(a) Derive the prot-maximizing and socially optimal levels of output for the rm. Denote them by agand 913\

A firm produces q units of output which it sells for a fixed price P. Let its production cost be q2. Suppose, however, that each unit it produces imposes external harm of h. (a) Derive the profit-maximizing and socially optimal levels of output for the firm. Denote them by qp and q, respectively. How do they compare? Are they both necessarily positive?! (b) Suggest a policy that will induce the firm to produce the socially optimal level of outputi.e., that will result in qp=qs (assuming qs is positive).