1. Let the demand for rides at an amusement park equals Q = 40 - P and the marginal cost of production equal a constant $10. Assume that there are no fixed costs so that average total costs are also a constant $10. Assume that the producer is a monopolist.
a. Suppose the monopolist charges a fee per ride but not an entrance fee. How much should the monopolist charge per ride? What will be the monopolist's profits?
b. Suppose the monopolist can charge both an entrance fee and a per ride fee. How much should the monopolist charge for the entrance fee? How much should the monopolist charge for the per ride fee? What will be the monopolist's profits?
c. Suppose that marginal cost of production is not constant but instead MC = Q. For example the marginal cost of producing the first unit is $1, the marginal cost of producing the second unit is $2, etc. How much should the monopolist charge for the per ride fee?
2. Assume that the demand for a product equals Q = 40 - P and the marginal cost of production equals a constant $10. Assume that there are no fixed costs so that average total costs are also a constant $10. Rather than charge a single-price, assume that the monopolist charges two prices; a high price for the first units (or block) purchased and a lower price for subsequent purchases.
a. How much should the monopolist charge for the first block? What will be the quantity purchased?
b. How much should the monopolist charge for subsequent purchases? What will be the quantity purchased?
c. What will be the monopolist's profits under block pricing? Compare the profits under block pricing with the profits of a single-price monopolist.
3. Assume that a monopolist has two types of customers: type A and type B. Type A customers have a demand of P = 16 - Q and type B have a demand of P = 8 - Q. The marginal cost of production is a constant $4 and there are no fixed costs. Suppose the monopolist can charge different prices to the two groups.
a. What price should the monopolist charge to type A customers?
b. What price should the monopolist charge to type B customers?
c. What will be the monopolist's profits?
d. Bonus. Suppose the monopolist cannot price discriminate and must sell at the same price to both groups. What price will the monopolist charge?
4. Suppose the market for cable TV consists of three customers who have the following reservation prices:
Reservation Price
Customer A Customer B Customer C
Sports Channel 200 30 100
Disney Channel 50 150 100
Assume that the marginal cost of production is $40 per channel per customer. Assume that there are no fixed costs.
a. Suppose the cable channels are sold separately. What price should the cable company charge for the sports channel? What price should it charge for the Disney channel? (Assume that the cable company cannot price discriminate; i.e. it has to charge each customer the same price for a given channel). What will be its profits?
b. Suppose the channels are sold as a bundle. What price will the cable company charge for the bundle? What will be its profits?
c. Suppose the cable company uses a mixed bundling strategy. What price will the cable company charge for each channel? What price will it charge for the bundle? What will be its profits?
5. Suppose the demand curve for razors is equal to Q = 10 - P. Gillette is the dominant firm in the industry and has constant marginal costs equal to 3. There are also a number of smaller competitors. The supply curve of the competitors, known as the fringe, is equal to QF = P - 4.
a. Sketch Gillette's residual demand curve.
b. How many razors should Gillett produce? What price will it charge?
c. How many razors will the fringe produce?
d. How much profits will Gillette make, assuming that it has no fixed costs?
6. Suppose there are two firms in an industry, Boeing and Airbus. The demand for aircraft equals P = 12 - Q. Both firms have constant marginal costs equal to 6 and no fixed costs.
a. Draw the Cournot reaction function for both Boeing and Airbus. Place Airbus' quantity on the vertical axis and Boeing's quantity on the horizontal axis.
b. Solve for the Cournot equilibrium quantity and price.
c. Assume instead that this is an industry with three firms, all with a constant marginal cost equal to 6. Solve for to the Cournot equilibrium quantity and price.