A2-5. Suppose a firm operating in a perfectly competitive industry has costs in the short run given by: SRTC = 8 + 1/2q2 and therefore MC = q. (a) Derive expressions for fixed costs (FC), those that do not vary with output, variable costs (VC), those that do vary with output, average variable cost (AVC), and average total cost (ATC). [4] (b) At what quantity is AVC at its minimum (at what AVC level)? At what quantity is ATC at its minimum (at what ATC level)? Calculate ATC at q = 2 and q = 8 and sketch MC, AVC and ATC between 9 0 and q-8. [6] (c) Assuming that the firm is a price-taker operating in a competitive market, derive an expression for the firm's supply curve, (the profit maximizing output for the firm as a function of the market price, i.e., qs= f(p). Assuming the firm is one of 100 identical firms in the industry, what is the short-run supply curve for the industry, i.e., QS =f(p)? If demand is given by QD = 1000 - 100p, what are the short-run equilibrium price, market quantity, and firm quantity? Is this a long-run equilibrium? [Hint: Calculate firm profit in equilibrium.] [6] (d) If the minimum point of the short run ATC curve for all firms(existing and potential) is also the minimum point of the long run average cost curve (LRAC), calculate the long-run equilibrium price, market quantity, and firm quantity. What is the long-run equilibrium number of firms in the industry? [4]