Question

4. Assume that this economy – suppose it is China – has the following production function: Y = F(K, L) = K0.5L0.5

a. State the per-worker production function.

b. Suppose the saving rate is 24 percent, the depreciation rate is 6 percent and the population growth rate is 2 percent. Calculate the following three variables in the steady state: capital stock per worker, output per worker, and consumption per worker.

c. Draw a graph for the Solow Model in the steady state. Clearly show the above three variables on the graph. Remember to label the graph clearly.

d. In 2016, China relaxed their One-Child Policy and allowed only children to have two kids. Suppose this increase the population growth rate from 2% to 3%. What effects does this have on the Solow model? How does this impact total output in the steady state? How does this impact output per worker in the steady state?

e. What may be an indirect (non-Solow) economic consequence of the new Two-Child policy? This can be micro or macro-related, from this class or otherwise. Back up your argument with economic theory.

Answer 1

a) Y = F(K, L) = K0.5L0.5

Divide both side by L

Y/L=K0.5L0.5/L

y= (K/L)0.5= k0.5 (Per worker production function)

b) Suppose the saving rate is 24 percent, the depreciation rate is 6 percent and the population growth rate is 2 percent.

s=0.24, d=0.06, n=0.02

For steady state:

Change in k=0

sy-(n+d)k=0

0.24(k0.5 )= (0.06+0.02)k

0.24/0.08= k/k0.5

3= k0.5

k= 9 capital per worker at steady state

y=k0.5 = 3 Output per worker at steady state

c= y-sy= 3-3(0.24)= 3-0.72= 2.28 Consumption per worker at steady state.

c)

y* is output per worker and k* is capital per worker at steady state and the gap between curve y and sk that c is the consumption per worker at steady state.

d)  Suppose this increase the population growth rate from 2% to 3%.So new n,= 0.03.

For steady state:

Change in k=0

sy-(n+d)k=0

0.24(k0.5 )= (0.06+0.03)k

0.24/0.09= k/k0.5

2.66= k0.5

k= 7.075 capital per worker at steady state

y=k0.5 = 2.65 Output per worker at steady state

output per worker decreases in steady state. Also as population increases it cause rise in total output.