Question-2 (Duopoly) (60 points) There are two rms 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 = 90 + qs, where qc is the nulnber that C rm sells and gig is the number that S rln sells. The cost of producing pumpkins for either firm is $0.50 per pumpkin no matter how man),r pumpkins they produces. 1. Every spring, each of the rms 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 rm assumes that the other rm will sell the same number this year as its sold last year. So, for example, if rnl S sold 400 pumpkins last year, rm C believes that firm S will sell 400 pumpkins again this year. If rm S sold 400 pumpkins last year. what does firm C think the price of pumpkins will be if rm C sells 1,200 pumpkins this year? OI If firm S sold 400 pumpkins last. year, firm C believes that ifhe sells q'C pumpkins this year then the inverse demand function that he faces is p = 1.75 93-11260\" Therefore if rm 3 sold 400 pumpkins last year, rm C's rnm'ginal revenue this year will be 1.75 5'5? 3" 800. More generally, if rm S sold rigl pumpkins last year. then firm C believe-4 that if he sells (1:27 pumpkins this year and his marginal revenue this year will be _ . Suppose that in year 1. rm C produced 200 pumpkins: and rm S produced 1,000 pumpkins. In year 2, how many would firm C produce? How many would [irm S produce-3 Write down two simultaneous equations that could be solved to [ind outputs 93 and go such that, if rm C is producing qc and rm S is producing 95-, then they will both want to produce the same amount in the next period. . Solve the two equations you wrote down in the last. part for an equilibrium output for each rms