d) Consider a demand curve given by P = AQ 0.25 where P and Q represent price and quantity demanded respectively, and A is a positive constant. Show that the price elasticity of demand is constant, for all values of A, and is always equal to 4. Find the marginal revenue function and sketch the demand curve and its associated marginal revenue curve.

Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter3: Benefits, Costs, And Decisions
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d) Consider a demand curve given by P = AQ 0.25 where Pand Q represent price and quantity
demanded respectively, and A is a positive constant. Show that the price elasticity of
demand is constant, for all values of A, and is always equal to 4. Find the marginal revenue
function and sketch the demand curve and its associated marginal revenue curve.
Transcribed Image Text:d) Consider a demand curve given by P = AQ 0.25 where Pand Q represent price and quantity demanded respectively, and A is a positive constant. Show that the price elasticity of demand is constant, for all values of A, and is always equal to 4. Find the marginal revenue function and sketch the demand curve and its associated marginal revenue curve.
a) If a business has a long-run cost (TC) function given by
TC = aq^3 - bq^2 + ca
%3D
where q = the rate of output, and a, b and c are all positive parameters, show that
average cost is always positive if and only if b^2 < 4ac and a >0.
Transcribed Image Text:a) If a business has a long-run cost (TC) function given by TC = aq^3 - bq^2 + ca %3D where q = the rate of output, and a, b and c are all positive parameters, show that average cost is always positive if and only if b^2 < 4ac and a >0.
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