Midterm Exam for Practice: Economics 160A

Answer ALL questions. To get credit you need to provide full justification.

1) Suppose there is a single firm producing fire alarms in Santa Cruz. The firm faces the
inverse demand P(Q) = 40 – 0.01Q, where Q is the number of fire alarms sold. The
total cost of the firm is 10Q + 0.005Q2.
a) What is the profit maximizing price and quantity sold? What is the deadweight loss
of monopoly in the fire alarms market of Santa Cruz? (10 Points)
b) Suppose the government imposes a sales tax of t = $9 per fire alarm sold. Write
the profit function of the firm including the sales tax. What is the profit maximizing
price and quantity sold? How much money does the government raise with the
tax? (10 Points)
c) Find the value of sales tax t per fire alarm sold that maximizes the revenue of the
government. (10 Points)
2) Two firms produce “differentiated” bricks in Santa Cruz. We will call them firms 1 and
2. The market demand for firm 1 is 1(1,2) = 30 − 21 + 2. The market demand for
firm 2 is 2(1,2) = 30 − 22 + 1. The marginal cost of the firms is 0. The two firms
compete in prices --- Bertrand competition.
a) What are the equilibrium prices in this market? (10 Points)
b) Suppose that firm 1 is the leader and firm 2 is the follower. What are the equilibrium
prices in this market? (10 Points)
3) Two firms produce apples in Santa Cruz—call them firm 1 and firm 2. Apples produced
by firm 1 are indistinguishable from apples produced by firm 2. The marginal cost of
producing a bushel of apples is 200. The total demand for apples in Santa Cruz is
given by P = 1400 – Q, and the firms compete in quantities, i.e., Cournot competition.
Let q1 and q2 denote the production of apples by the two firms, and Q = q1 + q2.
Assume throughout this problem that the firms have unlimited production capacities
at their marginal cost of 200.
a) What are the equilibrium quantities produced in this market and what is the
equilibrium price for a bushel of apples? (10 Points)
b) Find consumer surplus in part a). (10 Points)
4) Suppose that Billy’s Bulbs has a monopoly on selling light bulbs in Santa Cruz.
Demand for light bulbs is given by P = 20 – Q. Billy’s Bulbs has a marginal cost of 2.
a) What quantity will Billy’s Bulbs sell as a monopolist? What will be the monopoly
price and profits? (10 Points)
b) Now suppose that Laura’s Lights enters the market, also with a marginal cost of 2.
The two firms compete in quantities (i.e., Cournot competition) so that inverse
demand is given by = − −20 B LP q q . Find the Nash Cournot equilibrium quantities
sold by each firm in this market. What are the profits of each firm? (10 Points)
c) Suppose that the entry cost for Laura’s Lights is zero. Also suppose that, before
Laura’s Lights enters the market, Billy’s Bulbs can commit to produce its quantity
Bq . What is the optimal quantity for Billy’s Bulbs to commit to? What are its profits
if it commits to this quantity? (10 Points)

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