A monopolist faces a price function given by P = z(36 - 2Q), where P is price, Q is total output and z is the quality of product sold, which can take on only two values. The monopolist can choose between a low quality product z = 1 or a high-quality product for which z = 2. We assume that marginal cost is is constant at zero. Fixed cost, however, depends on the product design and increases with the quality chose. Specifically, fixed cost is equal to 65z^(2) .
(a) Calculate the profit if the monopoly chooses to sell a low-quality product.
(b) Calculate the profit if the monopoly chooses to sell a high-quality product.