A. 1. Suppose that a pollution-producing firm faces inverse demand for output y that is given by p(y) = A - y and total cost of production cyz /2. Each unit of output generates z units of pollu- tion that negatively impacts a nearby resident, who has quasilinear preferences represented by the utility function U(m, Z) = m - YZ2, where y is a positive scalar and Z is the total pollution generated. (a) Suppose that the firm acts as a price-setting monopolist. Identify the equilibrium level of pol- lution and describe how the net disutility caused by firm pollution varies with the exogenous parameter values. Next, specify the quantity and price regulations that could be employed to restore efficiency here under the assumption that efficiency is defined by firm profits plus the utility of the nearby resident (i.e., specify the precise quantity and price regulations that should be imposed). Under what conditions (if any) does social efficiency imply that pollution should be eliminated entirely? Is it possible that firm profits actually increase under quantity regulation relative to unregulated monopoly pricing? Be sure to justify your responses. (b) Now, introduce consumer surplus (measured based on the area under the inverse demand curve) as a third component of social welfare (in addition to firm profits and the utility of the nearby res- ident). Derive the change in consumer surplus associated with the quantity regulation from (a). Is total social welfare still unambiguously higher under quantity regulation than in its absence? Is it now possible that the competitive market price (at which p(y) = MC(y)) would maximize this new social welfare metric? Be sure to justify and provide intuition for your responses. Then, discuss how (if at all) the presence of externalities affects the inefficiency of monopoly power relative to perfect competition