Optimal Two-Part Pricing under Demand Uncertainty

Abstract

This paper examines the pricing behavior of a risk-averse monopolistic firm under demand uncertainty. The firm produces a single good at a constant marginal cost. To facilitate sales, the firm uses a two-part pricing contract that includes a membership fee and a selling price per unit. The good is sold to a continuum of heterogeneous consumers who are subject to a common demand shock. We show that the global and marginal effects of risk aversion are to push the unit price closer to the constant marginal cost, and to shrink the market coverage so as to limit the firm's risk exposure to the demand uncertainty. The more risk-averse firm as such charges a higher membership fee to consumers. We further show that an increase in the fixed cost of production induces the firm to lower (raise) the unit price, to raise (lower) the membership fee, and to shrink (enlarge) the market coverage under decreasing (increasing) absolute risk aversion. The firm's optimal two-part pricing contract, however, is unaffected by changes in the fixed cost under constant absolute risk aversion. Finally, we show that a mean-preserving-spread increase in the demand uncertainty induces the firm to lower the unit price, to raise the membership fee, and to shrink the market coverage under either decreasing or constant absolute risk aversion. The firm's risk preferences as such play a pivotal role in determining the optimal two-part pricing under demand uncertainty.