Boris works across town for Mac the farmer. Mac produces 50 bunches of kale per day, with Cobb-Douglas output Q_kale = LK, and faces $10 per machine hour capital rents, which are all paid by a government grant (all kale farmers who operate efficiently face zero fixed costs), and pays Boris $20 per hour for his labour. Boris then takes his pay and consumes kale and other (Marshallian) goods according to U(k,y) = 20k - 2k² + y

Sketch Boris utility curve, and his budget constraint if kale costs $4 per bunch. Recall that Boris budget comes from his daily pay.

Do Boris preferences satisfy the rules of preference ordering? Are there any constraints on his consumption of either good?

Determine Boris optimal consumption of kale each day.

How many other goods can Boris purchase?

If capital is fixed at the optimal level in the short run, determine the efficient price if Mac can act as a monopolist. Sketch the supply and demand curves, and identify the monopoly equilibrium.

Donald is another farmer who faces identical costs as Mac. He is considering entering the market.

Determine how much profit Mac loses when Donald enters the market.

Solve the profit for both farms once Donald has established himself in the market.

Mac realizes that both farmers could make more money if they can agree to collude. If collusion costs the farmers $4 per day, can the two farmers sustain a collusive agreement under a grim-trigger strategy? Assume they face and interest rate of 25%.