A Monopolist Can Produce Any Amount of Output at a Constant Marginal Cost of 4 Per Unit

1.A monopolist can produce any amount of output at a constant marginal cost of 4 per unit. The demand for the product is:

YD = 40 - 4·P

a.If the monopolist must set a uniform price for all customers and quantities, what is his profit maximizing price and output?

b.Suppose the monopolist finds that he has 2 types of customers, dumb and dumber. By treating his customers separately, he finds that the dumb customers have a demand for his product

YD = 20 - P

and the dumber have demand function YD = 20 - 3·P. (These two demand functions add up to the demand function given earlier.) If the monopolist can set different prices for the dumb than he does for the dumber, what prices does he charge to each?

c.By how much do profits rise when the monopolist gains the ability to price discriminate?

2.A monopolist can produce any amount of output at a constant marginal cost of 2 per unit. The demand for the product is:

YD = 40/P2

a.If the monopolist must set a uniform price for all customers and quantities, what is his profit maximizing price and output?

b.Suppose the monopolist finds that he has 2 types of customers, dumb and dumber. By treating his customers separately, he finds that the dumb customers have a demand for his product

YD = 10/P2

and the dumber have demand function YD = 30/P2.

(These two demand functions add up to the demand function given earlier.) If the monopolist can set different prices for the dumb than he does for the dumber, what prices does he charge to each?

c.By how much do profits rise when the monopolist gains the ability to price discriminate?

3.Suppose a monopolist starts off facing a demand curve YD = 40 - 4·P, and the monopolist can produce at a marginal cost MC = (1/2)·Y.

a.What is the profit maximizing price and quantity?

b.Suppose the monopolist establishes a new market (new customers) for his product. The new customers have a demand function YD = 20 - 4·P. What price will the monopolist want to charge his two sets of customers? (Keep in mind that the monopolist's marginal cost will change once she begins selling to these new customers.)

c.Suppose the monopolist is prohibited from price discrimination, and must sell all units to any customer at the same price. What would be the new price and quantity?

d.How much profit does the monopolist lose when he loses the ability to price discriminate?

4.Suppose a monopolist starts off facing a demand curve YD = 40 - 4·P, and the monopolist can produce at a marginal cost MC = (1/2)·Y.

a.What is the consumer's surplus when the monopolist charges the monopoly price and quantity?

b.What is the consumer's surplus if the monopolist produces so that price is equal to marginal cost?

c.Suppose the monopolist can charge the consumer a fee for the right to purchase goods (in addition to the price per unit). If the monopolist charges the monopoly price per unit, what price could he charge.

d.Suppose the monopolist can charge the consumer a fee for the right to purchase goods (in addition to the price per unit). If the monopolist charges the competitive price per unit, what price could he charge.

e.Would the monopolist prefer to charge the fee + monopoly price as in (c) or the fee + competitive price as in (d)? Explain. (3 words are sufficient.)