Q1 A firm is facing the following cost function C(Q) = AQ5/4 where A is a positive constant and Q is the quantity. The profit function is of the form II=PQ-C(Q) where P is the price. a) Express the profit-maximising price as a function of quantity. b) Invert the price function and explain what the economic meaning of the inverted function is. c) Assume that the firm is facing a production capacity constraint (K) such that we have: 0 ≤ Q≤ K. Explain how much the firm should produce and, if necessary, include any relevant conditions that need to be satisfied. Explain how your answer changes as A increases.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
ChapterB: Differential Calculus Techniques In Management
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Q1
a)
b)
A firm is facing the following cost function
C(Q) = AQ5/4
where A is a positive constant and Q is the quantity. The profit function is of the form
II = PQ-C(Q)
where P is the price.
Express the profit-maximising price as a function of quantity.
Invert the price function and explain what the economic meaning of the inverted
function is.
c) Assume that the firm is facing a production capacity constraint (K) such that we have:
0 ≤ Q≤ K. Explain how much the firm should produce and, if necessary, include any
relevant conditions that need to be satisfied. Explain how your answer changes as A
increases.
Transcribed Image Text:Q1 a) b) A firm is facing the following cost function C(Q) = AQ5/4 where A is a positive constant and Q is the quantity. The profit function is of the form II = PQ-C(Q) where P is the price. Express the profit-maximising price as a function of quantity. Invert the price function and explain what the economic meaning of the inverted function is. c) Assume that the firm is facing a production capacity constraint (K) such that we have: 0 ≤ Q≤ K. Explain how much the firm should produce and, if necessary, include any relevant conditions that need to be satisfied. Explain how your answer changes as A increases.
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