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14.4 Consider the model of Bertrand competition with differentiated products
from the text. Let the demand curves for firms A and B be given by
Equation 14.10 and Equation 14.11, and let the firm’s marginal costs be
constant, given by cA and cB. It can be shown that the best-response
function for firm A is
pA 
1  2 pB  c A
4
pB 
1  2 p A  cB
4
and for firm B is
a. Graph the two best-response functions. Find the Nash equilibrium
assuming cA ＝ cB ＝ 0 algebraically and indicate it on the graph.
b. Indicate on the graph how an increase in cB would shift the bestresponse functions and change the equilibrium.
c. Indicate on the graph where analogue to the Stackelberg equilibrium
might be, with firm A choosing price first and then firm B. Is it better
to be the first or the second mover when firms choose prices?
14.10 Suppose that the total market demand for crude oil is given by
QD ＝ 70,000 － 2,000P
where QD is the quantity of oil in thousands of barrels per year and P is
the dollar price per barrel.
Suppose also that there are 1,000 identical small producers of crude oil,
each with marginal costs given by
MC ＝ q + 5
where q is the output of the typical firm.
a. Assuming that each small oil producer acts as a price taker, calculate the
typical firm’s supply curve (q = . . .), the market supply curve (QS = . . .),
and the market equilibrium price and quantity (where QD = QS).
b. Suppose a practically infinite source of crude oil is discovered in New
Jersey by a would-be price leader and that this oil can be produced at a
constant average and marginal cost of AC = MC = $15 per barrel.
Assume also that the supply behavior of the competitive fringe
described in part a is unchanged by this discovery. Calculate the demand
curve facing the price leader.
c.
Assuming that the price leader’s marginal revenue curve is given by
MR  25 
Q
1,500
how much should the price leader produce in order to maximize profits?
What price and quantity will now prevail in the market?