2. Suppose the total cost function for a firm is given by C =qw2/31/3 where w and u are prices of a unit of labor and capital, and q is output (a) Use Shephard's lemma to compute the demand functions for each input 7 and k (as functions of q, v, w) [Hint: Partially differentiate C with respect to input price]
2. Suppose the total cost function for a firm is given by C =qw2/31/3 where w and u are prices of a unit of labor and capital, and q is output (a) Use Shephard's lemma to compute the demand functions for each input 7 and k (as functions of q, v, w) [Hint: Partially differentiate C with respect to input price]
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Only part b) please, thank you!
![2. Suppose the total cost function for a firm is given by
C =qw2/31/3
where wand v are prices of a unit of labor and capital, and q is output
(a) Use Shephard's lemma to compute the demand functions for each input 7 and
k (as functions of q, u, w) [Hint: Partially differentiate C with respect to input
price]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3585354-64d7-4f4a-b055-4a9b75b3799d%2F70c4d51d-c899-4205-8464-8ddb835713b1%2F69g6l7p_processed.png&w=3840&q=75)
Transcribed Image Text:2. Suppose the total cost function for a firm is given by
C =qw2/31/3
where wand v are prices of a unit of labor and capital, and q is output
(a) Use Shephard's lemma to compute the demand functions for each input 7 and
k (as functions of q, u, w) [Hint: Partially differentiate C with respect to input
price]
![(b) Use the results in (a) to find the underlying production function of q [Hint: Elim-
inate the ratio of input prices, w/v, from your answer in (a) so you get q as a
function of 1 and k]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3585354-64d7-4f4a-b055-4a9b75b3799d%2F70c4d51d-c899-4205-8464-8ddb835713b1%2Faiav76_processed.png&w=3840&q=75)
Transcribed Image Text:(b) Use the results in (a) to find the underlying production function of q [Hint: Elim-
inate the ratio of input prices, w/v, from your answer in (a) so you get q as a
function of 1 and k]
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