6. Suppose there are 2 firms in oligopoly market, and the market demand is P = 50 - Q, and MC = 10 + Q₁, i = 1, 2.

(a) \((4\%)\) What are the Cournot equilibrium quantities and price in this market?

(b)(3%) What would be the equilibrium price in this market if the two firms acted as a profit-maximizing cartel?

Suppose now the two firms become Stackelberg duopolists in which Firm 1 is a leader and Firm 2 a follower. Assuming that the market demand is the same as before, but the marginal cost for both firms is now MC = $20. If the follower takes the leader's output as fixed at Q₁, answer the following questions: (c) \((6\%)\) What's the Stackelberg equilibrium quantity for each firm? What's the market price?

(d)(4%) What's the profit for each firm?

7. Suppose that the market for corn is initially in equilibrium and is perfectly competitive. The demand curve can be expressed as P = 10 - Qᵈ; the supply curve is P = 0.25Qᵗ. Quantity is expressed in millions of bushels. Now suppose that the federal government imposes a price floor of $3 per bushel of corn. Answer the following questions: (a) \((3\%)\) What is the size of the surplus created by the price floor?

(b)(3%) Assuming the most efficient producers are active, what's the deadweight loss due to the price floor?

(c)(6%) Assuming the least efficient producers are active, what's the producer surplus (PS) under the price floor? What's the deadweight loss due to the price floor?

8. Consider a market of risk-averse decision makers, each with a utility function U = √I. Each decision maker has an income of $90,000, but faces the possibility of a catastrophic loss of $50,000 in income. Each decision maker can purchase an insurance policy that fully compensates her loss. This insurance policy has a cost of $11,600. Suppose each decision maker potentially has a different probability q of experiencing the loss. (6%) What is the smallest value of q so that a decision maker purchases insurance?

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