# Solutions ```Econ 101 Discussion Section - Handout #12, November 20th
TA Name:
Price discrimination:
Orange, the monopoly firm in computer market having a constant marginal cost 30. There
are two types of consumer in the market, corporate user and personal user. The demand
curves are given by the following equations
Corporate users: Q = 50 – P/3
Personal users: Q = 110 – P
(a) Suppose Orange can implement third degree price discrimination. Derive the profit
maximization prices, consumer surplus and Orange’s profit.
(b) Derive the aggregated market demand. Then, derive the profit maximization price,
consumer surplus and Orange’s profit.
Game theory:
Orange and Wizards are two big companies in computer market competing each other.
Recently they announce to release their new operating systems called Penguin and
Wizards 10 and they need to set the prices simultaneously. To make the argument simple,
let us assume they have only two choices high price or low price. If both of them set high
price, they both earns \$10,000 and if one of them set low price while other one set high
price, the firm with high price completely lose the market share and earns \$0. At the same
time the firm with low price receives \$15,000. Finally, if both of them set low price, the
both earns \$6,000.
(a) Complete the payoff matrix below.
Orange \ Wizard
H
L
H
L
(b) Find the dominant strategy and the set of equilibrium prices under rationality
assumption.
Natural monopoly:
Consider the monopolistic company in a car market Toyotaka. The Toyotaka’s variable
cost and marginal cost are given by VC = 10q and MC = 10. In addition to that, Toyotaka
needs to build a plant in order to operate. Building a plant costs the firm 7000.
(a) Derive the total cost for the firm. Does the technology of the firm exhibit economy of
scale?
The demand curve for car is given by Q = 210 – P.
(b) Derive MR and find monopoly price, quantity and profit Find the price, quantity and
profit under marginal cost regulation. The marginal cost regulation is the regulation
under which the firm charges price equal to average marginal cost.
Extension question
There is a potential entrant Honjyo that has exactly the same production technology. If
Honjyo enters the market, demand is equally spit so that Honjyo faces demand given by Q
= 105 – 0.5p. After entering the market Honjyo act as a monopolist over its demand.
(c) Derive MR and find monopoly price, quantity and profit. Will Honjyo enter the
market?
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