Question

A U.S. apparel manufacturer is considering moving its production abroad. Suppose its production function​ is:

q=L^0.60*K^0.40

In the United​ States, w=6 and r=4. At its Asian​ plant, the firm will pay a 10​% lower wage and a 10​% higher cost of​ capital: ​w*=6​/1.10 and ​r*=1.10*4. What are L and K and what is the cost of producing q=100 units in both​ countries?  ​(for all​ responses, enter a real number rounded to two decimal​ places)

In the​ U.S., L is 100​, K is 100​, and the cost of production is ​$ 1000. I

n​ Asia, L is ----,k is ---, and the cost of production is ---

What would the cost of production be in Asia if the firm had to use the same factor quantities as in the United States?

The cost of production would be ---

Answer 1

In Asia, w* = 6/1.10 = 5.45; r* = 1.10*4 = 4.4

Cost is minimzed when MRTS = w*/r*
So, MRTS = MPL/MPK = (dq/dL)/(dq/dK) = (0.60)L0.6-1K0.4/0.4L0.6K0.4-1 = 3L-0.4K0.4/2L0.6K-0.6 = 1.5K.4+.6/L.4+.6 = 1.5K/L
So, 1.5K/L = w*/r* = (6/1.1)/(1.1*4)
So, K = 6L/(1.5*1.1*1.1*4) = L/(1.1*1.1) = L/1.21

So, q = 100 = L0.6K0.4 = L0.6(L/1.21)0.4 = L0.6L0.4/(1.21)0.4
So, L0.6+0.4 = 100(1.21)0.4 = (100)*(1.08)
So, L = 108

K = L/1.21 = 108/1.21 = 89.27
So, K = 89.27

Cost of production = w*L + r*K = (5.45)*(108) + (4.4)*(89.27) = 588.6 + 392.788 = 981.39

Cost of production with factors used in the US = (5.45)*(100) + (4.4)*(100) = 545 + 440 = 985