Controlling Prices to Increase Social Welfare

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**How to Maximize Social Welfare**

On the graph below, you can clearly see how the ratio of social cost to profit from the previous slide decreases as price approaches zero.

Remember that Klemperer shows us that we need to reduce this ratio to increase total social welfare. This suggests that if we could somehow limit the price that a firm sets on its invention to some value below the monopoly price, we could make the patent less costly to society. On the next slide, we discuss how anti-trust policy can be used to manipulate the price.

As we attempt to increase social welfare by reducing the price, the firm's profit, π will decrease as well. How, then, do we keep the firm's total reward, V, constant? Recall that

[2]

Thus, as π is reduced, for a while we can keep V constant by increasing L, the length of the patent. However, this process cannot go on indefinitely. At some point, reducing π below a certain value won't be offset even by increasing L to infinity. This means that there is a minimal positive profit flow, subject to equation [2].

Though the ratio of social cost to profit approaches zero as price approaches zero, it is not immediately
obvious that choosing the minimal *feasible* profit flow minimizes this ratio. It turns out that this is true
if V is small enough, so for small rewards, profit flow should be set as low as possible, with the resulting L large.
In fact, Gilbert and Shapiro identify several more assumptions under which arbitrarily long
patents are optimal. These include:

- Small enough V, as just mentioned
- Expressing social cost in terms of profit, s(π), s''(π)>0, so increasing profit is increasingly costly in terms of social welfare.
- Both social cost and profit are concave when written in terms of firm output.