A monopoly faces market demand Q=30-P and has a cost …



Econ 101 - Spring 2003

PS #8 - XtraQ

DUE: Thursday April 24

A monopolist faces the following market demand for his monopolized product: XD=30-P

The monopolist has the following short run total cost function: srtc(X)=X2/2.

Note: This implies that the monopolist's marginal cost function is: srmc(X)=X

a. Assume that the monopolist behaves as a simple monopolist. Find the profit maximizing price and quantity and the resulting profit to the monopolist. Show your answer in a diagram.

b. Calculate the own price elasticity of the demand at the profit-maximizing price.

c. Calculate consumers' surplus (CS) and producer's surplus (PS). Show CS and PS on the diagram.

d. Assume that the government puts a price ceiling on the monopolist at Pceiling=$18. How much output will the monopolist produce? What will be the profit of the monopolist? Calculate the CS, PS in this case.

e. Instead of the price ceiling, now suppose that the government charges the monopoly a $130 business fee. The monopolist must pay this fee if he wishes to operate. Find the profit maximizing price and quantity and the resulting profits to the monopoly.

f. What is the allocatively efficient level of output for this monopoly?

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