Value-Based Pricing Alternatives for Personalised Drugs: Implications of Asymmetric Information and Competition

Abstract

The market for new drugs is changing: personalised drugs will increase the heterogeneity in patients’ responses and, possibly, costs. In this context, price regulation will play an increasingly important role. In this article, we argue that personalised medicine opens new scenarios in the relationship between value-based prices, regulation and industry listing strategies. Our focus is on the role of asymmetry of information and competition. We show that, if the firm has more information than the payer on the heterogeneity in patients’ responses and it adopts a profit-maximising listing strategy, the outcome may be independent of the choice of the type of value-based price. In this case, the information advantage that the manufacturer has prevents the payer from using marginal value-based prices to extract part of the surplus. However, in a dynamic setting where competition by a new entrant is possible, the choice of the type of value-based price may matter. We suggest that more research should be devoted to the dynamic analysis of price regulation for personalised medicines.

Appendix

1.1 Marginal Value-Based Prices

Let us assume that the firm is about to list a drug that has been approved so that any sunk cost for its discovery has already been borne. If the firm decides to list only for the patients with the highest effectiveness, the price is $\lambda E_{\text{H}}$ and the corresponding profit $\varPi_{n}^{m} = \left( {\lambda E_{\text{H}} - c} \right)n$. If the firm asks for listing for both types of patients, price and profit are respectively, λE_L and $\varPi_{1}^{m} = \left( {\lambda E_{\text{L}} - c} \right)$. The firm chooses the alternative that allows the maximization of the profit by comparing,

$$\varPi_{n}^{m} = \left( {\lambda E_{\text{H}} - c} \right)n,$$

with,

$$\varPi_{1}^{m} = \left( {\lambda E_{\text{L}} - c} \right).$$

We can write these conditions in terms of E_H for choosing the first alternative:

$$\left( {\lambda E_{\text{H}} - c} \right)n - \left( {\lambda E_{\text{L}} - c} \right) > 0 ,$$

$$\lambda \left( {nE_{\text{H}} - E_{\text{L}} } \right) + c\left( {1 - n} \right) > 0,$$

$$E_{\text{H}} > \frac{{E_{\text{L}} }}{n} - \frac{{c\left( {1 - n} \right)}}{n\lambda }.$$

Hence, the maximum profit is,

$$\varPi_{n}^{m} = \left( {\lambda E_{\text{H}} - c} \right)n\quad {\text{if}}\;\;E_{\text{H}} \ge \frac{{E_{\text{L}} }}{n} - \frac{{c\left( {1 - n} \right)}}{n\lambda },$$

$$\varPi_{1}^{m} = \lambda E_{\text{L}} - c\quad {\text{if}}\;\;E_{\text{H}} < \frac{{E_{\text{L}} }}{n} - \frac{{c\left( {1 - n} \right)}}{n\lambda }.$$

1.2 Average Value-Based Prices

If the firm decides to list only for the patients with the highest effectiveness, the price will be equal to $\lambda E_{\text{H}}$ and the profit will be $\varPi_{n}^{a} = \left( {\lambda E_{\text{H}} - c} \right)n$. If the firm asks for listing for both types of patients, the price is $\lambda E_{\text{A}} = \lambda \left( {nE_{\text{H}} + \left( {1 - n} \right)E_{\text{L}} } \right)$ and the profit is $\varPi_{1}^{a} = \left( {\lambda E_{\text{A}} - c} \right)$. The firm chooses the alternative that allows the maximization of profit by comparing,

$$\varPi_{1}^{a} = \left( {\lambda E_{\text{A}} - c} \right),$$

with,

$$\varPi_{n}^{a} = \left( {\lambda E_{\text{H}} - c} \right)n,$$

so that,

$$\varPi_{1}^{a} = \lambda \left( {nE_{\text{H}} + \left( {1 - n} \right)E_{\text{L}} } \right) - c,$$

which can be written as,

$$\varPi_{1}^{a} = n\left( {\lambda E_{\text{H}} - c} \right) + \left( {1 - n} \right)\left( {\lambda E_{\text{L}} - c} \right),$$

$$\varPi_{1}^{a} = \varPi_{n}^{a} + \left( {1 - n} \right)\left( {\lambda E_{\text{L}} - c} \right).$$

This proves that under average value-based prices, listing of both sub-groups is always preferred by the manufacturer.