Consider a South Carolina seed company holding the patent of a new seed variety for soybean (monopoly rights). The firm serves farmers across SC and other Southern states. It faces the following inverse demand function, p(q) = 100 -0. 1q, where q is the quantity of seed bags (50 lb.) per week and p is $/bag. The cost function is equal to C(q) = 4q. A. Find the monopolist profit-maximizing output, its price, and its profits. B. To increase the availability of the new seeds in the SC market, the local government is negotiating with the monopolist to produce at the competitive equilibrium output level (i.e., where P=MC). Find the competitive equilibrium output. C. Find the subsidy per unit of output that the government needs to offer the monopolist to induce the firm to produce the competitive equilibrium output you found in part B). (Hint: The total revenue of the monopolist with the subsidy is TR = p(q)q + sq, where s is the subsidy per unit of output). D. What is the total cost that the government incurs with the subsidy? How did profits change after the subsidy?