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**

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