Question

A U.S. electronics manufacturer is considering moving its production abroad. Suppose its production function is: q=L^0.6K^0.4

In the United States, w=$6 and r =4. In Mexico, the wage is 40% lower than in the United States but the firm faces the same cost of capital: w*=$3.60 and r*=4

What are L and K and what is the cost of producing q=100 units in both countries? (for all the following questions, enter a numeric response using a real number rounded to two decimal places)

In the U.S., L is _, K is _, and the cost of production is $_

In Mexico, L is _, K is _, and the cost of production is $_

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

The cost of production would be $_

Answer 1

Least cost combination is determined at the point where MRTS = w/r
MRTS = MPL/MPK
MPL =

MPK =

So, MRTS =

United States
MRTS = w/r gives,
3K/2L = 6/4 = 3/2
So, K = L
q = 100 = L^0.6K^0.4 = L^0.6L^0.4 = L^0.6+0.4 = L
So, L = 100 = K
Cost = wL + rK = 6(100) + 4(100) = 600 + 400 = 1000

Mexico
MRTS = w*/r*
3K/2L = 3.6/4 = 36/40 = 9/10
So, K = (9/10)*(2L/3) = 0.6L
q = 100 = L^0.6K^0.4 = L^0.6(0.6L)^0.4 = (0.6)^0.4L^0.6+0.4 = 0.82L
So, L = 100/0.82 = 121.95
K = 0.6L = 0.6(121.95) = 73.17
Cost = w*L + r*K = (3.6)(121.95) + 4(73.17) = 439.02 + 292.68 = 731.7

Cost if firm had to use the same factor quantities as the United States = w*L + r*K = (3.6)(100) + 4(100) = 360 + 400 = 760

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

In Mexico, L is 121.95, K is 73.17, and the cost of production is $731.7