[Note: This is for a graduate-level macroeconomic theory course in which we are

Question

[Note: This is for a graduate-level macroeconomic theory course in which we are using Romer's Advanced Macroeconomics textbook. I've already solved Part A easily but not sure about B through D. The result may be intuitive but I need to know how to show it mathematically. Thank you.]

a. What are the factor prices (MPK and MPL) in each economy when factors are immobile?

b. Now suppose capital (but not labor) is free to move. In which direction will the flows take place, and when will they cease?

c. Now suppose labor (but not capital) is free to move. In which direction will the flows take place, and when will they cease?

d. Compare and contrast the equilibria in (b) and (c).

Explanation / Answer

Y= K1/4 L3/4

a) MPK=(K-3/4)L3/4/4 = L3/4/ 4 K3/4

MPL= 3K1/4 L-1/4 / 4 = 3K1/4 /4 L1/4

country A

MPK = (100)3/4/4 (100)3/4 = 1/4

MPL = 3 (100)1/4 /4 (100)1/4= 3/4

country B

MPK = (50)3/4/4 (100)3/4 = 1/ 4 (2)3/4

MPL = 3 (100)1/4 /4 (50)1/4= 3 (2)1/4 / 4

MPK is higher in country A and MPL is higher in country B

ans b) Now suppose capital (but not labor) is free to move

as MPK is higher in country A so , capital will move from country B to A , as more capital move to Country A , MPK in A will decrease and as less cpital will be there in country B, so MPK in B will increase, this process of movement will continue until MPK in both countries will become equal.

ans c) Now suppose labor (but not capital) is free to move

as MPL is higher in country B so , capital will move from country A to B , as more capital move to Country B , MPL in B will decrease and as less cpital will be there in country A, so MPL in A will increase, this process of movement will continue until MPK in both countries will become equal.

ans d)

in case of b) equilibium is achieved where MPK in both countries become equal.

in case of c) equilibium is achieved where MPL in both countries become equal.

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