There are two firms in the pumpkin industry: C and S. 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 C firm sells and qS is the number that S firm sells. The cost of producing pumpkins for either firm is $0.50 per pumpkin no matter how many pumpkins they produces. 1. Every spring, each of the firms 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 firm last year. In fact, each firm assumes that the other firm will sell the same number this year as its sold last year. So, for example, if firm S sold 400 pumpkins last year, firm C believes that firm S will sell 400 pumpkins again this year. If firm S sold 400 pumpkins last year, what does firm C think the price of pumpkins will be if firm C sells 1,200 pumpkins this year? 2. If firm S sold 400 pumpkins last year, firm C believes that if he sells qtC pumpkins this year then the inverse demand function that he faces is p = 1.75 − qtC/1, 600. Therefore if firm S sold 400 pumpkins last year, firm C’s marginal revenue this year will be 1.75−qtC/800. More generally,if firm S sold qSt-1 pumpkins last year, then firm C believes that if he sells q tC pumpkins this year and his marginal revenue this year will be ___??? 3. Suppose that in year 1, firm C produced 200 pumpkins and firm S produced 1,000 pumpkins. In year 2, how many would firm C produce? How many would firm S produce? 4. Write down two simultaneous equations that could be solved to find outputs qS and qC such that, if firm C is producing qC and firm S is producing qS, then they will both want to produce the same amount in the next period. 5. Solve the two equations you wrote down in the last part for an equilibrium output for each firms.
There are two firms in the pumpkin industry: C and S. 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 C firm sells and qS is the number that S firm sells. The cost of producing pumpkins for either firm is $0.50 per pumpkin no matter how many pumpkins they produces.
1. Every spring, each of the firms 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 firm
last year. In fact, each firm assumes that the other firm will sell the same number this year as
its sold last year. So, for example, if firm S sold 400 pumpkins last year, firm C believes that
firm S will sell 400 pumpkins again this year. If firm S sold 400 pumpkins last year, what does
firm C think the price of pumpkins will be if firm C sells 1,200 pumpkins this year?
2. If firm S sold 400 pumpkins last year, firm C believes that if he sells qtC
pumpkins this year then
the inverse demand function that he faces is p = 1.75 − qtC/1, 600. Therefore if firm S sold 400
pumpkins last year, firm C’s marginal revenue this year will be 1.75−qtC/800. More generally,if firm S sold qSt-1 pumpkins last year, then firm C believes that if he sells q tC pumpkins this
year and his marginal revenue this year will be ___???
3. Suppose that in year 1, firm C produced 200 pumpkins and firm S produced 1,000 pumpkins.
In year 2, how many would firm C produce? How many would firm S produce?
4. Write down two simultaneous equations that could be solved to find outputs qS and qC such
that, if firm C is producing qC and firm S is producing qS, then they will both want to produce
the same amount in the next period.
5. Solve the two equations you wrote down in the last part for an equilibrium output for each
firms.
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