Department of Economics
Public Goods and Efficiency
Two consumers are resident in Smallville. The two consumers, Smith
and Jones, have the following demand curves for hours of movie watching on
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 movies they watch. Smith and Jones are
the only two consumers in the market. Movies are made available each
Sunday by Smallville Broadcasting Company (SBC).
There are three diagrams at the bottom that may help you with this
exercise. Feel free to draw on them and be sure to label them carefully.
1. When movies are made available only in broadcast format are they a
good, a public good, a
collective good, or a
2. When movies are made available only in cable format, like Comcast,
are they a private
good, a public good, a
collective good, or a
3. At present movies are available in Smallville only in broadcast format, like the network TV
broadcasts of ABC, CBS and NBC that you are familiar with. If SBC, the
broadcasting company in Smallville, broadcasts 1 hour of movies how much would
Smith be willing to pay?
P=12-1 = 11
4. When movies are available in broadcast format how much would Jones be
willing to pay for one hour of viewing?
P = 12 - 2(1)
movies are available in broadcast format what is Smith’s and Jones’ combined
willingness to pay for one hour of viewing?
For two hours of viewing?
(12-2) + (
12 -2(2)) = 18
6. Given your earlier answers, what is the market demand curve for
broadcast movies? Be careful, Jones would not pay anything to watch more
than six hours.
For up to six hours of viewing time the market demand curve is:
P = 24 - 3 Q
For six to twelve hours of viewing time the market demand curve is:
P = 12 - 1 Q
7. If marginal cost of an hour of broadcast is $6 per hour what is the
socially optimal number of hours of broadcast movies?
figures below, find the place where MC crosses the market demand curve. 6
8. What is consumer surplus, given your previous answers?
There is a presumption in your
calculation that if an hour of broadcast movies is available for no fee then
both Smith and Jones will watch it. Since smith and
jones don't have to pay for their TV viewing it is the entire area under the
market demand curve.
1/2 (24 - 6)(6) + 6*6 = 54 + 36 = 90
9. How much must SBC collect in advertising revenue in order to be willing
to provide the socially optimal number of hours of broadcast?
36 SBC is able to collect
advertising revenue in the amount you just determined. What is the
amount of producer surplus?
10. As a function of her reservation price, what is the quantity of movies
demanded by Smith?
Q = 12 - P
11. As a function of his reservation price, what is the quantity of movies
demanded by Jones?
Q = 6 - 1/2 P
12. Suppose that SBC lays fiber optic cable in Smallville and ceases
broadcast operations. Now movies are only available via cable. If one does
not pay the cable fee then one cannot view the movie. If Smith pays to view
the movie it is still possible for Jones to view the same movie, and vice
versa. The marginal cost of providing an hour of movies is still $6, and
for the time being we'll suppose that there are no fixed costs. At a price of $6 per hour how many hours of movies will Smith
purchase? At a price of $6 how many hours of movies will Jones purchase?
13. At a price of $6 per hour how many hours of movies are made available
by SBC to its subscribers?
Only six hours. Because a movie is either a public
good or a collective good there is no rivalry in consumption. Smith and
Jones can watch concurrently so SBC need 'broadcast' only 6 hours.
14. At a price of $6 per hour how much consumer surplus
accrues to Smith when
movies are supplied via cable?
=1/2 (12-6)6 = 18
15. At a price
of $6 per hour how much consumer surplus accrues to Jones when movies are
supplied via cable?
= 1/2 (12 - 6 )3 = 9
16. What is
the amount of total consumer surplus?
17. Using your
answers to questions 12 and 13, how much producer surplus accrues to SBC?
6*6 from SMith and 6*3 from Jones for a total of 54. Their cost is 6*6 =
36, so their surplus is 18.
18. Is consumer surplus greater when movies are provided in broadcast
format or in cable format? Greater
in broadcast format,
the same for both
less in broadcast format.
answer to question 16 differs from your answer to question 8 because the total
amount paid by Smith or Jones to the cable company depends on the number of
hours they watch TV not on the total number of hours that are made available
on the network.
The only difference between 8 and 16 is that Smith and
Jones must pay to watch TV, in both cases a total of 6 hours are available.
20. Smith and
Jones both live in the same apartment building in Smallville that already has
been wired for cable service. A third tenant, Doe, moves into the
building. Doe's preferences are such that at any given price he does not
want to watch more TV than either Smith or Jones. What is the marginal cost to SBC of providing one hour of
movies to Doe?
0, since Doe can watch concurrently with the other two
and SBC does not need to offer more hours of TV to satsify Doe.
that as a result of Doe's viewing habits SBC must now offer more hours of
movies than it did in any of the previous questions. Now what is the
marginal cost to SBC of adding Doe to their network? $
6 per hour
22. Earlier it
was stated that the marginal cost of providing an hour of movies was $6 and
that there were no fixed costs. The $6 is the fee per hour SBC must pay to
content providers like Disney. If SBC buys a one hour show then they pay
$6, if they buy a two hour show they pay $12, and so on, regardless of the
number of viewers that tune in to the show. In the short run there are
certainly fixed costs associated with creating and running a cable network.
In the long run all costs are, of course, variable. The flat monthly fee
charged to its customers by a cable company like Comcast reflects
their marginal cost of
providing a TV show,
their marginal cost of providing an additional hour of showtime,
their average fixed cost of
running the network.
cable network technology exists for SBC to discriminate perfectly between
Smith and Jones (Doe has moved out of town). What price and quantity
should SBC offer to Smith? If they can discriminate
between Smith and Jones then they are in the position of a monopolist with
each of them. Smith will watch more TV than Jones at any price.
So, SBC will burden Smith with the cost of content acquisition and will
regard Jones as the marginal customer. You need to construct the MR curve for
Smith and determine where where MR = MC. Smith's Price =
Smith's Quantity =
What price and quantity
should SBC offer to Jones? Jones' Price =
Jones' Quantity =
Since Jones is the marginal customer, the cost of the
content shouldered by the offering to Smith, and the same content can be
delivered to Jones at no extra cost, SBC should charge a price to Jones that
maximizes its revenue from Jones. This occurs where Jones MT curve
crosses the horizontal axis at 3 and corresponds to a price of $6
24. Under the
circumstances of question 23 (cable with discrimination), what is consumer
? 4.5 for
Smith and 4.5 for Jones. Total = 9.0
25. Under the
circumstances of question 23 (cable with discrimination), what is producer surplus?
collected from Smith is 9*3, revenue collected from Jones is 6*3 for a total
of 45. It costs SBC 18 to provide the movies, again because there
remains a public/collective good aspect that means that Smith and Jones are
presumed to watch concurrently. The surplus for SBC is 27
surplus (the sum of consumer and producer surplus) is greatest when hours of
movies are provided in a
broadcast format, a
cable format with no discrimination, a
cable format with perfect
discrimination This disregards the question of