On their own, firms have little incentive to invest in pollution abating technologies such assmokestack filters (a capital good). As a result, governments have increasingly turned to "cap-and-trade" programs. Under these programs the government puts an overall "cap" on the amount of permissible pollution and firms are permitted to pollute only to the extent to which they own sufficient numbers of pollution permits or \vouchers". If a firm does not need all of its vouchers, it can sell them at a market price pv to firms that require more. In this writing assignment we will examine the response of firms, in both the short run and long run, to the introduction of a Cap-and-Trade system.

Consider the production of thingamabobs { which sell at the market price p { by firms using a technology that emits pollution through smokestacks. The technology for producing thingamabobs requires capital (with rental price r) and labor (with wage w) and, without considering pollution, has decreasing returns to scale. Imagine that firms are different in their ability to mix inputs to produce output. As such, some firms have lower operating costs and can earn higher profits.

In particular, suppose that firms possess the following features:

A. Under the Cap-and-Trade system, each firm must ensure that it has sufficient pollution vouchers v to emit the level of pollution that escapes the smokestacks, but it can reduce the pollution by installing increasingly sophisticated smokestack filters s that cost ps per unit.

B. Relatively little pollution is emitted initially in the production process, but as the factory is used more intensively, pollution per unit of output increases { and thus more pollution vouchers have to be purchased per unit absent any pollution abating smokestack filters.

C. Smokestack filters are such that initial investments in filters yield high reductions in pollution, but as additional filters are added, the marginal reduction in pollution declines. You can now think of the firm as using two additional inputs { pollution vouchers and smokestack filters { to produce thingamabobs legally.

D. Before the introduction of the Cap-and-Trade system, each firm producing thingam-abobs holds some positive amount of capital { a sunk cost { and zero smokestack filters.

Explain how the introduction of this policy will affect the production decision of firms.