The Problem of Availability of Patented Drugs Due to Product Patent and Parallel Trade: A Theoretical Approach

Abstract

This chapter examines the effect of the Patent Act on the availability of an essential drug in developing countries. Price discrimination by a Multinational Corporation (MNC) alleviates the problem of non-availability of the drug in a developing country compared to a uniform pricing strategy. Incorporating an upstream-downstream structure, we show that in the presence of parallel trade the MNC can earn a higher profit by serving both the developed and developing countries than by confining its operations in the developed country. Also allowing parallel trade instead of restraining it results in a higher profit to the MNC.

Appendix A

7.1.1 Deterring Parallel Trade

MNCs can also counter parallel trade by strategically pricing its product. In fact, the potential for parallel trade emerges when there is a large price differential for the medicine between the two markets. The manufacturer can however, “choke off” the potential for parallel trade by charging a price in a way such that the lower uniform price of the developing country prevails in the developed market. The manufacturer then sets $p_A^W$ in such a way that the retail price of the medicine are the same in the market of ${M_{{dl}}}$ and ${M_d}$ or in other words p ^B = p ^A. With p ^B = p ^A however the incentive for parallel trade is curbed. To set the same retail price for both the countries ${p^A} = \frac{{{a_1} + P_A^W}}{2}{ }$ should be equal to $\frac{{3{a_2} + c}}{4}$ or in other word

$$ { }\frac{{{a_1} + P_A^W}}{2} = \frac{{3{a_2} + c}}{4} $$

(A.1)

$$ \Rightarrow P_A^W = \frac{{3{a_2} + c - 2{a_1}}}{2} $$

(A.2)

At price, ${ }P_A^W = \frac{{3{a_2} + c - 2{a_1}}}{2}$ the retail price for the medicine in country ${M_d}$ is $\frac{{3{a_2} + c}}{4}$ and there is no scope for parallel trade. The quantity that is demanded

$$ {q^A} = \frac{{4{a_1} - 3{a_2} - c}}{4} $$

(A.3)

By charging the low price of the developing country, the profit that the manufacturer earns from the country ${M_d}$

$$ {\Pi_{{Md}}} = \frac{{(3{a_2} - c - 2{a_1})(4{a_1} - 3{a_2} - c)}}{8} $$

(A.4)

Let ${ }\Pi_U^M$ be the total profit the manufacturer earns (from the developed and the developing market) by charging the lower uniform price of the developing country in the developed world. Therefore

$$ \Pi_U^M = \left[ {{\Pi_{{Md}}} = \left\{ {\frac{{(3{a_2} - c - 2{a_1})(4{a_1} - 3{a_2} - c)}}{8}} \right\} + \Pi_M^{{{M_{{dl}}}}} = \frac{{{{({a_2} - c)}^2}}}{8}} \right] $$

(A.5)

If $\Pi_P^M \;>\; \Pi_U^M$, the manufacturer earns higher profit by accommodating parallel trade than by deterring it by charging the lower uniform price of ${M_{{dl}}}$.

Cross-multiplying and simplifying the terms of $\Pi_P^M$ and ${ }\Pi_U^M$ we get the following expressions $5a_1^2 + 6{a_1}{a_2} - 12{a_1}c - 12{a_2}c + 14{c^2} + 3a_2^2$ and $108{a_1}{a_2} - 48a_1^2 - 12{a_1}c - 12{a_2}c + 12{c^2} - 48a_2^2$

$$ \therefore \Pi_P^M - \Pi_U^M = 53a_1^2 + 51a_2^2 + 8{c^2} - 102{a_1}{a_2} $$

(A.6)

For $\Pi_P^M \;>\; \Pi_U^M$, we need to show that

$$ \begin{array}{lll} 53a_1^2 + 51a_2^2 + 8{c^2} \;>\; 102{a_1}{a_2} \hfill \cr \Rightarrow 53a_1^2 + 51a_2^2 - 102{a_1}{a_2} + 8{c^2} \;>\; 0 \hfill \cr \Rightarrow 2a_1^2 + 8{c^2} + {(\sqrt {{51}} a_1 - \sqrt {{51}} a_1)^2} \;>\; 0 \end{array} $$

(A.7)

which is always true. From the above result, we therefore conclude that for all values of ${a_1}{ }$ and ${ }{a_2}$ the strategy of accommodating parallel trade dominates the strategy of deterring parallel trade.

Table A.1 Comparison of retail prices of selected generic products across countries in the year 2002–2003 (prices converted into Indian rupees, conversion rate of exchange considered 1USD = Rs 45.50,1 GBP = Rs 83.51 1 PAK Rs = Rs.84 and 1 Indonesian Rp = Rs.005)