Assume that a profit maximizing monopolist faces an inverse demand function give by p(.), where p'(y),0, and a total cost function given by c(y), where c'(y)>0. Suppose the government wishes to combat the undesirable allocational effects of a monopoly through the use of a subsidy.

a)Set up the monopolists profit maximization problem and derive the FONC in the presence of the per unit subsidy on output.

b)Show the competitive output inducing subsidy can be written as s=p(y_c)-MR(y_c)... (note** y_c is the same as saying the output of a competitive industry).