Legal rules in competitive markets: The case of two industries
The previous sections considered legal rules in market settings when firms in an industry created external harm, but this harm was assumed not to impact on another market or industry. We now relax this assumption. That is, suppose that there are two industries, i and v. Industry i (the 'injuring' industry) imposes a cost on industry v (the 'victim' industry). Both markets are perfectly competitive. To simplify the analysis, we make a series of assumptions:
- • Consumers of i and v regard the goods as neither substitutes nor complements. The benefits of consumption of each good are identical, so that the industries have the same demand curves, Qi = Qv ^ иЩ) = u'(Qv).
- • Firms in each industry have identical constant marginal costs of
ci = cv = c.
- •As a result of the constant marginal cost assumption, we can treat firms in each industry as a single representative price taking firm. The representative firm in industry i produces Qt units of output, and the firm in industry v produces Qv units of output.
- • The marginal costs of care in each industry i are constant and equal to Wj per unit of the good produced.
- • The expected harm per unit of the good is constant (but obviously depends on the level of care taken per unit), and is equal to H(x;).
Under these conditions, total welfare is:
Notice that the harm here has the characteristics of a public bad - one unit of output produced in industry i affects all firms in industry v. The situation we have in mind is as follows. Suppose that firms in industry i use a production technique which emits pollution into a river system. Industry v uses water in the river system to produce beer. The greater the total output of industry i, the greater is the total amount of water pollution. Contaminated water harms the beer industry, and beer-producing firms cannot take actions (other than reducing their production levels) to reduce this harm. The per unit costs to the beer industry of water pollution are H(xt ). The total harm of pollution rises with the quantity produced in both industries.
The efficiency conditions are:
Equation (4.12) states that good i should be produced up to the point where the marginal consumption benefits equal the marginal costs of care, plus the marginal costs of harm (which depend on the output in industry v). Expression (4.13) is similar, and states that good v should be produced up to the point where the marginal consumption benefits equal the marginal costs of harm (which depend on output in industry i). Equation (4.14) says that care should be taken up until the point where the marginal cost is equal to the sum of the marginal benefits, — Q*H'(x*). Equation (4.14) is therefore a Samuelson-type condition for public goods [see Samuelson (1954, 1955)].