For many firms, production takes place in two or more different plants whose operating costs can differ. In this question you will be asked to set up a multiple plant monopolist optimization model and economically interpret the marginal condition for optimal production. To this end, let p() be the inverse demand function facing the multiple plant monopolist, where (derivative of )p(y1 + y2 ) < 0, y1 is the output produced at plant 1, and y2 is the output produced at plant 2. Note that there is one good produced by the multiple plant monopolist, its just that now it is produced at two different plants. Let c1() and c2() be the total cost functions for producing the output at plant 1 and plant 2, respectively, where (derivative of) c(y1) > 0 and (derivative of)
c2(y2) > 0 are assumed to hold.
a)What would be the multiple plant monopolists profit maximization problem? and how would I derive the FONC? First Order Necessary Condition for that problem?