Quantitative Question Consider a situation where a single upstream firm acts as a monopolist and serves two identical downstream firms that compete in quantities. The downstream firms much purchase one unit of the upstream firm's product at a price of p as an input to produce their own product, but face no other costs. The inverse demand function in the downstream market is p = 200-q 1-92 where q, and q 2 are downstream firm 1 and 2's respective quantities. The upstream firm faces a constant marginal cost of production of 30. a) Find the quantity produced by each downstream firm as a function of the upstream firm's price (Hint: This is just a Cournot problem) b) Find the equilibrium quantities and prices in both the upstream and downstream markets. c) Suppose the upstream firm decided to vertically integrate with one of the downstream firms (Assume that they do not foreclose on the other firm). What do you suppose would happen in this market? (Don't calculate anything here; an explanation is sufficient.)