Brown and Smith each own an apple orchard on the outskir
Question and Solution
Brown and Smith each own an apple orchard on the outskirts of Ohio which produce identical apples. Each year, when the a
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Brown and Smith each own an apple orchard on the outskirts of Ohio which produce identical apples. Each year, when the apples on the trees ripen, both Brown and Smith pick all of the apples off their trees, and each of them stores the apples in a building located on the orchard grounds. The cost of picking and storing the apples is zero. Every Wednesday morning after the apples have been harvested, Brown and Smith take some of their apples to the local Farmers Market, where they are offered for sale. The cost of transporting the apples to the market is zero, since they both like to attend the market whether or not they are selling apples. One of the rules at the market, however, is that the sellers have to offer for sale everything that they bring to the market. As it turns out, Brown and Smith are, and always have been, the only apple vendors at the market. Over the years they have observed that the price they get for their apples is given by the relationship: P = 120 - (QB + QS) where QS and QB are the number of bushels of apples offered for sale by Smith and Brown, respectively. a) Suppose Smith expected that Brown was going to bring QB bushels of apples to the market this Wednesday. Assuming that Smith wants to maximize her profits from apple sales, how many apples should Smith bring to the market? The number of bushels Smith should bring is given by the formula: QS = b) In equilibrium, how many apples will both Smith and Brown bring to the market? (Assume that they choose their apple quantities simultaneously.) The number of apples that Smith and Brown will bring is: QS = QB = c) Now, suppose that, on this particular Wednesday, Smith has an early morning appointment with her dentist, after which she will return to her orchard to pick up her apples. Because of the timing of this appointment, she will necessarily arrive at the market after Brown. And, as luck would have it, the dentist is located across the street from the market, so that Smith can see how many apples Brown has already brought to sell as she goes home to get her own apples. Brown knows that Smith will arrive late, and that Smith will know, prior to deciding how many apples to bring, the number that were brought to the market by Brown. How many apples will each bring to the market? The number of apples that Smith and Brown will bring is: QS = QB =
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