Cost Functions

QChapter 8, problem #1

You are the manager of a monopoly, and your demand and cost functions are given by P = 300 –

At what price and quantity are firm’s profits maximized?

What are profits given the price and quantity you found in part a?

What is the own price elasticity of demand at the profit-maximizing price and quantity combination?Is demand inelastic, elastic, or unit elastic?

At what price and quantity are the firm’s revenues maximized?

Calculate the maximum revenues (given what you found in part d).

What is the own price elasticity of demand at the revenue-maximizing price and quantity combination?Is demand inelastic, elastic, or unit elastic?

Chapter 8, problem #5

Chapter 8, problem #7

You are the manager of a firm which produces according to the cost function C(Q) = 75+5Q2.Determine the profit maximizing output and price and the level of profits.Discuss what (if anything) will happen to profits in the long run, if:

You are in a perfectly competitive market and price other firms charge is $25.

You are a monopolist and inverse demand for your product is given by P = 250-2.5Q.

You are in a monopolistically competitive market and inverse demand for your product is given by P = 250 – 2.5Q.

Chapter 8, problem #15

2.5Q and C(Q)=1000 + 2.5Q2.

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