Adams and Yellen (1976) A firm is selling good 1 and good 2. Pat wants to...

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Adams and Yellen (1976) A firm is selling good 1 and good 2. Pat wants to purchase at most one of each object, and has valuation v₁ for good 1, v2 for good 2, and v₁ + v2 for both. If Pat purchases good k for pk, then Pat receives utility vk - pk (and similarly for bundles). The firm has 3 options for selling to Pat: (a) Pure Components Firm sells goods separately at price p₁ and p2. Pat can choose to either 1) buy only good 1, 2) buy only good 2, 3) buy both goods, or 4) buy nothing. i. Write out Pat's utility in each option. ii. Let v₁ <p₁ and 2 > P2. Which option will Pat choose? Show why. (b) Mixed Bundling Firm sells goods 1 and 2 separately at price p₁ and p2, and together as a bundle at PB (where PB < P₁ + P2). i. Write out Pat's Utility in each purchase option. ii. Let v₁ p₁ and 2 < P2. A. Argue that Pat will not choose to purchase good 2. B. Give a condition that guarantees Pat will choose to only purchase good 1. C. Give a condition that guarantees Pat will choose to purchase the bundle. (c) Two Customers Now consider the case when there are two customers Pat and Kelly. Let , , , u be the valuations of Pat and Kelly for goods 1 and 2. Let u <uf and <2. The firm wants to take a pure components approach. It considers two possible prices for each of the goods: pf = vand p = vt, and p = vand p = (Figure). p²/ (1,0) Pi pH i. Suppose that the firm price of goods 1 and 2 at (p. p). What will each agent buy? Compute the firm's revenue at this set of prices. ii. Do the same for (p.p), (pp), (pp). iii. Give conditions for (pH, p) to be the firms profit maximizing set of prices. 1 Adams and Yellen (1976) A firm is selling good 1 and good 2. Pat wants to purchase at most one of each object, and has valuation v₁ for good 1, v2 for good 2, and v₁ + v2 for both. If Pat purchases good k for pk, then Pat receives utility vk - pk (and similarly for bundles). The firm has 3 options for selling to Pat: (a) Pure Components Firm sells goods separately at price p₁ and p2. Pat can choose to either 1) buy only good 1, 2) buy only good 2, 3) buy both goods, or 4) buy nothing. i. Write out Pat's utility in each option. ii. Let v₁ <p₁ and 2 > P2. Which option will Pat choose? Show why. (b) Mixed Bundling Firm sells goods 1 and 2 separately at price p₁ and p2, and together as a bundle at PB (where PB < P₁ + P2). i. Write out Pat's Utility in each purchase option. ii. Let v₁ p₁ and 2 < P2. A. Argue that Pat will not choose to purchase good 2. B. Give a condition that guarantees Pat will choose to only purchase good 1. C. Give a condition that guarantees Pat will choose to purchase the bundle. (c) Two Customers Now consider the case when there are two customers Pat and Kelly. Let , , , u be the valuations of Pat and Kelly for goods 1 and 2. Let u <uf and <2. The firm wants to take a pure components approach. It considers two possible prices for each of the goods: pf = vand p = vt, and p = vand p = (Figure). p²/ (1,0) Pi pH i. Suppose that the firm price of goods 1 and 2 at (p. p). What will each agent buy? Compute the firm's revenue at this set of prices. ii. Do the same for (p.p), (pp), (pp). iii. Give conditions for (pH, p) to be the firms profit maximizing set of prices. 1