Department of Economics
University of California
Economics 121: PROBLEM SET 2
Due: Thursday, October 7, 2004, 12:30 PM (in lecture)
Decide whether the following statements are true, false or uncertain, and then
explain the reasoning behind your answer.
The Bertrand Paradox will arise for a duopoly on the Hotelling line as transportation costs go to zero.
UNCERTAIN. - Recall that price in the model is P + tx. If t = 0, then each consumer will
only pay the price regardless of its position on the Hotelling line.
If t=0, we can assume that consumers view the products as perfect substitutes. In this
price will converge to the marginal cost.
However, if marginal costs differ across firms, then firms will compete on price. If we
assume two firms with different costs, say MC1 > MC2. Then, when the firms compete on
price, firm 2 will be able to price just below MC1
If production exhibits learning by doing
, then a scope
economy arises between the product produced
at different points in time.
Assume there are two periods and define
as output in the first and
second periods, respectively.
The cost of producing either output alone without the other
would be the same, but when some of
has been produced in the first period, then the
cost of producing
in the second period is lower than when
is produced stand
Note that the source of the scope economy here is not a shared input since
production in the second period does not affect cost in the first, but rather a cost
complementarity: more produced in the first period, the less the cost in the second.
When firms in an industry act as price takers, their index of scale economies, s, will be less than 1
when the industry reaches equilibrium.
FALSE: s = AC/MC. When firms act as price takers (i.e. a competitive industry), when s <
1 then AC < MC and firms are making a profit. In equilibrium, however, profits will be
zero, since firms enter until profits are zero. Profits are just zero when AC = MC, or when
s = 1.
Engineering economists have found that the cost of producing small cars (S) and trucks (T) can be
expressed as follows:
C(S, T) = 10 + S + 2T + ST
if S > 0 and T > 0
C(S, T) = 8 + 2T
if S = 0 and T > 0
C(S, T) = 4 + S
if S > 0 and T = 0
Both S and T are measured in thousands of vehicles per year.
Find the incremental cost function
of producing trucks when a positive amount of small cars are
produced: S > 0.
(S,T) = C(S,T) - C(S,0) )= 10 + S + 2T + ST - (4 + S) = 6 + 2T + ST
Evaluate incremental cost of trucks at T = 10 when S = 10 and then again when S = 20.