Question

Consider countries A and B with the same (unchanging) population. In country A, people devote 60% of GDP to investment and the production function is Y=3√K, where Y denotes real GDP and K denotes the stock of physical capital. In country B, people devote 15% of GDP to investment and the production function is Y=5√K.

a. Discuss the underlying intuition of the differences between countries A and B as described above (hint: there are two differences).

b. Assume that both countries begin with the capital stock of 400. For each country, what is the amount of investment (denoted I) and consumption (denoted C) at that point? Report your calculations in this Word file using the stated notation (for multiplication use x). Provide brief explanations. Support your answers with a diagram (make it large so that you can also add answers from the sub-questions c. and d. below).

c. Now consider each country adjusting to its steady state (denoted by asterisk for each variable). Also assume a depreciation rate of 3%. What is the steady-state capital stock of countries A and B? Show all your calculations, provide some brief explanations and indicate your answers in the earlier diagram.

d. What is the steady-state consumption of countries A and B? Show all your calculations, provide some brief explanations and indicate your answers in the earlier diagram. In which country would you rather live, and why?

Answer 1

A)i) Country A saving rate or Investment is 60% while ,country B saving rate is 15%

ii) Country A Technology is less capital efficent compare to country B because same capital stock generate 0.6 of total output in country A compare to country B.

B)Ya=3√400=3*20=60

Saving/ Investment=0.6*60=36

Consumption=60- saving=60-36=24

Yb=5√400=5*20=100

Investment=0.15*100=15

Consumption=100-15=85

C) Steady state where Investment= depreciation

Country A,

0.6*3√k=0.03k

1.8/0.03=√k

√k=60

k=3600

Ya=3*√3600=3*60=180

Country B,

0.15*5√k=0.03k

0.15*5/0.03=√k

√k=25

K=625

Yb=5*√625=5*25=125

D)Steady state consumption,

Ca=0.4ya=0.4*180=72

Cb=0.85yb=0.85*125=106.25

Given country B has a higher level of consumption in Steady state level,so i prefer country B.