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Econ 301

PROBLEM SET 5: Monopoly and Price Discrimination

QUESTION 1:

Let’s say the cost function and the demand function of a monopolistic firm areas follows

C=10+Q2

P=20-Q

(a)What is the price and output this monopolistic firm will produce?

(b)What will be the price and quantity if the government mandated that this monopolist behaves as a perfect competitor (charges price of a perfect competitor and sells quantity of a perfect competitor)?

(c) What is the PS, CS, and total welfare when in perfect competition? Compute the numerical value of PS, CS and TW.

(d)What is the PS, CS, and Total welfare is monopoly? Compute numerical values.

(e)Compute the deadweight loss when you move from perfect competition to monopoly?

(f)If the government sets a price of p=10, what is the new price and quantity?

QUESTION 2: TWO PART TARIFF

Consider the market for a product with two types of potential users: group a and group b. Let’s assume that the population is normalize to 1 and there are 0.5 individuals of group a and 0.5 individuals of group b. Their corresponding demand curves areas follows.

Pa  = 5 − 0.5 ∗ Qa                                                                       Pb   =  10 − Qb

Let this monopolist face a constant MC of  MC=2

(a)What is the optimal (profit-maximizing) two-part tariff that induces both types of consumers to buy?

(b)What is the optimal two part tariff when only high demand consumers purchase the good?

(c) Which of the pricing schemes yields a higher total profit?

(d) Re-do a-b-c and determine which pricing scheme yields to a higher total profit is there are 0.75 individuals of group a and 0.25 individuals of group b.

QUESTION 3: FIRST DEGREE PRICE DISTRIMINATION

A monopolist has the following demand curve and total cost functions

P=30-Q

C = Q2  + 100

(a)Find the Quantity that the monopolist sells under first degree price discrimination

(b)What is the price that this monopolist would charge for the last unitsold?

(c)What is the CS and the PS?

QUESTION 4:THIRD DEGREE PRICE DISCRIMINATION

There are two types of consumers and the monopolist can tell them apart. Q1 represents the demand function for the entire group 1 and Q2 represents the demand function for the entire group 2

Q1  = 300 − 10P1

Q2  = 100 − 5P2

The total cost function is

TC = 1000 + 10Q

(a) What price does this firm charge to each group?

(b) If the government forces this firm to charge the same price to all customers, what would that price be?

QUESTION 5: TWO PART TARIFF

Consider the market for a product with two types of potential users: group a and group b. Let’s assume now that the following represent the demand for every individual in group a and b, respectively. There are 10 individuals of type a and 5 individuals of type b

Pa  = 5 − 0.5 ∗ Qa                                                                       Pb   =  10 − Qb

Let this monopolist face a constant MC of  MC=2

(a)What is the optimal (profit-maximizing) two-part tariff that induces both types of consumers to buy?

(b)What is the optimal two part tariff when only high demand consumers purchase the good?

(c) Which of the pricing schemes yields a higher total profit?