2. [40 Points] Consider to economies that have the same quantities of labor (L 4

ID: 1143385 • Letter: 2

Question

2. [40 Points] Consider to economies that have the same quantities of labor (L 400) and capital (K 400), and the same technology (A 100). The economies of the countries are described by the following Cobb-Douglass production functions: Norta Economy: Y ALK23 Soutl Economy: Y AL3/3 K1/3 a. Which economy has the larger total production? Explain or show your work b. In which economy is the marginal product of labor larger? Explain or show your work. c. In which economy is the real wage larger? Explain or show your work. d. In which economy is labor's share of income larger? Explain or show your work.

Explanation / Answer

Consider the given problem here there are two economies “north” and “south” economy and their production function are also given in the question. Now, both the economies have same value of “A”, same labor supply and capital supply.

So, the production of “north” is given by, “Yn = A*L^1/3*K^2/3 = 100*400^1/3*400^2/3.

=> Yn = 100*400 = 40,000 = Yn.

Similarly, the production of “south” is given by, “Ys=A*L^2/3*K^1/3=100*400^2/3*400^1/3.

=> Ys = 100*400 = 40,000 = Ys. So, both have same level of production.

b).

Now, for “north” the “MPL” is given by.

=> MPL = A*(1/3)*L^(-2/3)*K^2/3 = (A/3)*(K/L)^2/3 = (100/3)*(400/400)^2/3 = 33.33 = MPLn.

Similarly, for “north” the “MPL” is given by.

=> MPLs = A*(2/3)*L^(-1/3)*K^1/3 = (2A/3)*(K/L)^1/3 = (200/3)*(400/400)^1/3 = 66.67 = MPLs. So, if we compare both these expression we get “MPLn < MPLs”. So, “South Economy” has the larger marginal product of labor.

c).

Now, we know under perfectly competitive market the “real wage” is equal to “MPL”, => for “north” the real wage is given by “wn = MPLn”. Similarly, for “south” the real wage is given by “ws = MPLs”. Now, in “south” “MPL” is larger compare to “North”, => “real wage” is larger in “south” compare to “North”.

d).

Now, under the given production function the labor share is nothing but the “exponent” of “labor”, => the “power” of labor. So, for “North” the labor share is “1/3” and for “South” the labor share is “2/3”, => “South” has the larger labor share compare to “North”.

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2. [40 Points] Consider to economies that have the same quantities of labor (L 4

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