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ProblemSet3_keySP10

# ProblemSet3_keySP10 - Problem Set 3 Bundling Game Theory...

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Unformatted text preview: 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. The best prices under individual pricing are \$ 5000 for Item A and \$ 1500 for Item B which yields a total revenue of \$ 13000. Charging \$ 7000 for the bundle is optimal yielding a total revenue of \$ 14000. (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. The best prices under individual pricing are \$ 5000 for Item A and \$ 6000 for Item B which yields a total revenue of \$ 16000. The best bundling price is \$ 7500 and yields a total revenue of \$ 15000. Individual pricing is better. (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. The best prices under individual pricing are \$ 6000 for Item A and \$ 1500 for Item B which yields a total revenue of \$ 15000. The best price under bundling is \$ 7500 and yields a total revenue of \$ 15000. Both methods are optimal. (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. The best prices under individual pricing are \$ 5000 for Item A and \$ 7000 for Item B which yields a total revenue of \$ 17000. The best price under bundling is \$ 16000 and yields a total revenue of \$ 16000. Individual pricing is optimal for the monopolist. (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. The best prices under individual pricing are \$ 5000 for Item A and \$ 7000 for Item B which yields a total revenue of \$ 12000. The best price under bundling is \$ 7000 and yields a total revenue of \$ 14000. Bundling is optimal. (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. The best prices under individual pricing are \$ 4000 for Item A, \$ 3000 for Item B and \$ 11000 for Item C which yields a total revenue of \$ 28000. The best price under bundling is \$ 9000 for all 3 and yields a total revenue of \$ 27000. Individual pricing is optimal....
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ProblemSet3_keySP10 - Problem Set 3 Bundling Game Theory...

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