2a. Parte (70%)
1. All consumers have identical demand for a product. Each person's demand curve is P = 30 – 2Q. The marginal cost of production is $2. Devise a two-part tariff that will exhaust all consumer surplus.
The company could charge marginal cost of $2 and an up-front fee equal to the consumersurplus. At a $2 price, the quantity sold is 14. Consumer surplus is equal to the area of the triangle below the demand curve, but above marginal cost (see Figure 7.5). The resulting up-front charge is $196.
2. Cellwave is a cellular phone company. Answer the following questions relating to its pricing policies:
a. When Cellwave started out it sold to a group of homogenous retailcustomers. Each person’s monthly demand for cell phone minutes was given by P = $2 - .02Q, where P = the price per minute and Q = the quantity of minutes purchased each month. Cellwave’s marginal cost is 10 cents per minute. Suppose that Cellwave charges a single per minute price to all customers (independent of the number of minutes they use each month). What is the profit-maximizing price? Depict thischoice on a graph. On a per customer basis, what are the company’s profit, consumer surplus, and the deadweight loss?
Optimal quantity is where MR = MC: 2 - .04Q = .10; Q* = 47.5 minutes; P* = $1.05 per minute;
Per customer basis: profit = ($1.05-.10) × 47.5 = $45.125; Consumer surplus = ½ × 47.5 × (2-1.05) = $22.56; DWL = ½ × (95 – 47.5) × (1.05 -.10) =22.56;
b. Suppose thatCellwave chooses to charge a two-part tariff (with a monthly fixed charge and a per minute rate) rather than a single per minute price. What two-part tariff extracts the entire consumer surplus? What are the company’s profits (on a per customer basis)? How many minutes does each customer use per month? What is the deadweight loss?
The optimal two-part tariff will charge 10 cents/minute (the marginalcost) and an upfront fee equal to the entire consumer surplus = ½ × (2-.10) × 95 = $90.25. The profits are $90.25 per customer. Each consumer uses 95 minutes per month and there is no deadweight loss.
c. After several years of operation, Cellwave developed a new group of business customers (in addition to its old customer base). The business customers had homogenous demands. Each of thesecustomer’s monthly demand for cell phone minutes was given by P = $2 - .004Q. Graph the two demand curves for the two customer groups on the same figure along with the marginal cost. Suppose that Cellwave wants to menu price by offering two plans with different monthly fixed charges. Each plan would allow free calls up to some maximum limit of minutes per month. No calls are allowed beyond thesemaximums. Assume that Cellwave designs a plan that extracts all consumer surplus from the retail customers. Shade the area of the graph that shows how much consumer surplus must be given to each business customer to make the plan work. Explain why.
Each business customer must get at least the area of the abc triangle as consumer surplus or he will not buy the high-end plan. This is the surplus thathe would receive if he purchases the low end plan. If the high-end plan is priced too high, he will buy the low-end plan instead and the menu plan will not work.
3. Candak Corporation produces professional quality digital cameras. The market for professional digital cameras is monopolistically competitive. Assume that the inverse demand curve faced by Candak (given its competitors’ prices)can be expressed as P = 5,000 - .2Q and Candak’s total costs can be expressed as TC = 20,000,000 + .05Q2. Answer the following questions.
d. What price and quantity will Candak choose?
To find the optimal price and quantity, we set marginal revenue equal to marginal cost. Marginal revenue equals 5000 - .4Q (the derivative of total revenue) and marginal cost equals .1Q (the derivative of...