You can answer just Q6.

ILIOTOPSOILy. 5. There are a large number of identical firms in a perfectly competitive industry. The market demand is given by D(p) = a - bP, where a > 0 and b > 0. A typical firm's long-run average cost function is given by LRAC(q) = k - lq + mq2, where k > 0, l > 0, m > 0 and k > Am. a Derive the expression of the long-run equilibrium output and price for a typical firm in this market. b) How many identical firms will there be when this industry is in long-run equilibrium? 6. Suppose a competitive firm's production function is q(x) = ax3 -b, where a > 0 and b 2 0. q is the number of final product per week. x is the number of input. The cost of one unit of x is c, where c > 0. a What is the firm's output level and profit at price of po ! b) Suppose b = 0. At what price does the firm reach the shut-down point in the short run