# 4. Consider a market in which there are two single product producers, P1 and P2, and a single retailer R. P1 and P2 sell their product to R at wholesale

4. Consider a market in which there are
two single product producers, P1 and
P2, and a single retailer R. P1 and P2
sell their product to R at wholesale
prices w1,w2 respectively, which P1 and
P2 choose simultaneously and indepen-
dently. Marginal production costs are
zero and there are no retail costs. The
producers do however face a. ﬁxed cost
F 2 0 of operating in the market: F
does not depend on volume. R then
sells the products on to consumers at
prices 191,192, respectively. Demand is
given by {91 = 2160 — 10191 + 5,02, _ (1)
QQ _ 2160 + 5p, — 10,02. (a) First consider R’s problem.
are the optimal retail prices p1, p2
as a function of the wholesale
prices 3501,2502? (b) are the corresponding quan-
tities 91,92, again expressed in
terms of 201,302? (c) Express P2’s proﬁt as a function
of 2501,2302. (d) are the equilibrium whole-
sale prices w1,w2? (e) are the equilibrium quanti-
ties 91,92? (f) are the equilibrium retail
prices 111, 132? (g) are the equilibrium proﬁts
717,711,712 for the retailer and each
of the two producers? Now suppose that R merges with
P1 to become the merged entity
M. So M now produces product 1
and sells both products 1 and 2 in
the retail market. You can think
of the situation as 101 = O with 102
being set by P2. (h) Express P2’s proﬁt as a function
of 102. (i) is the equilibrium wholesale
price 1192 of product 2? (i) are the equilibrium proﬁts
of M, P2? (k) Explain why it is still proﬁtable for
M to continue selling product 2. (1) Who beneﬁts and who is harmed
by this merger? Now suppose that F is so high that
it is no longer proﬁtable for P2 to
stay in the market. (m) For what values of F would P2
want to be in the market absent a
merger but not with a merger? Suppose further that this situation
is equivalent to one in which [)1 =
216 and p2 = 270. (n) is the expected proﬁt of M
in this case? (o) Who benefits and who is harmed
by this merger?
(p) is the term used for the prob-
lem described here?

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