Y7

Problem III: In a perfectly competitive market in the short run, demand is given by the function p = 100 - 0.03 Q where p is the good's price and Q is market demand. There are 100 identical firms, each with the variable-cost function vc(q) = 4 q+ 2.5 q2 where q is the firm's quantity produced. Fixed costs are zero for all firms. a. Show that for any positive quantity q, Mc(q) > AVC(q). What does this imply about firms' supply functions? b. Compute the supply function for an individual firm, and the market supply function. c. Find the equiilbrium price and quantity. d. Find the profits of an individual firm in the equilibrium. 6+ 6+ 6+6 = 24 marks, plus 1 mark for your answer to question 27 or 29 (see instructions at those questions) = 25 marks totalProblem III: In a perfectly competitive market in the short run, demand is given by the function p = 100 - 0.03 Q where p is the good's price and Q is market demand. There are 100 identical firms, each with the variable-cost function vc(q) = 4 q+ 2.5 q2 where q is the firm's quantity produced. Fixed costs are zero for all firms. a. Show that for any positive quantity q, Mc(q) > AVC(q). What does this imply about firms' supply functions? b. Compute the supply function for an individual firm, and the market supply function. c. Find the equiilbrium price and quantity. d. Find the profits of an individual firm in the equilibrium. 6+ 6+ 6+6 = 24 marks, plus 1 mark for your answer to question 27 or 29 (see instructions at those questions) = 25 marks total