Abatement of Pollution in Models with Stochastic Penalties

Abstract

Suppose a competitive firm pollutes. In the absence of regulation, the firm's instantaneous profit function is 7r(q) = pq Co where q is output, p is price, is variable cost, and Co is fixed cost. Assume V(0) = 0 and V(q) > 0. The latter condition implies iT(q) C3, and vice versa. The firm will not pay $1,000 for compliance to avoid a $10 fine. Conversely, the firm is better off to pay $1,000 for compliance than to be fined $2,000. In either case, the firm does not change its output. The effect of a fixed fine on abatement is not continuous except trivially. Either there is no effect, or there is a jump from the original level of abatement if the firm complies. Suppose instead of a fixed fine, there is a fine of y dollars per unit of output. Then under non-compliance the profit function is T (q) y q, and maximum profit under non-