Heavy-Tailed Distributions and Robustness in Economics and Finance by Marat Ibragimov Rustam Ibragimov & Johan Walden

Author:Marat Ibragimov, Rustam Ibragimov & Johan Walden
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

2.5.4 Optimal Bundling with Heavy-Tailed Valuations and Profit-Maximizing Prices

We turn to the case in which the prices for goods on the market and their bundles are set by the monopolist. To simplify the presentation of the results and their arguments, we assume that the marginal costs c i of goods in M are identical: c i  = c, i ∈ M; however, extensions are possible for the case of arbitrary c i . Suppose that the seller can provide bundles B of goods in M for prices per good p ∈ [0, p max], where p max is the (regulatory) maximum price, with the convention that p max can be infinite. For a bundle of goods B ∈ 2 M , denote by p B the profit-maximizing price per good for the bundle, so that the seller’s expected profit from producing and selling bundles of B’s (at the price p B per good) is

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