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Flo is a farmer and grows flowers on her farm, which is located right next to Beatrice’s property. Beatrice is a beekeeper. Each of Beatrice’s beehives pollinates an acre of Flo’s flowers. Flo’s cost function is Cf (f) = 5(f − 1 3 b) 2 , and Beatrice’s cost function is Cb(b) = 10(b− 1 2 f) 2 , where f is the number of acres of flowers and b is the number of beehives. Each acre of flowers yields $50 worth of flowers, and each beehive yields $100 worth of honey.
(a) Calculate f and b at the decentralized equilibrium.
(b) Calculate Flo’s and Beatrice’s profits at the decentralized equilibrium.
(c) Is the decentralized allocation Pareto inefficient? Why?
(d) What conditions must the Pareto efficient allocation of f and b satisfy?
e) Calculate the Pareto efficient allocation of f and b and the corresponding profits at this allocation.
(f) Now suppose that the current allocation is the decentralized equilibrium allocation. Suppose that Flo and Beatrice bargain over f and b as follows: Beatrice offers to pay Flo the amount T if Flo produces a certain quantity f. If Flo rejects, both agents stick to the decentralized equilibrium quantities. What will Beatrice offer be? What will be the resulting allocation? What will be the corresponding profits?
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