HW15_sol - Intermediate Microeconomics Winter 2008 Problem...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Intermediate Microeconomics, Winter 2008 Problem Set No 15 Solutions Q1. Suppose a monopolist faces a demand function D ( p ) = 100 - Ap and suppose costs are c . If A = 5 and c = 2, find the optimal quantity and the optimal price that the monopolist will set. Find the optimal price and the optimal quantity as a function of general A and c . In order to write profit as a function of quantity only, we need to find the inverse demand function faced by the monopolist. The demand function is q = 100 - Ap , so, solving for p , the inverse demand function is p ( q ) = 100 A - q A . The monopolist’s problem is to choose q to maximize π ( q ). max q π ( q ) max q q * p ( q ) - C ( q ) max q q * ( 100 A - q A ) - cq We can confirm that profit is a concave function of q , and therefore the maximum is attained where: π 0 ( q ) = 0 100 A - 2 q A - c = 0 2 q A = 100 A - c 2 q = 100 - Ac q = 50 - Ac 2 Plugging in A = 5 and c = 2, we get q = 45. Q2. Suppose the demand function for AA and UA for flights between Chicago and Detroit is D ( p ) = 100 - Ap . If AA and UA each choose to supply a quantity of 30, what will be the price? If UA chooses a supply of q UA =30, what will be the price as a function of the quantity that AA supplies? Given the choice q UA = 30, and given constant marginal costs c = 1, what is the optimal supply of AA? (You might want to choose
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 3

HW15_sol - Intermediate Microeconomics Winter 2008 Problem...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online