Optimal Pricing and Inventory Planning with Charitable Donations

Problem definition: This paper investigates firms' optimal operational decisions and after-tax profits with regard to tax deduction for charitable donations. Academic/practical relevance: Motivated by the steady growth in noncash donations from U.S. companies, our work is the first to provide theoretical guidance on operational planning under tax deduction for both precommitted donations and end-of-season donations. Methodology: We analyze the impact of tax deduction for a profit-driven firm under a two-period price-markdown newsvendor model and characterize the firm's optimal price and quantity decisions. Results: The firm's optimal donation behavior is driven by two factors-fixed cost and demand uncertainty. Specifically, a positive fixed cost can induce precommitted donation during the regular selling season, and demand uncertainty can induce end-of-season donation during the clearance period. Managerial insights: The enhanced tax deduction that is designed to encourage charitable donations results in unexpected behavior by the firm. For example, the firm's optimal clearance price can increase with the amount of leftover inventory, and the firm's optimal after-tax profit can increase as the tax rate increases. While the value of the deduction is tied to the fair market value (and the price) of the product, surprisingly, the firm may find it more profitable to charge a lower price, because the lower price may scale up the demand uncertainty and consequently increase the expected tax subsidy under the enhanced tax deduction. Our analysis reveals important insights about the impact of the tax law on a monopolist's optimal operational decisions and profit.