# Freezeme is the unique supplier of refrigerators in a market with two types of consumers

1. [30 points] Freezeme is the unique supplier of refrigerators in a market with two types
of consumers. Each consumer is interested in buying at most one unit. Refrigerators
might come in di¤erent qualities. From any given quality level S, a consumer of type
1 derives a utility of
U1 = S ?? p;
and a consumer of type 2 gets utility
U2 = S ?? p;
where p is the price, and > 1 is a constant. If a consumer does not buy, his/her
utility is 0. Freezeme found out that there are 100 consumers of type 1 and 70 of type
2.
Freezeme has a marginal cost of production of 10 (regardless of quality) and the
(quantity-independent) cost of developing a product of quality S is S2
2 .
(a) Suppose Freezeme develop two refrigerators, one of quality S1, the other one of
quality S2, with S2 > S1. Freezeme.s product manager I.S. Cold claims that
their products can be considered as being vertically di¤erentiated. Is she right?
Explain your answer. [4 points]
(b) Suppose that Freezeme could distinguish between consumers of type 1 and con-
sumers of type 2. Freezeme wants to develop two di¤erent fridges to serve the two
di¤erent types of consumers. What would Freezeme.s optimal price and quality
for each group of consumers be? [For each given quality, the .rm uses uniform
1
pricing. That is, the .rm charges pi for product with quality Si, i = 1; 2.] Assume
that the .rm can prevent arbitrage. [8 points]
(c) Under which condition is the quality produced for type 2 consumers greater than
the quality for type 1 consumers? Explain why the .rm would ever want to o¤er
a product of lower quality to the higher valuation type consumers. [4 points]
Assume for the remainder of this problem that Freezeme is unable to distinguish
between consumers of type 1 and consumers of type 2. Also assume that the
condition you identi.ed in part (c) holds.
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