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
\[ C = qw^{2/3}v^{1/3} \]
where \( w \) and \( v \) 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 \( l \) and \( k \) (as functions of \( q, v, w \)) [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
\[ C = qw^{2/3}v^{1/3} \]
where \( w \) and \( v \) 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 \( l \) and \( k \) (as functions of \( q, v, w \)) [Hint: Partially differentiate \( C \) with respect to input price]
![(b) Use the results in (a) to find the underlying production function of \( q \) [Hint: Eliminate the ratio of input prices, \( w/v \), from your answer in (a) so you get \( q \) as a function of \( l \) 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: Eliminate the ratio of input prices, \( w/v \), from your answer in (a) so you get \( q \) as a function of \( l \) and \( k \)]
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