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thakur ghimire esenting Games (1) v Search (Alt+Q) ign Layout References Mailings Review View Help Grammarly Acrobat PDFelement 4) This question Illustrates the duopoly model

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thakur ghimire esenting Games (1) v Search (Alt+Q) ign Layout References Mailings Review View Help Grammarly Acrobat PDFelement 4) This question Illustrates the duopoly model of competition. Duopoly is a market with two competing firms. There are two bagel stores in the Harlem area - College Bagels (Firm 1) and Harlem Bagels (Firm 2). The bagels sold by the two stores are identical in every way. CB and HB can choose the price of their bagel to be $0, $1, $2, $3, $4, $5, or $6. This type of oligopoly model where firms compete by choosing prices is called Bertrand Competition. The total daily demand for bagels in Harlem at each of these prices is given below Price, p Quantity Demanded, Q $0 600 $1 500 $2 400 $3 300 $4 200 $5 100 $6 0 Assume there is no cost of producing a bagel. The profit to each bagel store can be calculated asProfit = Total Revenue - Total Cost Since Total Cost = 0, Profit = Total Revenue. The revenue earned is the product of the bagel price (p,) chosen by the firm and the quantity of bagels sold by the store (Q.). Total Revenue to firmi = p. . Q, Assume both bagel stores simultaneously choose their prices, I.e. CB cannot observe HB's posted price when it chooses the price of its bagels and the same is true for HB. Consumers always buy bagels from the store that has a cheaper price, so if CB chooses a price that is lower than HB's then it gets all of market demand, while HB sees no demand. Conversely, if HB's price is lower it serves the entire demand in the market while CB gets no demand. If the two stores set the same price, consumers distribute themselves equally across the stores, so each store gets exactly half of market demand. a. Show that for each firm, choosing a price p, = $0 is a dominated strategy. Show that p, = $6 is also a dominated strategy for both firms. b. Using the monopoly price and profits calculated In part b) of Q4, argue that choosing a price higher than monopoly price is a dominated strategy. C . Using the Information obtained in parts a) and b) find the set of rationalizable strategies for this game. Find a Nash Equilibrium. d. How much quantity is sold in the market? What are the profits to each individual firm and total industry profits? Compare the market outcome with Bertrand competition to the monopoly outcome derived in Q 4) of Problem Set 1. Assume that the two firms share the monopoly profits equally by splitting the resulting demand equally with each other

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