this to your answer in (b).

Answer 1

a) Y/N = A*k^{​​​​​1/3},

k = K/N

.

B) at Steady state, s*y = (d+n)*k

s= (d+n)*k^{​​​​​​2/3}

n = d = .1

Then in F, .2= .2k^2/3

So k*= 1

In P, .4= .2*k^2/3

k*= 2^3/2

= 2.828

.

C) y* in F , y*= 1

In P, y*= √2

.

D) c= (1-s)*y

In F, c*= (1-.2)*1 = .8

In P, c*= .6*√2 = .848

so higher per capita consumption in nation P

.

e) MPN = dY/dN

= (2/3)*k^(1/3)

so as higher k in P, so higher is value of MPN

so it's answer is linked to value of k in b)