Suppose now that in addition to levying a fine, the government can confiscate illegally produced goods. The economic value of the goods that are confiscated is P. Since there is a probability p that a unit of the good will be confiscated, the expected value of a confiscated good is pP. Since these goods are destroyed, this is a social cost. The per unit opportunity cost of the resources that are used to produce the goods is c. Therefore the per unit social cost of each unit that is produced is:
But we also know that:
This implies that:
Therefore the social cost of each unit that is produced is:
Since the fine revenue is returned in a lump-sum fashion to consumers, total welfare when goods are confiscated is:
It may seem slightly strange that the price P enters negatively into the expression for welfare here. Ordinarily, P is a transfer from consumers to producers. It enters here, however, because of the fact that goods are confiscated and destroyed.
What is the optimal enforcement policy in this case? The change in welfare with respect to p is:
Now Q (p) = so we get:
If demand for the good is inelastic (so that 1 + ?D > 0), and if B'(Q) > h, then this expression is negative. In this case, it can never be efficient to have p > 0. This implies that if the external harm from consumption of the good is sufficiently low, no goods should be confiscated. Instead, if fines can be increased without limit, then the optimal policy is to not confiscate any goods, set p & 0, and set f very high, so that pf = h.
On the other hand, if demand for the good is elastic, or if B'(Q) < h, then the expression in (9.35) may be positive for some positive values of p. If fines cannot be increased without limit, then the optimal enforcement policy p* obeys:
The right-hand side is the marginal resource cost of increasing enforcement. The left-hand side is the marginal benefit of increasing enforcement, and is comprised of two parts. The term [B'(Q) - h]Q'(p*) is the marginal welfare gain that comes about as consumption is reduced and there is less external harm. If the external harm h is sufficiently high, this term is positive. The term -Q[1 + ?DW(p*) is the change in the resource costs as fewer goods are produced and confiscated. When demand is elastic (so that 1 + ?D < 0), this term is also positive, so resource costs decline as p rises.