Question

4. Carl and Simon are two rival pumpkin growers who sell their pumpkins at the Farmers’ Market in Lake Witchisit, Minnesota. They are the only sellers of pumpkins at the market, where the demand function for pumpkins is q = 3, 200 − 1, 600p. The total number of pumpkins sold at the market is q = qC + qS, where qC is the number that Carl sells, and qS is the number that Simon sells. The cost of producing pumpkins for either farmer is $.50 per pumpkin no matter how many pumpkins he produces.

(a) What is the inverse demand function for pumpkins at the Farmers’ Market? What is the marginal cost of producing a pumpkin for either farmer?

(b) Every spring, each of the farmers decides how many pumpkins to grow. They both know the local demand function and they each know how many pumpkins were sold by the other farmer last year. In fact, each farmer assumes that the other farmer will sell the same number this year as he sold last year. So, for example, if Simon sold 400 pumpkins last year, Carl believes that Simon will sell 400 pumpkins again this year. If Simon sold 400 pumpkins last year, what does Carl think the price of pumpkins will be if Carl sells 1,200 pumpkins this year?

Answer 1