Optimal Design of a Pharmaceutical Price–Volume Agreement Under Asymmetric Information About Expected Market Size

Price–volume agreements are commonly negotiated between drug manufacturers and third-party payers for drugs. In one form a drug manufacturer pays a rebate to the payer on a portion of sales in excess of a specified threshold. We examine the optimal design of such an agreement under complete and asymmetric information about demand. We consider two types of uncertainty: information asymmetry, defined as the payer's uncertainty about mean demand; and market uncertainty, defined as both parties' uncertainty about true demand. We investigate the optimal contract design in the presence of asymmetric information. We find that an incentive compatible contract always exists; that the optimal price is decreasing in expected market size, while the rebate may be increasing or decreasing in expected market size; that the optimal contract for a manufacturer with the highest possible demand would include no rebate; and, in a special case, if the average reservation profit is non-decreasing in expected market size, then the optimal contract includes no rebates for all manufacturers. Our analysis suggests that price–volume agreements with a rebate rate of 100% are not likely to be optimal if payers have the ability to negotiate prices as part of the agreement.