# 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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