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PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE
Facultad de Ciencias Económicas y Administrativas
EAA200B-5 Fundamentos de Dirección de Empresas
Ayudant́ıa # 1
Raicho Bojilov
Valentina Diaz Valenzuela
Francisca Ignacia Stange Mart́ınez
Second Semester 2020
1 Exercise
Suppose that there are three firms 1, 2, and 3 that can produce each one unit of a certain product. The
costs of production of the firms are 2, 4, and 5 respectively. There are also three consumers A, B, and C
that each are willing to buy one unit of the good. The valuations of the product by the consumers are 7, 6,
and x, x ∈ [0, 6).
(a). Please express the total value created in the industry/market as a function of x.
(b). Suppose that x = 4, 5 and that firm 1 can produce up to 2 units of the good at a cost of 2. Please
find the total value created in the industry/market.
(c). Suppose that x = 4, 5 and that firm 1 can produce up to 2 units of the good. The first unit can
be produced at a cost 2 and the second unit at a cost of 6. Please find the total value created in the
industry/market.
2 Exercise
Suppose that there are two upstream firms, A and B, that provide a particular input. Each can produce
one unit of an input at a cost of 1. There are two downstream firms, 1 and 2, that need one unit of the
input in order to produce one unit of a consumer good at a constant cost of production of 1. Each of the
downstream firms can produce at most one unit of the final good. Firm 1 can produce the input
itself at a cost 1 + c, c ∈ (0, 1) . Meanwhile, firm 2 can produce the input at a cost 1 + C, C ∈ (c, 1) . If a
firm does not operate in the market, it gets a profit of 0. The downstream firms engage in price competition
in the market for the final good.
The consumers in this economy gets utility 3− p from consuming 1 unit of the good at a price p and the
purchase of any additional units of the good does not increase the consumer’s utility. Similarly, if consumers
do not buy the consumer good, their utility is 0. The downstream firms announce non-renegotiable prices
of the final good and consumers buy the final good as long as the utility from the purchase is not negative
(≥ 0).
(a) Suppose that there are two consumers. Please find the total value created in the industry/market.
(b) Suppose that there are two consumers. Please indicate the maximum and minimum value captured
by the upstream firms and the downstream firms.
(c). Suppose that firms A merges with firm 1, while firm B merges with firm 2. Let the new consolidated
companies be A1 and B2. Now, suppose that there are three consumers in the market for the final good.
Please find the total value created in the industry/market.
(d). Suppose that firms A merges with firm 1, while firm B merges with firm 2. Let the new consolidated
companies be A1 and B2. Now, suppose that there are three consumers in the market for the final good.
Please indicate the maximum and minimum value captured by the consumers and the merged firms.
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