Problem 1:

Weekly residential trash hauling is subject to enormous economies of density. Once a single firm is in the neighborhood picking up garbage, it costs very little to pick up refuse from another customer. As a result, collusion among private companies often seeks to divide market areas to maximize monopoly profits. To illustrate the competitive process in markets dominated by few firms, assume that a two-firm duopoly dominates the market for weekly residential trash hauling in Akron, Ohio and that the firms face a linear market demand curve for annual garbage services:

P = 4,000 - 4Q

whereP is price and Q is the number of customers served per year. Thus Q = Q_A + Q_B. For simplicity, also assume that both firms offer an identical service quality, have no fixed costs and variable cost VC_A = $800Q_A and VC_B= $960Q_B, respectively.

a. Derive the output reaction curves (functions) for Firms A and B.

b. Calculate the Cournot market equilibrium price and output solutions for each firm.

c. How much profit will each firm earn at the Cournot equilibrium?

d. How much would each firm produce, what price would each charge and how much profit would each earn if each were to be the sole monopoly seller in the market? (Note: There are 2 outcomes here, one where firm A is the only seller and one where firm B is the only seller).

e. How do the profits compare under the Cournot solution and the two monopoly outcomes?

Rather than the Cournot or monopoly outcomes, suppose that Firm A is the Stackelberg leader in this market. How much will each firm sell and at what price?

Problem 2:

Suppose you are the manager for a firm that has a monopoly on the product you produce and sell. Market research has shown that the demand by a typical customer for the product you sell is given by:

P = $180 - 3Q

Assume you have no fixed costs. From your production department, you are told that the variable costs of production are given by:

VC (Q) = .75Q²

a. If you decide to offer the product for sale to all buyers at a single price, what price will you charge and how much will you sell to a typical customer? 

b. What profits per consumer will the firm earn under this pricing strategy?

c. Now suppose you decide to use a simple block pricing strategy whereby you offer your product as a single package of a predetermined number of units. How much will you sell to a typical customer? (Hint: What is the optimal bundle size?)

d. What price per consumer will the firm charge under this pricing strategy?

e. Compare the profits under the two pricing strategies. Comment on the comparison.