Consider the following short-run production function (where L = variable input, Q = output): Q=6L−0.4L2 Suppose...
Consider the following short-run production function (where L = variable input, Q = output):
Q=6L−0.4L2
Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input (L) as it needs at $20 per unit.
What is the marginal revenue product function (MRPL)?
$20
$60−$8L
$10
$6−$0.40L
What is the marginal factor cost function (MFCLMFCL)?
$6−$0.40L
$60−$8L
$10
$20
What is the optimal value of L, given that the objective is to maximize profits?
_________(calculate the answer) units
Homework Answers
Q = 6L - 0.4L2
(1) (B)
MPL = dQ/dL = 6 - 0.8L
MRPL = MPL x Output price = $10 x (6 - 0.8L) = $60 - $8L
(2) (D)
MFCL = Wage rate = $20
(3) Profit is maximized when MRPL = MFCL
60 - 8L = 20
8L = 40
L = 5
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