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ECS1010.08.post

# ECS1010.08.post - UNIT IV INFORMATION WELFARE 7/22 Decision...

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UNIT IV: INFORMATION & WELFARE Decision under Uncertainty Externalities & Public Goods Review 7/22

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Cartel Enforcement Consider a market in which two identical firms can produce a good with a marginal cost of \$1 per unit. The market demand function is given by: P = 7 – Q Assume that the firms choose prices. If the two firms choose different prices, the one with the lower price gets all the customers; if they choose the same price, they split the market demand. What is the Nash Equilibrium of this game?
Cartel Enforcement Consider a market in which two identical firms can produce a good with a marginal cost of \$1 per unit. The market demand function is given by: P = 7 – Q Now suppose that the firms compete repeatedly, and each firm attempts to maximize the discounted value of its profits ( δ < 1). What if this pair of Bertrand duopolists try to behave as a monopolist (w/2 plants)?

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Cartel Enforcement What if a pair of Bertrand duopolists try to behave as a monopolist (w/2 plants)? P = 7 – Q; TC i = q i Monopoly Bertrand Duopoly Π = TR – TC Q = q 1 + q 2 = PQ – Q P b = MC = 1; Q b = 6 = (7-Q)Q - Q = 7Q - Q 2 - Q FOC: 7-2Q-1 = 0 => Q m = 3; P m = 4 w/2 plants: q 1 = q 2 = 1.5 q 1 = q 2 = 3 Π 1 = Π 2 = 4.5 Π 1 = Π 2 = 0
Cartel Enforcement What if a pair of Bertrand duopolists try to behave as a monopolist (w/2 plants)? Promise: I’ll charge P m = 4, if you do. Threat: I’ll charge P b = 1, forever , if you deviate . 4.5 … 4.5 … 4.5 … 4.5 … 4.5 … 4.5 … 4.5 = 4.5/(1- δ ) 4.5 … 4.5 … 4.5 … 9 0 0 0 If δ is sufficiently high, the threat will be credible, and the pair of trigger strategies is a Nash equilibrium. δ * = 0.5 Trigger Strategy Current gain from deviation = 4.5 Future gain from cooperation = δ (4.5)/(1- δ )

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Decision under Uncertainty In UNIT I we assumed that consumers have perfect information about the possible options they face (their income and prices); and about the utility consequences of their choices (their preferences). Now, we will ask whether our model can be extended to deal with more realistic cases in which decisions are made without perfect information. We will also ask how imperfect (asymmetric) information affects market outcomes and their welfare consequences.
Decision under Uncertainty The Economics of Information : How can I maximize utility given incomplete info? How much info should I gather? We can distinguish between 2 sources of uncertainty: The behavior of other actors (strategic uncertainty) states of nature (natural uncertainty) Will it rain? Or not? Is there oil in the drilling hole? Will the roulette wheel come up red? (1 -- 35) Is the car a lemon?

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Decision under Uncertainty Expected Value v. Expected Utility Risk Preferences Reducing Risk: Insurance Contingent Consumption Adverse Selection (and Moral Hazard)
Expected Value & Expected Utility Which would you prefer?

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ECS1010.08.post - UNIT IV INFORMATION WELFARE 7/22 Decision...

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