5) (10 points) Consider an upstream and downstream monopolist problem. The upstream monopolist sells inputs, r, to the d

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5 10 Points Consider An Upstream And Downstream Monopolist Problem The Upstream Monopolist Sells Inputs R To The D 1 (47.32 KiB) Viewed 40 times

5) (10 points) Consider an upstream and downstream monopolist problem. The upstream monopolist sells inputs, r, to the downstream monopolist at the price q and faces the cost of producing output c(x) = 20x²/2 with the marginal cost 20.x. The downstream monopolist uses the inputs to produce output, y, with the production function y x. The downstream monopolist faces the inverse demand curve p(y) = 200 10y with marginal revenue M Rdownstream = 200 20y and faces the cost function c(y) = qy with marginal cost of q per unit of output. (Hint: The marginal revenue of the upstream monopolist is M Rupstream = 200 - 40x.) - a) Calculate q, p, y and x. Additionally calculate the the profit for both the upstream and downstream monopolist. b) Suppose the downstream monopolist purchased the upstream monopolist, what would be the values of p, y and z. Note that the firm no longer has to pay q because they produce the input themselves.