Question

18. Consider two competitive economies that have the same quantities of labor (L 400) and capital (K 400), as well as the same technology (A 100). Remember that factors cannot move across countries. The economies of the countries are described by the following Cobb-Douglas production functions: North Economy: Y.4L.3K7 South Economy: Y-AL'K3 a. Which economy has the larger total production? Explain. b. In which economy is the marginal product of labor larger? Explain. c. In which economy is the real wage larger? Explain. d. In which economy is labor's share of income larger? Explain. e. How your answers in b and c would change if labor were mobile? f Under labor mobility, which country should have the larger quantity of labor? Explain.

This is a macroeconomics problem. I am primarily concerned with parts e) and f). Thank you!

Answer 1

Consider the given problem here the production function of both the regions are given. Now, the “L” and “K” in both the economy is same, => “L=K=400”.

=> the production in “North” is given by, “Y=A*L^0.3*K^0.7”, => “Y = 100*400^0.3*400^0.7”, => Y = 100*400 = 40,000.

=> the production in “South” is given by, “Y=A*L^0.7*K^0.3”, => “Y = 100*400^0.7*400^0.3”, => Y = 100*400 = 40,000.

So, the production in both the economy is same.

Now, the “MPL” in “North is given by.

=> MPL = A*0.3*L^-0.7*K^0.7 = A*0.3*(K/L)^0.7 = 100*0.3*(400/400)^0.7 = 30 = MPL in North.

Now, the “MPL” in “South is given by.

=> MPL = A*0.7*L^-0.3*K^0.3 = A*0.7*(K/L)^0.3 = 100*0.7*(400/400)^0.7 = 70 = MPL in South.

e).

So, here we can see that the “MPL” is larger in “South” compare to “North”. Now, under the perfectly competitive market the “real wage” is equal to “MPL”, => “W/P = MPL”, => real is also higher in “South”. Now, if migration is allowed, => labor in “North” starts migrating to “South” because of the higher wage. Now, as the labors starts migrating to “South”, => real wage as well as the productivity in “North” starts increasing and the process will continue until perfect equality will established.

So, in equilibrium “MPL” in both economy are same as well as “real wage”.

f).

So here initially both the had same amount of labor which is “Ln=Ls=400”. Now, under the migration labor will migrate to “south” from “north”, => at the new equilibrium where “MPL” and real wage are same both “south” must have more labor compare to “north”.