Methods: We developed a three-stage Markov model of disease progression. We assumed that the new drug reduces the transition probability between two model stages. We assumed that the population was heterogeneous with respect to the transition probability affected by the drug, that this probability can be observed and used in setting limited use conditions, and that limited use conditions can be set either by the payer or by the manufacturer. We assumed that the manufacturer knows the payer's willingness to pay threshold. We defined the manufacturer's profit maximization problem as one in which the manufacturer chooses the price of the new drug as well as the range of transition probabilities for which this drug should be used in order to maximize profits.
Results: An optimal price and set of limited use conditions can be found by the manufacturer to maximize profits. The optimal price depends on the shape of the distribution of the heterogeneous transition probability. A theoretical upper limit on the price that is acceptable to the payer can be found; however, it is always optimal to set a price below this limit. In some instances, the optimal price is as high as 98% of the upper limit, while in others it may be as low as 45% of this upper limit. As the variance in the distribution of the heterogeneous transition probability increases, the optimal price and profit decrease. The manufacturer's optimal profit increases as the quality of life adjustment associated with being sick decreases and as the cost of being sick increases. When the manufacturer sets the price optimally the payer's total net monetary benefit is positive.
Conclusions: This work shows how a drug manufacturer would optimally set prices and limited use conditions to maximize profits, and it identifies important factors in determining the price and profits of the manufacturer. It is important for payers to understand how manufacturers make their decisions so that they can understand the implications of potential contract and reimbursement terms with manufacturers.