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Exercise 1: Monopoly A monopolist's cost function is TC(y) = gy* - by' + 35y +9. It faces the demand function y = 40 - F. Solve for monopolist's output, price, profits and consumer surplus when: (a) Price is unregulated. (b) Price is set such that the monopolist produces the competitive output. Note: Both FOC and SOC need to be checked to determine profit maximization. Exercise 2: Negative Externality A perfectly competitive market exists for wheat. The inverse demand is P = 200 - Q where P is the price of wheat and Q is the total quantity of wheat. The private total cost for the unregulated market is C = 50 + 80Q + 0.502. The production of wheat creates an externality where the total external cost is E = 0.502 (a) Solve for the unregulated competitive equilibrium of wheat and the socially optimal level of wheat. (b) Derive the Pigouvian tax (per unit of output of wheat) that results in the social opti- mum. (c) One big company, WheatsRUs, buys out all the farmers of wheat and becomes a mo- nopolist. Using the same functional forms, solve for the unregulated monopoly equilibrium. (d) Given the socially optimal level of wheat in (a), what is the optimal tax that should be placed on the monopolist