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2. Assume the inverse demand for commercial airplanes is P = 200 – Q, where P is the market price and
Q is the total market quantity. Q = qA + qB, where qA is the number of airplanes produced by Ai
us
and qB is the number of airplanes produced by Boeing. In the absence of any subsidies (see below),
Ai
us and Boeing each have constant marginal costs of 80 and no fixed costs.
However, the EU (where Ai
us is headquartered) and the US (where Boeing is headquartered) have
the option to subsidize their respective airplane manufacturing industries. Define sA as the per-unit
subsidy that the EU provides to Ai
us, and sB as the per-unit subsidy that the US provides to Boeing.
With subsidies sA and sB, Ai
us’s marginal cost is (80 – sA), and Boeing’s marginal cost is (80 – sB).
a. If Ai
us and Boeing compete according to the assumptions of the Cournot model, choosing their
output simultaneously and noncooperatively, and treating their rival’s output as fixed,
how many commercial airplanes will each firm produce in equili
ium? (8 points)
You must show your work for full credit.
Note: Your answer to this question should be two functions: qA*(sA, sB) and qB*(sA, sB).
Note the arguments in those functions – if you have qA(qB, sA) and qB(qA, sB), you aren’t done yet!
b. Given your answers to part a, find both !"!
∗
!#!
and !"!
∗
!##
and explain (in words) what each means.
(4 points)
c. If the EU provides a per-unit subsidy of sA to Ai
us,
and the US provides a per-unit subsidy of sB to Boeing,
Total Welfare in the EU (TWEU) is given by the formula
TWEU(sA, sB) = !$%" [14,400 − 2*&
' + 120*& − *&*( − 240*( + *('].
Similarly, Total Welfare in the US (TWUS) is given by the formula
TWUS(sA, sB) = !$%" [14,400 − 2*(
' + 120*( − *&*( − 240*& + *&'].
Assume that the EU and the US compete in “Cournot-like” fashion. That is, assume that the EU
and the US choose their subsidies (sA and sB, respectively) simultaneously and noncooperatively,
treating their rival’s subsidy as fixed, each attempting to maximize their own Total Welfare.
Derive the equili
ium (numerical) values of sA* and sB*. (4 points)
d. Do the EU and the US generate more Total Welfare by choosing sA* and sB* from part c, or
y choosing sA = sB = 0? Justify your answer numerically, and explain (in words) why this is true,
using appropriate economics vocabulary. (4 points)
it
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3. Each identical firm in a perfectly competitive market has the same cost function: C(q) = 4q XXXXXXXXXX.
The MARKET demand curve for the product that these firms produce is Q = 1200 – P.
a. What is each firm’s equili
ium price (P*) and quantity (q*) in a long-run equili
ium?
(4 points)
. What is the MARKET equili
ium price (P*) and quantity (Q*) in a long-run equili
ium?
(3 points)
c. How many identical firms are in this market in a long-run equili
ium? (2 points)
d. Use two diagrams to clearly illustrate your answers to parts a and b. Clearly indicate the values
of P*, Q*, and q* from parts a and b in appropriate places on these diagrams. (6 points)
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4. In class, we compared two policies to help farmers: “old school” agricultural price supports and
“new school” deficiency payments. A third option might be to subsidize agricultural commodities.
Consider the market for cotton. The inverse demand curve for cotton is P = 100 – Q, where P is the
price for a bale of cotton and Q is thousands of bales. The inverse supply curve for cotton is P = Q.
a. What is the market equili
ium price and quantity of cotton? (2 points)
b. Suppose the government offered to support a price of $60 per bale with a deficiency payment.
That is, cotton producers can sell as much cotton as they want for whatever price consumers are
willing to pay for that quantity, and the government will pay the difference between the price that
consumers pay and $60. How much cotton will be sold? How much will this price support cost
the government? How much deadweight loss does this create? (4 points)
c. Suppose that instead, the government offered to subsidize cotton $20 per bale. That is, the
government pays farmers $20 per bale of cotton sold. How much cotton will be sold? How much
will this subsidy cost the government? How much deadweight loss does this create? (3 points)
d. Now consider a recession, in which the demand for cotton falls. Consider the deficiency payment
policy in part b, in which the government supports a price of $60 per bale. What will happen to
the cost of this policy to the government during a recession (will it increase or decrease)?
Clearly explain your answer (in words). (3 points)
e. Now consider a recession, in which the demand for cotton falls. Consider the subsidy policy in
part c, in which the government pays farmers $20 per bale of cotton sold. What will happen to
the cost of this policy to the government during a recession (will it increase or decrease)?
Clearly explain your answer (in words). (3 points)
j
a
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5. Assume the market for dry cleaning in a small town is perfectly competitive. The inverse market
demand curve for dry cleaning is P = 120 – Q. The inverse market supply curve is P = Q.
a. What is the equili
ium price and quantity of dry cleaning? (2 points)
. Most dry cleaners use a chemical solvent called perchloroethylene that is carcinogenic to humans
(it can cause cancer). More exposure creates greater risk, such that the marginal external costs
associated with dry cleaning are not constant, but increase with the quantity produced: MCX = Q.
Given this marginal external cost, what is the efficient quantity of dry cleaning? (3 points)
c. Illustrate your answers to parts a and b using an appropriate diagram. Clearly label any
curves that you draw. (3 points)
d. Suppose that you are on the town council, and you have the authority to impose specific (per-unit)
taxes on local businesses. What specific (per-unit) tax would you impose on this perfectly
competitive dry cleaning market to maximize Total Welfare? (3 points)
Note: Your answer should be a numerical value.
e. Now assume that the market for dry cleaning in a small town is a monopoly. The inverse market
demand curve for dry cleaning is P = 120 – Q. The monopolist’s marginal cost curve is MCP = Q.
What is the equili
ium price and quantity of dry cleaning? (2 points)
f. Compare and contrast the welfare generated by the market equili
ium price and quantity in a
perfectly competitive market versus a monopoly in the presence of this marginal external cost.
That is, with the marginal external cost MCX = Q, and without any policy (no tax),
(3 points)
i. Is Consumer Surplus higher in the perfectly competitive market or in the monopoly?
ii. Is Producer Surplus higher in the perfectly competitive market, or in the monopoly?
iii. Is Total Welfare higher in the perfectly competitive market, or in the monopoly?
Note: I do NOT expect you to calculate Consumer Surplus, Producer Surplus, or Total Welfare.
Just tell me in which market structure each value would be higher.
g. Would the specific tax (same numerical value) you described in your answer to part d
increase or decrease Total Welfare in the monopoly dry cleaning market? (2 points)
h. Would anyone in this town be in favor of the specific tax you described in your answer to
part d if the market for dry cleaning was a monopoly? Clearly explain your answer. (2 points)
T
f