Question B2: Corrective taxes A firm uses two dirty inputs, a and y, which contribute to output q(z,y) and external harm H(x, y). The output price is p and the price of each input is equal to one. [25 marks] a) The socially efficient levels of the two inputs are those that maximise the firm's profits minus external harm, pq(x,y)-z-y-H(x,y). Take first-order conditions with respect to z and y. b) Next, consider the firm's profit maximisation problem. First, assume that output cannot be taxed, but both inputs can. If the input taxes are 7 and Ty respectively, the firm maximises pq(x, y)(1+T)-(1+y)y. Take first-order conditions with respect to z and y. What should 7 and 7, be set to, to implement social efficiency? c) Now imagine that neither input can be taxed, although output q can be. If the tax on each unit of output is , what will the firm maximise? Take first-order conditions with respect to z and y. d) Under what conditions will it be possible to implement social efficiency with an output tax alone? Explain.