Optimal Two-Part Pricing Under Demand Uncertainty

This chapter examines the two-part pricing problem of a risk-neutral monopoly (the seller) for a good sold to buyers who face uncertainty about their demand for the good. If buyers are risk neutral, we show that marginal-cost pricing is not only profit-maximizing but also socially efficient. If buyers are risk averse, the demand uncertainty calls for the insurance need of buyers, which induces the seller to deviate from marginal-cost pricing. We show that the optimal unit price is higher or lower than the constant marginal cost, depending on the nature of the goods (normal or inferior) and on the signs of cross-derivatives of buyers’ multivariate utility function. Employing a quasi-linear specification that reduces the general multivariate utility function to a special univariate utility function, we show that the seller optimally raises (lowers) the unit price and lowers (raises) the fixed fee from their risk-neutral counterparts if buyers’ total and marginal benefits are positively (negatively) correlated. We further show that these results are robust to the introduction of competition to the seller.

Keywords: Demand uncertainty, Insurance, Risk aversion, Two-part pricing.