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1. Suppose that the demand for pizza is given by Qd = 100 - 2P, where Qd is the
quantity demanded in slices per day and P is the price in dollars per slice. The supply
of pizza is given by Qs = 50 + 4P, where Qs is the quantity supplied in slices per day.
What is the equilibrium price and quantity of pizza in this market?
a) P = $5, Q = 70
b) P = $10, Q = 40
c) P = $7.5, Q = 55
d) P = $12.5, Q = 25
Answer: c) P = $7.5, Q = 55
Rationale: The equilibrium occurs where Qd = Qs, so we can set the two equations
equal to each other and solve for P: 100 - 2P = 50 + 4P, which implies P = $7.5. Then
we can plug this value into either equation to get Q: Qd = 100 - 2(7.5) = 55 or Qs = 50
+ 4(7.5) = 55.
2. Consider a market with two firms, A and B, that produce a homogeneous good. The
inverse demand function for the good is P = 120 - Q, where P is the price in dollars per
unit and Q is the total quantity in units. The marginal cost of production for each firm is
constant and equal to $20 per unit. Assume that the firms compete as Cournot
duopolists, i.e., they choose their quantities simultaneously and independently. What is
the profit-maximizing quantity for firm A?
a) QA = 20
b) QA = 25
c) QA = 30
d) QA = 35
Answer: b) QA = 25
Rationale: The profit function for firm A is given by πA = (P - MC)QA = (120 - QA - QB -
20)QA, where QB is the quantity chosen by firm B. To maximize profit, firm A sets its
marginal revenue equal to its marginal cost: MR = MC, which implies (120 - 2QA - QB)
= 20, or QA = 50 - (1/2)QB. Similarly, the profit-maximizing condition for firm B is QB =
50 - (1/2)QA. Solving these two equations simultaneously gives QA = QB = 25.
3. Suppose that a monopolist faces a linear inverse demand function P(Q) = a - bQ,
where P is the price in dollars per unit and Q is the quantity in units. The monopolist
has a constant marginal cost of c dollars per unit and no fixed cost. What is the
deadweight loss caused by the monopoly pricing compared to the socially optimal
pricing?
a) DWL = (a - c)^2 / (8b)
b) DWL = (a - c)^2 / (4b)
c) DWL = (a - c)^2 / (2b)
d) DWL = (a - c)^2 / b
Answer: a) DWL = (a - c)^2 / (8b)
Rationale: The monopoly quantity is determined by setting marginal revenue equal to
marginal cost: MR(Q) = MC(Q), which implies a - 2bQ = c, or QM = (a - c) / (2b). The
monopoly price is then PM = a - bQM = a - b(a - c) / (2b) =
(a + c) / 2. The socially optimal quantity is determined by setting price equal to
marginal cost: P(Q) =
MC(Q), which implies a - bQ* = c, or Q* =
(a - c) / b. The socially optimal price is then P* =
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