Consider a firm that employs capital (K) and labour (L) and uses the production technology Q = 3K + 4L. Let factor prices be r = $40 for capital and w = $20 for labour. a) What is the firm’s minimization problem? b) Plot the isoquant for Q =100. What is the Marginal Rate of Technical Substitution (MRTS)? c) For any output Q, what is the optimal combination of K and L given the input prices? Hint
Consider a firm that employs capital (K) and labour (L) and uses the production technology Q = 3K + 4L. Let factor prices be r = $40 for capital and w = $20 for labour. a) What is the firm’s minimization problem? b) Plot the isoquant for Q =100. What is the Marginal Rate of Technical Substitution (MRTS)? c) For any output Q, what is the optimal combination of K and L given the input prices? Hint
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.10P
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Consider a firm that employs capital (K) and labour (L) and uses the production technology Q = 3K + 4L. Let factor prices be r = $40 for capital and w = $20 for labour.
a) What is the firm’s minimization problem?
b) Plot the isoquant for Q =100. What is the Marginal Rate of Technical Substitution (MRTS)?
c) For any output Q, what is the optimal combination of K and L given the input prices? Hint
set MRTS = r/w and solve for L)
d) What is the cost function? Confirm C(Q=100) = 500
e) Given the above, what must the supply curve look like in long-run equilibrium?
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