Consider a competitive firm that has the cost function, TC(Q) and faces the demand P = P(Q), that is, the inverse demand function with price as a function of quantity. Write down the profit function of the firm.Show that the MR=P(1+1ϵd)MR=P(1+1ϵd)Show that ϵd=PMR−Pϵd=PMR−P.Assuming a linear demand function, P=a−bQP=a−bQ, find the MR function.Draw both the demand and the MR curves. Using the expression ϵd=PMR−Pϵd=PMR−P, locate the point on the demand curve where ϵd=1ϵd=1. Also, indicate the regions where the demand is inelastic and elastic.Please try to type your answers and mathematical equations using the icon as highlighted in the following image.

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider a competitive firm that has the cost function, TC(Q) and faces the demand P = P(Q), that is, the inverse demand function with price as a function of quantity.

Write down the profit function of the firm.
Show that the MR=P(1+1ϵd)MR=P(1+1ϵd)
Show that ϵd=PMR−Pϵd=PMR−P.
Assuming a linear demand function, P=a−bQP=a−bQ, find the MR function.
Draw both the demand and the MR curves. Using the expression ϵd=PMR−Pϵd=PMR−P, locate the point on the demand curve where ϵd=1ϵd=1. Also, indicate the regions where the demand is inelastic and elastic.

Please try to type your answers and mathematical equations using the icon as highlighted in the following image.

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