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Profit-Maximization

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Hi,

You are the manger of a monopoly that sells a product to two groups of consumers in different parts of the country. Group 1's elasticity of demand is -2, while group 2's elasticity of demand is -6. Your marginal cost of producing the product is $10.

a) Determine your optimal markups and prices under third degree price discrimination.
b) Discuss the conditions under which third degree price discrimination enhances profits.

A monopolist can produce at a constant average (and marginal) cost of AC = MC = 5. It faces a market demand curve given by Q= 53-P.

a) Calculate the profit -maximizing price and quantity for this monopolist. Also calculate its profit.
b) Suppose a second firm enters the market. Let Q1 be the output of the first firm and Q2 be the output of the second. Market demand is now given by Q1 + Q2 =53-P. Derive the Cournot equilibrium quantities. What are the resulting market price and profits for each firm?
c) Suppose there are N firms in the industry, all with the same constant marginal cost, MC=5. Find the Cournot equilibrium. How much will each firm produce, what will be the market price, and how much profit will each firm earn? Also, show that as N becomes large the market price approaches the price that would prevail under perfect competition

Thanks,

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Solution Summary

This solution provides a detailed tutorial that explains how to solve the given economics questions regarding profit maximization.

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1. The markup rule is as follows

P = (ε/(1+ε))MC, where MC is marginal cost, P is optimal price that maximizes profit and ε is price elasticity of demand.

By this rule, for group 1, price should be P = (-2/-1)10 = 20

For group 2, P = (-6/-5)10 = 12.

When does third degree price discrimination work? The following conditions are necessary:

- The firm must have market control (i.e. they must be a leader in the industry, not a price taker)

- They must be able to differentiate buyers. The seller must be able to figure out who are their buyers, and what their ...

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