Copyright enforcement is often only possible for high-value consumers – it is easier to enforce a claim in the US than in Kenya, for instance. In the absence of enforcement, consumers can purchase bootleg copies, assumed to be of lower quality. How do firms react to such “targeted” enforcement?
Note that piracy doesn’t mean copies can’t be sold: since the bootlegged copies are not perfect, the original firm can sell their product at a price equal to the difference in inverse demands for the real and bootleg versions. Let q be the quantity the firm chooses to sell. Let E be the cutoff such that those with higher willingness to pay than the inverse demand at E cannot buy bootleg copies and those with lower willingness to pay can buy bootlegs. No price discrimination among groups is possible. If the firm wants to sells more than q(E), then it must choose a price to compete with bootleg copies, choosing q to maximize (V(q)-v(q))q, where V is inverse demand for the original good and v is inverse demand for the pirated good which consumers can acquire at cost zero. Alternatively, the firm can choose a quantity less than q(E), in which there is no competition with bootleg copies; in this case, a price higher than that prevailing in monopoly will be chosen, since only high-value consumers are being sold to.
When E is low, the scope for selling to only high-value consumers is low, so the firm competes with bootlegs and chooses a low price. As E increases, a level of enforcement is reached such that the firm sells only to high-value consumers at a high price, lowering consumer surplus both among those consumers (who pay a higher price), and among lower-value consumers who switch for original to pirated copies for which they have a lower willingness-to-pay; note here that higher enforcement increases the amount of piracy since at the discontinuity, the firm raises its price in response to stronger enforcement. Once E is high enough that the firm is choosing the no-enforcement monopoly price, increasing enforcement further strictly lowers total surplus, since the firm will never sell to the very low-value consumers, and high enforcement just means low-value consumers can’t buy pirated copies.
It’s strange that economists study IP/knowledge goods/zero marginal cost goods so infrequently, but some of the reason is surely because we all realize that the current worldwide IP regime is utter nonsense, economically. The relevant tradeoff is between incentive for new good creation and incentive for widespread dissemination at marginal cost of existing goods. An arbitrarily small number of economists think current US/EU/WIPO rules are too weak; rather, the opposite holds. In the toy model in the present paper, for instance, welfare is maximized at zero enforcement, even though pirated copies are only marginally substitutable. To a young economist, there seems very little incentive to work on copyright/patent issues, since policymakers have shown no willingness to incorporate even the most basic and obvious insights into the system which we already know…
http://www.bus.indiana.edu/riharbau/piracy.pdf (Working paper – forthcoming in Journal of Industrial Economics; I see on Harbaugh’s website that before he was an economist, he was the guy behind zhongwen.com, which a decade ago was substantially responsible for my not failing Chinese classes. Small world.)