Consider a market for a homogeneous product. The cost of production is C(y) = cy. Each buyer is interested in getting one unit of the product. There are two types of consumers: 1 and 2. Their utilities of getting one unit at price p is ; p, where 2 > > c. Their respective numbers are and N. - a) Characterize, in terms of the parameters, the monopoly price and quantity in this market. (2 points) b) Find the prices and quantities sold by a perfectly discriminating monopolist. (2 points) c) Suppose that the firm cannot differentiate buyers' types, but can offer different packages in the form of (p, t), where p is the price and t is the waiting time for the product. Let w; be the cost incurred by an i-type buyer for waiting one unit time. Assume W > W. If it turns out that it is profitable for the firm to make a single offer (p,t), what would be the value of t in such an offer? (2 points) d) Show that if it is profitable for the firm to offer more than one package (p,t), then it has to be that N(W2 W) > NW. (2 points) - e) Assume that the parameters satisfy - - W1 W2-W1 (2 ) > c and (W2 W) > NW. Derive the profit-maximizing package and characterize the buyers' behavior. (2 points)