Can patent duration hinder medical innovation

Abstract

We argue that, in the pharmaceutical industry, excessive patent duration can deter investments in innovative treatments in favor of me-too drugs. The point is that too-long durations foster incentives to collude to delay investments in R&D for innovative treatments. We give a set of sufficient conditions for which collusion is a subgame-perfect equilibrium; that is, the threat of punishing any deviator is credible. We then show that reducing current duration always breaks down market discipline, and so does an increase in duration for innovative treatments. Optimal patent duration must then be a trade-off between breaking down market discipline and rewarding innovation.

Appendices

Appendix 1: Computation of $\theta ^{i}$

When both firms try to develop the vaccine the payoff for firm i is:

$$\begin{aligned} \theta ^{i}=\alpha \left[ \alpha \frac{CF_{v}}{2}+\left( 1-\alpha \right) CF_{v}\right] +\left( 1-\alpha \right) ^{2}\left[ \Pi _{p}^{i}+\beta \theta ^{i}\right] -C \end{aligned}$$

where the first term correspond to the case when firm i is successful: with probability $\alpha$ firm j is also successful, hence they share the profits, and with probability $\left( 1-\alpha \right)$ firm j is unsuccessful, hence firm i get all the profits. The second term correspond to the case in which both firms are unsuccessful. In this case, firm i will enjoy the profits from his patents and will play the same game in the next period because the unsuccessful vaccine produces another patent on drugs. If only firm j is successful, firm i gets nothing. Whether firm i is successful or not it has to pay the cost C. Solving for $\theta ^{i}~$gives:

$$\begin{aligned} \left[ 1-\left( 1-\alpha \right) ^{2}\beta \right] \theta ^{i}=\frac{\alpha \left( 1-2\alpha \right) }{2}CF_{v}+\left( 1-\alpha \right) ^{2}\Pi _{p}^{i}-C \end{aligned}$$

$$\begin{aligned} \theta ^{i}=\frac{1}{\left[ 1-\left( 1-\alpha \right) ^{2}\beta \right] }\left[ \frac{\alpha \left( 1-2\alpha \right) }{2}CF_{v}+\left( 1-\alpha \right) ^{2}\Pi _{p}^{i}-C\right] \end{aligned}$$

Appendix 2: Proof of Proposition 1

Suppose both firms play the Collusion Strategy. Then, the payoff to each is $\frac{CF_{p}^{i}}{1-\beta }$. Suppose a firm uses another strategy. This must involve researching drugs for a number of periods (maybe zero) and then researching a vaccine until the game ends. This is optimal since the other firm is playing a Collusion Strategy, hence the other firm will play v forever and, as A3 hold, the best response for firm i is to play v. Consider the game at $t=0~$without loss of generality. If firm i plays v, it receives $\left[ \alpha CF_{v}+\left( 1-\alpha \right) \theta ^{i}-C\right]$. Hence, the Collusion Strategy is an equilibrium if and only if $\frac{CF_{p}^{i}}{1-\beta }\,\ge \left[ \alpha CF_{v}+\left( 1-\alpha \right) \theta ^{i}-C\right]$.