You and your friend Casey N. have just stared a new firm manufacturing electric longboards and are now confronted by your company's long-run options for production. You need to build a production facility and you need to choose between two locations: Ohio or Mississippi. a. Given the available technology, your firm's production function will be q = 2Lª Kb, regardless of where the production facility is located. Find an expression for your firm's MRTS. Explain what the MRTS means in as plain language as possible. b. Use whatever method you prefer to find expressions for the cost minimizing levels of L* and K*. Use your results to write out the firm's long-run cost function [C(w,r, q)]. 를 c. Suppose a = 1, b = regardless of where you locate the plant. If the firm locates in Ohio, the firm will have to pay a wage, w = $64, and a cost of capital of r = $100. If it locates the plant in Mississippi it would have to pay lower wages, w = $36, but the cost of capital would be higher, r = $121. Given the firm expects to produce 1000 units of output regardless of the location chosen, what are the cost minimizing Land K (it is fine to have fractional units of labor and capital) for each location, and in which country can the firm produce at the lowest cost?
You and your friend Casey N. have just stared a new firm manufacturing electric longboards and are now confronted by your company's long-run options for production. You need to build a production facility and you need to choose between two locations: Ohio or Mississippi. a. Given the available technology, your firm's production function will be q = 2Lª Kb, regardless of where the production facility is located. Find an expression for your firm's MRTS. Explain what the MRTS means in as plain language as possible. b. Use whatever method you prefer to find expressions for the cost minimizing levels of L* and K*. Use your results to write out the firm's long-run cost function [C(w,r, q)]. 를 c. Suppose a = 1, b = regardless of where you locate the plant. If the firm locates in Ohio, the firm will have to pay a wage, w = $64, and a cost of capital of r = $100. If it locates the plant in Mississippi it would have to pay lower wages, w = $36, but the cost of capital would be higher, r = $121. Given the firm expects to produce 1000 units of output regardless of the location chosen, what are the cost minimizing Land K (it is fine to have fractional units of labor and capital) for each location, and in which country can the firm produce at the lowest cost?
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.1P
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![1. You and your friend Casey N. have just stared a new firm manufacturing electric longboards and are now confronted
by your company's long-run options for production. You need to build a production facility and you need to choose
between two locations: Ohio or Mississippi.
=
a. Given the available technology, your firm's production function will be q 2Lª K¹, regardless of where the
production facility is located. Find an expression for your firm's MRTS. Explain what the MRTS means in as plain
language as possible.
b. Use whatever method you prefer to find expressions for the cost minimizing levels of L* and K*. Use your results
to write out the firm's long-run cost function [C(w, r,q)].
2
c. Suppose α = 11/1, b = 1/1/2
, b = regardless of where you locate the plant. If the firm locates in Ohio, the firm will have to
pay a wage, w = $64, and a cost of capital of r = $100. If it locates the plant in Mississippi it would have to pay
lower wages, w = $36, but the cost of capital would be higher, r = $121. Given the firm expects to produce 1000
units of output regardless of the location chosen, what are the cost minimizing L and K (it is fine to have
fractional units of labor and capital) for each location, and in which country can the firm produce at the lowest
cost?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad5f8718-b822-43a6-888a-6d9b997f8030%2F5f16bca2-9033-469e-b375-76cf0ecfbd15%2F3prdwc1_processed.png&w=3840&q=75)
Transcribed Image Text:1. You and your friend Casey N. have just stared a new firm manufacturing electric longboards and are now confronted
by your company's long-run options for production. You need to build a production facility and you need to choose
between two locations: Ohio or Mississippi.
=
a. Given the available technology, your firm's production function will be q 2Lª K¹, regardless of where the
production facility is located. Find an expression for your firm's MRTS. Explain what the MRTS means in as plain
language as possible.
b. Use whatever method you prefer to find expressions for the cost minimizing levels of L* and K*. Use your results
to write out the firm's long-run cost function [C(w, r,q)].
2
c. Suppose α = 11/1, b = 1/1/2
, b = regardless of where you locate the plant. If the firm locates in Ohio, the firm will have to
pay a wage, w = $64, and a cost of capital of r = $100. If it locates the plant in Mississippi it would have to pay
lower wages, w = $36, but the cost of capital would be higher, r = $121. Given the firm expects to produce 1000
units of output regardless of the location chosen, what are the cost minimizing L and K (it is fine to have
fractional units of labor and capital) for each location, and in which country can the firm produce at the lowest
cost?
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