A monopolist sells a product at price P and has no cost of production. The demand equation is Q = 2a – P, where Q is quantity and a is a demand shifter.
a. What is the profit equation for the monopolist? b. What is the profit-maximizing price as a function of a? Denote the profit- maximizing price as P. c. What profit is earned as a function of a? Denote the optimal profit at π. d. Now suppose that a is unknown, and the firm must forecast it. The firm sets its price based upon this forecasted value of a,â. The forecast error is a – â. What is the expression for the loss, π* - π(â)? Note that this expression will include both a and â. What relationship does this bear to a quadratic loss function?