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ProblemSet3SP10

# ProblemSet3SP10 - Problem Set 3 Bundling Game Theory and...

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Problem Set 3: Bundling, Game Theory and the Bertrand Model Question 1: In the following problems, assume that the monopolist can prevent arbitrage and knows the distribution of consumer types. Assume that each type forms an equal proportion of the population. This way, you may assume that there is one consumer of each type. Assume cost is zero. Does the monopolist prefer to sell the items A and B separate or in a bundle? What is (are) the optimal price(s)? (i) Type 1 is willing to pay \$5000 for Item A and \$2000 for item B. Type 2 is willing to pay \$6000 for Item A and \$1500 for Item B. (ii) Type 1 is willing to pay \$5000 for Item A and \$6000 for item B. Type 2 is willing to pay \$6000 for Item A and \$1500 for Item B. (iii) Type 1 is willing to pay \$6000 for Item A and \$2000 for item B. Type 2 is willing to pay \$6000 for Item A and \$1500 for Item B. (iv) Type 1 is willing to pay \$5000 for Item A and \$2000 for item B. Type 2 is willing to pay \$9000 for Item A and \$7000 for Item B. (v) Type 1 is willing to pay \$5000 for Item A and \$2000 for item B. Type 2 is willing to pay \$2000 for Item A and \$7000 for Item B. (vi) Type 1 is willing to pay \$5000 for Item A, \$3000 for item B, and \$1000 for Item C. Type 2 is willing to pay \$1000 for Item A, \$3000 for Item B, and \$5000 for Item C. Type 3 is willing to pay \$4000 for Item A, \$6000 for Item B, and \$11000 for Item C. Question 2: Refer back to Figure 10.5 from the lecture notes. Assume now that the marginal cost of producing pie is 1 and the marginal cost of producing halibut is also 1. What is the optimal pricing scheme (individual, bundling or mixed bundling) and what is (are) the price(s)? Question 3: Consider a monopolist who sells lamps and chairs. There are four types of consumers. Type 1 is willing to pay \$3 for a lamp and \$3 for a chair. Type 2 is willing to pay \$6 for a lamp and \$3 for a chair. Type 3 is willing to pay \$3 for a lamp and \$6 for a chair. Type 4 is willing to pay \$6 for a lamp and \$6 for a chair. The monopolist produces at marginal equal to 1. He knows the distribution of consumers which is equal parts for each type (this means you can assume there is one of each) and can prevent arbitrage. What is the optimal pricing scheme? Question 4: Consider the following game: l m r U 5,3 0,4 3,5 M 4,0 5,5 4,0 D 1,5 0,4 1,1 (i) Write down the best response function for the row player and the column player.

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