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Industrial Organization Field Exam
January
Instructions
Answer both questions. Note both questions have multiple parts. Try to be succinct in your answers, especially with respect to those questions that ask for discussion. Write legibly.
Question 1: IO Theory
There are two firms, A and B, that produce complementary products. Let ξi ∈ N denote the number of units a consumer buys from firm i, i ∈ {A, B}. Assume that a consumer of type θ derives utility U, given by
U =
y , if ξAξB = 0 θ + y , if ξAξB ≥ 1
where y is his consumption of the num´eraire good. Observe that a consumer wants at most one unit of each good and wants no units of either good if he cannot have a unit of the complementary product. Assume θ is distributed uniformly on the interval [θ¯− 1 , θ¯], θ¯ ≥ 1. The mass of consumers has measure one. Assume the cost of firm i, i ∈ {A, B}, of producing x units is
Ci(x) =
0 , if x = 0 cix + Fi , if x > 0
where ci > 0 and Fi ≥ 0. Let pi, i ∈ {A, B}, denote the price firm i charges for a unit of its product.
(a) Assuming the firms’ prices maximize joint profit, what does pA + pB equal? (Warning: This question isn’t hard, but it’s not trivial either.)
From now on, let θ¯ = 1 and suppose FA = FB = 0 and cA = cB = c < 1 /2.
(b) Suppose the timing is that the firms simultaneous set price and, then, consumers make their purchase decisions. What is (are) the equilibrium (equilibria) of this game?
Suppose now that price is determined in a Cournot-like fashion. Specifically, each firm chooses its output, xi, i ∈ {A, B}, a Walrasian auctioneer clears the market, and each firm receives
1 2
θ^ ¯ −
min{xA, xB } , if min{xA, xB } < 1 1 , if min{xA, xB } ≥ 1
per unit sold.
(c) What is (are) the equilibrium (equilibria) of this game?
(d) Comparing your last answer to the answer for the game in which the firms simultaneously set price, in which game are industry (joint) profits greater?
Now consider the following variation of the model. A consumer of type τ ’s utility is
U =
y , if ξAξB = 0 1 + y , if ξA = 0 and ξB ≥ 1 1 + y , if ξB = 0 and ξA ≥ 1 2 + τ + y , if ξAξB ≥ 1
where again y is his consumption of the num´eraire good. Assume again that there is a unit mass of consumers. Assume consumer type, τ , is distributed uniformly on [− 1 , 1]. For convenience, set cA = cB = 0.
(e) What are the goods for a consumer whose type lies in (0, 1]? What are the goods for a consumer whose type lies in [− 1 , 0)?
(f) Suppose the timing is that the firms simultaneous set price and, then, consumers make their purchase decisions. What is (are) the equilibrium (equilibria) of this game?
Question 2: Empirical IO
A researcher has data on two companies indexed i = 1, 2 who make advertis- ing decisions in multiple markets. It is assumed that advertising decisions are independent across different markets indexed m = 1,... , M. In each market the firms simultaneously decide whether to advertise or not. This interaction is modeled as a static game of complete information. The payoff function of each firm is characterized by the market and firm-specific scalar variable xim
