3 Question 2 (20 points) A monopolistic manufacturer (upstream) is linked to a monopolistic dealer (downstream), who sells the manufacturer's product. Demand for the product is P(Q) = 300 -2Q. The manufacturer has a constant marginal cost of 100 while the dealer has no costs (other than any imposed by the manufacturer). Throughout this question you must show all your workings. (a) Suppose that the manufacturer sells each unit of output to the dealer for a per unit price of W. (i) Derive the profit maximising number of units sold by the dealer as a function of W. [10 marks] (ii) Derive the manufacturer's profit maximising choice of W. [10 marks] (iii) Calculate the two firms' profits. [10 marks] (b) Now suppose that the manufacturer uses a two-part tariff (w, f). where f is the fixed charge. Find the (w, f ) combination that maximises the manufacturer's profit and explain why this profit is higher than its profit in (a)(iii). [10 marks] (c) Find the range of W values that yield both firms higher payoffs than in (a)(iii) and give an example (with calculations) of a (w, f ) combination that achieves this. Draw a diagram in [W. joint profit]-space to illustrate your result. [40 marks] (d) To what extent do you think the model in this question provides useful insights into vertical business relationships? [20 marks] Format BIU