Econ 100A: Microeconomics
\n\u201cMidterm 3\u201d homework exercise
\nJim Campbell
\nUniversity of California, Berkeley
\nDue by Dec. 2nd, 2022
\n11.59pm
\n\u0088 Please complete the assignment on your own paper and scan and upload to
\nGradescope. As part of your submission, you must indicate where on your
\nscan to find each answer.
\n\u0088 You must handwrite (not type) your answers, unless you have a specific DSP
\naccommodation that allows typing.
\n\u0088 You may discuss the homework with other students in groups, but each person
\nmust upload their own work, in their own words, in their own handwriting.
\n\u0088 You may not collaborate at large scale (i.e. on Ed Discussion, Discord etc.)
\nand you may not get \u2018professional\u2019 help (i.e. from Jim, the SLC etc.) with
\nthe specific questions on the exam. I am asking you to use this opportunity
\nto demonstrate your own knowledge and understanding of the material.
\n1
\nEcon 1, Fall 2022 | \u201cMidterm 3\u201d Jim Campbell | UC Berkeley
\n1. Consider a two player, simultaneous move game. The strategies available to each player and
\npayoffs are shown in the following matrix form:
\nPlayer 1
\nPlayer 2
\nL C R
\nT 6, 4 5, 2 8, 5
\nM 4, 4 9, 3 5, 9
\nB 7, 5 4, 4 5, 2
\nGame 5
\na) Find and write down the Nash equilibria in pure strategies, if any exist.
\nb) Say that instead of being a simultaneous move game this game had been sequential. First
\nplayer 1 will choose a strategy and then player 2 will observe the choice made by player
\n1 and choose a strategy. The full structure of the game, including all payoffs, is common
\nknowledge to both players. Sketch a game tree to represent the extensive form of this
\ngame. Find and write down the subgame perfect Nash equilibria.
\n2. In this question we will combine a very simplified model of an externality that has long-lasting
\nimpacts with the model of discounted utility that we learned in our game theory topic (sample nursing essay examples by the best nursing assignment writing service). Consider
\na hypothetical environmental externality: produced as the byproduct of industrial activity, each
\nunit of emission of a pollutant that is emitted once, today, causes $10 of external harm to society
\neach and every year, starting immediately, forever. Let\u2019s say that policymakers apply a discount
\nfactor of \u03b4 \u2208 (0, 1) to future gains and losses, in an analog of the discounted utility model except
\nfor cash payoffs rather than utilities.
\nWhat would the socially efficient Pigouvian tax on the emission of this pollutant be if we applied
\na discount factor of (i) \u03b4 = 0.5, (ii) \u03b4 = 0.9, and (iii) \u03b4 = 0.99? Give an intuitive explanation
\nof how to interpret the parameter \u03b4 in this context, and explain precisely but in simple terms
\nwhat the goal and effect of the Pigouvian tax would be.
\n3. Consider a model of Cournot duopoly. Two firms produce an identical product. The inverse
\ndemand function for the product is given by p = 60 \u2212 y, where y = y1 + y2 is the sum of the
\nquantity produced by the two firms. Production costs are zero for both firms.
\na) Find the quantity produced by each firm in the Nash equilibrium of this game. Find the
\nprice of the product and the profit of each firm.
\nb) Now say that marketing guru Jim has a proposal for firm 1. He would be able to convince
\npeople that the two firms\u2019 products were in fact slightly different from each other, so that
\nthe amount produced by each firm would not impact the price of the other\u2019s product
\nas much as it did before. The inverse demand function for each product would become
\np1 = 60 \u2212 y1 \u2212
\n1
\n2
\ny2 and p2 = 60 \u2212 y2 \u2212
\n1
\n2
\ny1. What is the most that firm 1 would be willing
\nto pay Jim to do this? Show your work and explain in a few sentences what you did to
\nfind your answer.
\n2
\nEcon 1, Fall 2022 | \u201cMidterm 3\u201d Jim Campbell | UC Berkeley
\n4. A profit-maximizing monopolist produces a good and sells it to three consumers, A, B and C.
\nIt has zero costs. The consumers have inverse demand curves given by
\npA = 10 \u2212 qA, (1)
\npB = 12 \u2212 2qB, (2)
\npC = 4 \u2212
\n1
\n2
\nqC. (3)
\na) If consumer B had been the only consumer and the monopolist had to set a single, uniform
\nprice for its product, what price would it choose and how many units would it sell? What
\nwould be the socially efficient price and quantity?
\nThe monopolist has decided to price its good using a two part tariff. It knows that it has three
\nconsumers, and it knows exactly what the demand curve is for each one.
\nb) Say that the monopolist could tell the consumers apart and set a personalized two part
\ntariff for each of them. What two part tariff would it set for each consumer?
\nc) Say that the monopolist cannot tell the three consumers apart and has to set just a single
\ntwo part tariff that all three consumers can then decide whether or not to pay. What two
\npart tariff would it set? Explain your answer.
\n3<\/p>\n","protected":false},"excerpt":{"rendered":"
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