Public Goods, Commons Goods and Collective Goods
Public Goods Mosquito control in Metropolis is a pure public
good. In Metropolis there are just two residents: Art (a) and Bart (b). Art
has the following marginal valuation for mosquito control: MVa =
100 - y, where y is the quantity of mosquito control. Bart's marginal
valuation of mosquito control is MVb = 60 - 3/5 y. Let the
marginal cost of mosquito control be constant at $40.
1. What is the greatest quantity of mosquito control that Art is willing
2. What is the greatest quantity of mosquito control that Bart is willing
3. What is the most that Art would be willing to pay for 50 units
of mosquito control?
4. What is the most that Bart would be willing to pay for 50 units of
5. What is Art's and Bart's combined willingness to pay for 50 units of
6. What is the socially optimal level of control?
7. What is Art's and Bart's combined marginal valuation of the socially
optimal level of control?
8. Would either Art or Bart bear the entire cost of the socially optimal
level of control?
9. Would Art and Bart agree to share equally the cost mosquito control at
the optimal level? Yes
B. The Commons An isolated village surrounded by
wilderness contains a cultivated banana grove. Bananas (B) are the
only consumption good. The number of villagers working in the grove is
Lg and the number of villagers working in the wilderness is Lw.
The grove produces bananas according to the function B = 12Lg - Lg2
. Bananas also grow in the wild, where the production is
governed by B = 2Lw. There are 12 identical workers in the village.
10. What is the marginal product of labor in the grove? MPg =
11. What is the marginal product of labor in the wilderness? MPw
12. If you were a benevolent dictator how would you allocate the workers
between the village grove and the wilderness in order to maximize output?
Nobody owns the wilderness. Suppose also that no one owns the grove
and you have retired as dictator.
13. The problem that faces the community is how intensively to harvest
the commons (the grove). Suppose that additional workers enter the
grove until the marginal product of another worker is zero. How many
workers will be put to work in the grove
and how any will go to work in the
wilderness ? What will be
total output under that arrangement?
14. It is proposed that the village be operated on communist principles:
Each person produces to his/her ability and each consumes to her needs.
The logical consequence is that villagers be assigned to the grove and to
the wilderness until the output per worker is the same in both places. Under
this new regime how will workers be allocated between the gorve and the
wilderness and what will be the total production of bananas?
Lg = Lw
= B =
15. Suppose that each villager is given 1/12th of the grove to work as
though it were his/her own. Under this arrangement will be total
Collective Goods Two consumers are resident in Smallville. The two consumers, Smith
and Jones, have the following demand curves for hours of TV watching per day:
Ps = 12 - Q
Pj = 12 - 2 Q
Where Ps and Pj represent marginal willingness to pay
values (reservation prices) for Smith and Jones, respectively, and Q
represents the number of hours of TV they each watch. Smith and Jones are
the only two consumers in the market. TV is made available each
day by Smallville Broadcasting Company (SBC). Initially SBC broadcasts over
the air. If you want to watch television you just need a TV set, which
Smith and Jones both own. Once you own a set, it costs nothing to
watch TV. SBC's marginal cost of an additional hour of broadcast TV is
$6. SBC is able to sell advertising time in order to just cover their cost
of acquiring and broadcasting shows. Consumers regard the advertising as
annoying, but tolerate it since it involves no out-of-pocket expense on
16. What is the socially optimal number of hours that should be
17. What is consumer surplus when TV shows are broadcast over the air?
18. What is producer surplus under the broadcast arrangement?
Suppose that SBC lays fiber optic cable in Smallville and ceases
broadcast operations. Now TV shows are only available via cable. If one does
not pay the cable fee then one cannot view TV shows. If Smith pays to view
shows it is still possible for Jones to view the same show, and vice
versa. The marginal cost of providing an hour of shows is still $6, and
for the time being we'll suppose that there are no fixed costs.
19. At a price of $6 per hour how many hours of shows will Smith
20. At a price of $6 how many hours of shows will Jones purchase?
21. How many hours of shows will SBC put on their cable service?
22. What is total consumer surplus?
23. What is producer surplus?