Suppose that the pumpkin market in Lake Witchisit is as we described it in the last problem
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(a) If Carl plants enough pumpkins to yield qtC this year, then Simon knows that the profit-maximizing amount to produce this year is _______.
(b) When Carl plants his pumpkins, he understands how Simon will make his decision. Therefore Carl knows that the amount that Simon will produce this year will be determined by the amount that Carl produces. In particular, if Carl’s output is qtC, then Simon will produce and sell 1, 200 – qtC /2 and the total output of the two producers will be _______. Therefore Carl knows that if his own output is qC, the price of pumpkins in the market will be _______.
(c) In the last part of the problem, you found how the price of pumpkins this year in the Farmers’ Market is related to the number of pumpkins that Carl produces this year. Now write an expression for Carl’s total revenue in year t as a function of his own output, _______. Write an expression for Carl’s marginal revenue in year t as a function of _______.
(d) Find the profit-maximizing output for Carl. _______. Find the profit-maximizing output for Simon. 600. Find the equilibrium price of pumpkins in the Lake Witchisit Farmers’ Market. _______. How much profit does Carl make? _______. How much profit does Simon make? _______. An equilibrium of the type we discuss here is known as a _______ equilibrium.
(e) If he wanted to, it would be possible for Carl to delay his planting until the same time that Simon planted so that neither of them would know the other’s plans for this year when he planted. Would it be in Carl’s interest to do this? Explain. (Hint: What are Carl’s profits in the equilibrium above? How do they compare with his profits in Cournot equilibrium?) _______.
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