f. In Chapter 14, we briefly mentioned the term decreasing cost industries, industries in which the long-run industry supply curve is downward sloping despite the fact that all firms might have identical production technologies. Suppose that in our example the pollution causes a decrease rather than an increase in (recurring) fixed costs for firms. Would such a positive externality be another way of giving rise to a decreasing cost industry?

B. * Suppose that each firm’s (long-run) cost curve is given by c1x2 5 bx 2 1 dX, where x is the firm’s output level and X is the output level of the whole industry. Note that x is contained in X, and thus we could write the cost function as c1x2 5 bx 2 1 dx 1 dX, where X is the output produced by all other firms. When each firm is small relative to the industry, however, the impact of a single firm’s pollution output on its own production cost is negligible, and it is a good approximation (that makes the problem a lot easier to solve) to simply write a single firm’s cost curve as c1x2 5 bx 2 1 dX and treat X as a fixed amount that the firm cannot influence. Furthermore, if all firms are identical, it is reasonable to assume that all firms produce the same output level x. Letting N denote the number of firms in the industry, we can therefore write X 5 Nx and rewrite the cost function for an individual firm as c1x2 5 bx 2 1 dN x.