Answer to Question #286684 in Macroeconomics for Msb

Question

Consider two countries in West Africa 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-Douglas production functions: 

Country X: Y = AK^0.3L^0.7

Country Y: Y = AK^0.7L^0.3

a) Looking at the two production functions, which country has larger production? Explain

b) In which country is the Marginal Product of Labor larger? Explain

c) In which country is the real wage larger? Explain

d) In which country is labors share of income larger? Explain

Answer 1

Solution:

a.). Country X: Y = AK^0.3L^0.7

Production (Y) = 100(400^0.3) 400^0.7 = 40,000

Country Y: Y = AK^0.7L^0.3

Production (Y) = 100(400^0.7) 400^0.3 = 40,000

Both country X and Y have the same production.

 

b.). Country X MP_L = $\frac{\partial Y} {\partial L}$ = 0.7AK^0.3L^-0.3 = 0.7(100) $\times$ (400^0.3) $\times$ (400^-0.3) = 70

Country Y MP_L = $\frac{\partial Y} {\partial L}$ = 0.3AK^0.7L^-0.7 = 0.3(100) $\times$ (400^0.7) $\times$ (400^-0.7) = 30

c.). Country X real wage:

Wage = P $\times$ MPL = 400 $\times$ 70 = 28,000

Real Wage = $\frac{W}{P} = \frac{28,000}{400} = 70$

Country Y real wage:

Wage = P $\times$ MPL = 400 $\times$ 30 = 12,000

Real Wage = $\frac{W}{P} = \frac{12,000}{400} = 30$

The real wage is larger in country X

d.). Share of income:

Share of income is larger in country X.