04 Jun while PECO faces inverse demand curve
Question
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Suppose US Airways is a monopolist airline from Philadelphia Airport, and PECO Energy is a
monopolist electricity supplier for Philadelphia residents. US Airways faces inverse demand curve
D
PU S (Q) = 100 Q
while PECO faces inverse demand curve
D
PP ECO (Q) = 100 3Q.
Both rms have cost function C(Q) = 0.5Q2 + 50.
1. Elasticity and Eciency.
(a) Which rm faces a more elastic demand curve?
(b) Recall from Econ 101 that a monopolists supply curve is its marginal cost curve.
Express each rms supply curve as a function of Q, P S (Q).
(c) For each rm, what price and quantity levels maximize total welfare? (total welfare
is the sum of producer and consumer surplus). How is this welfare allocated between
consumers and producers?
(d) How do these prices and quantities compare to the competitive equilibrium price and
quantity?
2. Show that the comparison in Question 1 generalizes. In other words, xing the maximum
willingness to pay at 100 and the supply curve at what you derived in part (b), suppose a
rm faces demand curve P D (Q) = 100 aQ for some a > 0.
(a) Is the elasticity of demand increasing or decreasing in a?
(b) Is the maximum total welfare increasing or decreasing in a? Prove and give economic
intuition for your result.
(c) Is the share of the surplus (percent of the total surplus) producers receive increasing or
decreasing in a? Prove and give economic intuition for your result.
3. Monopoly.
(a) Calculate the monopoly price and quantity traded for US Airways and PECO. Is the
monopolist price mark-up larger in the airline or electricity market, compared to the
competitive equilibrium? Why? How about the monopolist quantity reduction?
(b) What prots do US Airways and PECO earn as monopolists?
(c) Calculate the consumer surplus, producer surplus and dead weight loss (DWL) at the
monopoly price. Is producer surplus equal to prot? Why or why not?
(d) Which industry, airline or electricity, has the larger DWL when there is a monopoly?
Why?
4. Regulation.
Suppose Mayor Nutter decides to regulate the airline industry in Philadelphia, and tells US
Airways that it will pay it s dollars for each unit it sells.
(a) Set up US Airways new prot maximization problem.
(b) Fixing s, how much does US Airways produce?
(c) What level of s will induce US Airways to produce the competitive equilibrium quantity?
How much does this subsidy cost the city government?
(d) Suppose instead, Mayor Nutter oers to pay US Airways a lump sum subsidy L, which
is equal to the dierence between its monopoly prots and competitive equilibrium
prots, if US Airways produces at the competitive equilibrium price. Calculate L.
Which option is cheaper for the government?
5. Monopsony.
Now suppose that electricity is generated by many identical wind farmers, with the same
market supply curve you derived in 1b. PECO acts as a monopsonist and buys all the
electricity generated by these farmers, but does not produce any of its own electricity. PECO
can then sell this electricity to consumers at the monopoly price you calculated in Question
3.
(a) Write PECOs prot maximization problem as a monopsonist.
(b) Calculate the price PECO pays to the wind farmers and the quantity of electricity
purchased.
(c) What is the producer surplus received by the wind farmers?
(d) What is the prot earned by PECO?
(e) Note that the without PECO serving as an intermediary, the electricity market would
be perfectly competitive. Many wind farmers would sell electricity to many consumers.
Does the introduction of an intermediary improve or decrease total welfare?
6. Find an article in a reputable news source that discusses a rms strategy. Briey (1-2
paragraphs) relate the article to the competitive forces discussed in the Porter articles.
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