Problem Set 4 Answer Key

1. If, by monopoly, we are talking about a single-price monopolist (as opposed to one that practices price discrimination), then there is reason to believe that the monopolist is bad for the economy. Such a monopoly will cause dead-weight loss: the gain in producer surplus is less than the loss in consumer surplus.

4. TR = $2000; TC = $1200; Profit = $800; The monopolist should not change its price and output because of the imposition of the lump sum tax--it's a fixed cost. Profits are simply reduced to $500.

5. Since MC > MR, the monopolist should cut output (and thereby raise its price).

6. Unregulated monopolies never operate on the inelastic region of the demand curve. The profit maximizing rule is to produce where MR = MC. Since MC is always a positive number, this means that MR must be positive. Recall that MR = P [1 - 1/E ]. If MR is positive, then we know that E > 1. The intuition is the following: a monopolist wouldn't price where demand is inelastic since they could always raise price and increase their revenues (and since they'd be selling less, they'd have less cost also).

7. The profit-maximizing output and price should be straightforward. The lowest price the monopolist would be willing to operate at in the short run is the shutdown price. The shutdown price occurs at the lowest point on the AVC curve.

8. Price discrimination could be beneficial to the economy in the sense that it encourages the monopolist to eliminate dead weight loss by selling to more customers. The three conditions are in your notes.

9. No, the monopolist should not set the price of its software at 0. A profit-maximizing monopolist will follow the MR = MC rule for determining its output level. Since MC = 0, the MR will equal zero at the optimal output level. The price, however, is set off the demand curve. In particular, it can be shown that the monopolist in question will set its price so that the elasticity of demand is 1.

10. Price discrimination:
a) those who do not own a boat
b) adults
c) business travelers
d) rich

Q	P	TR	MR	MC	FC	VC	TC	PROFIT
1	50000	50000	50000	10000	50000	10000	60000	-10000
2	40000	80000	30000	10000	50000	20000	70000	10000
3	30000	90000	10000	10000	50000	30000	80000	10000
4	20000	80000	-10000	10000	50000	40000	90000	-10000
5	10000	50000	-30000	10000	50000	50000	100000	-50000

b) A single-price monopolist maximizes profit by selling Q = 3 (where MR = MC) at a P = $30,000. Profits are $10,000.
c) A price discriminating monopolist has an incentive to sell to all those who are willing to pay above the MC. Thus, the firm will sell to all 5 buyers (that last buyer will be indifferent) at the maximum price each is willing to pay. Thus TR=$150,000 and profits will be $50,000.

12.    Monopoly diagram
a)    P₂ and Q₂
b)    P₁ and Q₁
c)    acP₂
d)    abP₁
e)    bce

15.  Parsons Guards I
a)    Guards provide a general sense of security for all residents that exhibits non-rivalry and non-exclusivity.
b)    The marginal cost of hiring a guard is greater than the marginal benefit to any single individual.
c)    See below.

16.  Parsons Guards II
a)    2 guards with a net benefit of $800.
b)    See table above.
c)    Perhaps the Apartment Council could levy an annual security fee of $6 per resident to fund the 2 guards.

17. Mosquito abatement program.
a) Under majority rule, only Charlie would vote in favor of the abatement program (since he values the program at $100, which is more than the cost to each owner of $35). Thus, the abatement program would not be approved. From society's point-of-view this would be inefficient since the total value of the program to the three guys ($120) is greater than the total cost ($105).
b) Unanimity could be reached by having Charlie subsidize Art and Bob's "tax bill." Assuming Art and Bob are willing to pay their values, Charlie could pay $34 on behalf of Art and $16 on behalf of Bob in order to pay for the abatement program. All parties would thus benefit.

20. Private costs = $10,000; External costs = $5000 + 4000 + 1000 = $10,000; Social costs = private + external = $20,000

21. Perhaps property values are lower around airports, thus housing is relatively cheaper.

22. Fishermen and sludge.
a) The fishermen will buy the nets at a cost of $3250.
b) The factory will buy the nets for the fishermen at a cost of $3250.
c) The tax is likely to be set equal to the damage done by the sludge to the fishermen, namely, $5000. Given this potential tax liability, the factory will try to minimize its costs by avoiding the tax. Since the factory is precluded from bargaining with the fishermen as in part (b), they will be unable to buy the net system. The next best option is to install the water filter system at a cost of $4100 (which is better than paying $5000 in taxes).
d) As Coase would argue, the outcomes in parts (a) and (b) are identical: as long as property rights are well-defined and transaction costs are low, private bargaining will result in the most efficient outcome. In this case, efficiency requires that the nets be used. However, in part (c), transactions costs were high enough to prevent bargaining so that only a "second best" outcome prevailed.

24.    Pollution
a)    Cost to Factory A = (10)($60) = $600; Cost to Factory B = (10)($100) = $1000. Thus the total cost to the town of cutting 20 units of pollution is $1600.
b)    If each firm is given only 10 permits, they must each reduce their total pollution from 20 to 10 just as described in part (a) above. However, since Factory A can eliminate their pollution cheaper than Factory B can, Factory A is likely to sell their permits to Factory B at some price between $60 and $100 per permit. For example, a price of $80 would make both Factories better off.
c)    Suppose that the price of a permit is $80. Then, Factory A can cut its emissions by another 10 units (at a cost of an additional $600) and sell the permits to Factory B for $800. The net cost to Factory A is = 600 + 600 - 800 = $400. Factory B, therefore, is able to continue producing 20 units of pollution because they've now bought 10 additional permits at a cost of $800. The total cost to the town is $1200. Note that this is cheaper than the solution proposed in part (a) above!

Number of Guards	Total Cost of Guards	Marginal Cost of a Guard	Marginal Benefit per Resident	Marginal Benefit to all Residents	Total Benefit	Net Benefit
1	$300	$300	$10	$1000	$1000	$700
2	$600	$300	$4	$ 400	$1400	$800
3	$900	$300	$2	$ 200	$1600	$700
4	$1200	$300	$1	$ 100	$1700	$500