Question

arl and Simon are two rival pumpkin growers who sell their 27.1 (0) C 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 qs, where qc is the number that Carl sells 323 NAME mber that Simon sells. The cost of producing pu mpkins for either farmer is $.50 per pumpkin no matter how many pumpkins he produces (a) The inverse demand function for pumpkins at the Farmers' Market is 2and b 1/1,600. The c+qs), where a - $.50 marginal cost of producing a pumpkin for either farmer is (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 ar. 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 were sold by the other farmer last ye pumpkins will be if Carl sells 1,200 pumpkins this year? 1 If

Answer 1

Q = 3200 - 1600 P 1600 P = 3200 - Q P = 2- 0.000 625 Ac = (2 - .000 625 (qc - qs)) q_c = 0.5 ac Partialdifferential A_c/ Partialdifferential q_c = 2 - 0.00125 q_c - 0.00625 q_s - 0.5 = 0. 1.5 - 0.000625/0.0015 qs = q_c Symmetry directly 1.5 - 0.000625 qc/1.00125 = q_s The equilibrium is where because if it will always for the player producing case its because with same cost will not cutlass So stability \r\n 0.00125 qc + 0.000625 y_s = 1.5 times 2 0.000625 q_c + 0.00125 q_s = 1.5 0.0025 q_c + 0.00125 q_s = 3 0.000625 q_c + 0.001 = 1.5 q_c = 1.5/0.001875 = 800 q_c = q_s = 800