Question

Time	Current per capita capital	Per capita income	Savings per capita	Rate of deterioration of capital per capita	Next period per capita capital	Capital-Output Ratio	Growth rate of per capita income
t	k(t)	y(t)	sy(t)	(δ+n)k	k(t+1)	θ=k(t)/y(t)	(g*)
0	2.0						---
1
2
3
4
5
6
7
8
9
10

Population growth rate = .03

Savings rate = .5

capital depreciation rate = .2

capital share = .5

K(0) = 2

must be done by calculator, please show formula, not on excel

Answer 1

To write the production function in per effective worker terms, dividing both sides by EL,

Y/EL = (K^1/4EL^3/4)/EL

y = k^1/4

To reach the golden rule steady state, we must have Marginal product of capital, MPk = n + g +

MPk = (1/4)*k^-3/4

so, (1/4)*k^-3/4 = 0.02 + 0.03 + 0.1

On solving this we get, k* = 1.976

At this golden rule capital stock, y* = f(k*) = (k*)^1/4 = (1.976)^1/4 = 1.1856

To derive golden rule savings rate, we must have ( + n +g)k* = s_goldf(k*)

Using above calculations, 0.15*1.976 = s_gold(1.1856)

s_gold = 0.2964/1.1856 = 0.25 while the current saving rate is 0.30, thus, the economy is saving more.