5.7 ** Consider instances when a pollution tax is equivalent to an output tax by examining the following: (a) Suppose a firm's cost function satisfies assumption 5.2. Show that in this case, an emissions tax is equivalent to a sales tax. Determine the optimal sales tax. (b) Suppose now that a firm's cost function satisfies assumption 5.1. Show that it is in general not possible to achieve a first-best allocation by charging a sales tax. | Assumption 5.1 The cost function C(x,e) is twice continuously differentiable with C()>0, and for any production level x there is an emission level ex such that Ce(x,e) = 0. Furthermore Ce(x, e) 0.