1) Double marginalization and vertical mergers Consider downstream and upstream firms which are both monopolies. Each unit of downstream output requires exactly one unit of an upstream product as an input and also incurs other marginal costs of 5 per unit. The upstream firm produces the input at a marginal cost of 5 per unit. Let the demand for the product sold by the downstream firm be given by Q(P) = 50 - P where P is the downstream retail price. a) Suppose that the upstream firm sets a price w for the input to the downstream firm. Derive the profit maximizing price P for the downstream firm as a function of w. Use this function to obtain the derived demand for the upstream firm as a function of w. b) Use your answer to part a) to derive the profit function for the upstream firm as a function of w. Derive the profit-maximizing choice of w by the upstream firm. Calculate the choice of P given this profit-maximizing choice of w. Calculate the quantity sold by the downstream firm and the profits of the two firms. c) Now assume that the two firms merge. Write their joint profit function as a function of the downstream price P. Calculate the post-merger profit-maximizing downstream price, the resulting output, and the profits of the merged firm. d) What is the impact of this merger on total industry profits? What about on prices P charged to consumers