Consider an ecpnomy described by the production function : Y= F(K,L) = K 2/3 L 1
ID: 1195663 • Letter: C
Question
Consider an ecpnomy described by the production function : Y= F(K,L) = K2/3 L1/3.
a. Find the per worker production function.
b. Assuming population growth (n) and technological change change (g), find the steady-state capital stock per worker as a function of the savings and depreciaion rate, population growth and technological change.
c. Now assume that depreciation rate is 3% a year, population growth is 2% a year and technological change is 1% and the saving rate is 24%. Find the steady-state level of capital per worker and the corresponding levels of output per worker.
d. Now assume Marginal product of Capital(per worker) find the level of capital that maximizes consumptions per worker in the steady state.
e. What savings rate is necessary for the economy to reach this consumption maximizing steady state?( Hint use the answer from part b). How does this compare to the current saving rate 24%?
Explanation / Answer
1.
Y=K^2/3*L^1/3
Dividing equation by L both side, y is output per worker
y=Y(K,L)/L=(K/L)^2/3
2.
According to solow swan model: golden rule of saving rate state
(K/Y)={s/(n+g+ )}
(K/L)={s/(n+g+ )}^3
s=saving rate
n=population growth rate
=depreciation rate
3.
K/L={24/(3+2+1)}^3
K/L=64
Y/L=(64)^2/3=16
4. ‘golden rule’ is the ‘optimal’ saving rate (sG) that maximises consumption per head is MPk=+n
dY/dK=2/3k^1/3= +n
5.
same as part 2