# ECON 218 – Derive the output reaction curves (functions) for Firms A

Problem 3: (25points)
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:

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whereP is price and Q is the
number of customers served per year. Thus Q
= QA + QB. For simplicity, also
assume that both firms offer an identical service quality, have no fixed costs
and variable cost VCA =
\$800QA and VCB= \$960QB, 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?
Bonus(not required) (5 Points max):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 4: (25points)
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:

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

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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.

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