Question

Consider a country whose output can be produced with 2 inputs (capital and labor). The output per worker/capita production function is given by y=k^1/2, where y represents output per worker/capita and k is capital per worker/capita.  Assume the fraction of output saved/invested is (the savings rate) s = 25%, the population growth rate is 0%, the depreciation rate δ=5%, the level of technology is constant at A=1 and the assumptions of the Solow model hold.

1. What are the steady state levels of capital, income and consumption per capita?
2. Assume the country starts in year 1 and the level of capital per worker is 16.  In a table such as the one below, show how capital and output per worker change over time (the beginning is filled in as a demonstration).  Continue this table up to year 8.

3. Year	Capital per worker k	Output per worker y=k1/2	Investment per worker, i=sy	Depreciation, δk	Change in Capital stock per worker, sy- δk
   1	16	4	1	.8	.20
   2	16.2

Answer 1

a)

We know that change in capital per worker is given by

where s=saving rate

f(k)= output per worker

depreciation rate

k=capital per worker

In steady state change in capital per worker is zero, i.e. . So,

We are given f(k)=y=k^1/2

s = 25%,

5%

Put various value in the above equation

,

y=k^1/2 =(25)^1/2=5

Per capita Consumption=y-sy=(1-s)y=(1-0.25)*5=3.25

In steady state,

Per capital capital=25

Per capita income=5

Per capital consumption=3.25

b)

Year	Capital per worker	Output per worker	Investment per worker, i=sy=0.25y	Depreciation,	Change in Capital stock per worker, sy- δk
	k	y=k1/2		δk=0.05k
1	16.00000	4.00000	1.00000	0.80000	0.20000
2	16.20000	4.02492	1.00623	0.81000	0.19623
3	16.39623	4.04923	1.01231	0.81981	0.19249
4	16.58873	4.07293	1.01823	0.82944	0.18880
5	16.77752	4.09604	1.02401	0.83888	0.18513
6	16.96265	4.11857	1.02964	0.84813	0.18151
7	17.14416	4.14055	1.03514	0.85721	0.17793
8	17.32209	4.16198	1.04050	0.86610	0.17439