Examine a monopolistic firm. The firm faces a marketdescribed by the demand function p = A - By, where p is the pricethe firm receives if it sells quantity y of output. Thefirm's cost function is given by C (y) = (1/2)y^(2)
(a.) Find the profit-maximizing quantity of output andthe corresponding profit for this firm.
(b.) Show that if the firm could sell more output at the(constant) equilibrium price, it would do so. (To do thistake a derivative of the firm's payoff under the assumption thatprice is constant rather than a function of output, and thenevaluate this derivative at the equilibrium price and quantity from1a.)
(c.) Let p* be the equilibrium price and y* theequilibrium quantity, so that p* = A-By*. Now suppose thedemand in the market shifts, so that the new demand curve is p =A'- B'y*. Hence, if the firm does not change its quantity,its price will also not change. Is the quantity of output y*still optimal, given this new demand curve? If not, will the firm decide to produce more or less?