Homework # 2 1. Consider a perfectlyr competitive firm with a total cost function given by TC = q: + 100 . a) If the price of output is 860; how much output should the rm produce? b) Find the rms prots at this level of output. c) Find the equation of the firms short-run supply curve. :31) If there are 100 identical rms in the market. nd the equation of the industry supply curve. 2. Widgets are produced by a number of identical firms under conditions of perfect competition. Demand for widgets is given by Q = 3000 5.013. The total long-run production cost for a typical firm is given by [To] = gr; 20gr + 400. a) Derive the long-run equilibrium price and quantity. How many firms are in the market? What is the output and prot of the typical rm? b) Suppose the demand for widgets increases to Q = 3000] \"SP. Assuming that in the short run the cost given above applies as well and new entry into the widget market is impossible I:i_e.= the number of rms is xed at the level that you derived in part a; derive the new: short-run equilibrium price and quantity. What is the output and prot of the typical rm\"? c) Since the widget market is perfectly competitive; entry into the market is 'ee in the long run. Derive the new longrun equilibrium price and quantity after the increase in demand\".J How many rms are in the market? What is the output and profit of the typical rm?I 3. The licorice industry is perfectly competitive. Each of the indusn'yis identical firms produces 2 million strings of licorice per year. The strings have an average cost of $133} each; and they sell for $0.31} each. a) What is the marginal cost of strings? Why? b) Is this industry in longrun equilibrium? Why or why not? 4. A monopolist can produce at constant average and marginal cost of AC = MC = 5. The firm faces a demand curve given by Q = 53 P. a) Derive the profitmaximizing pricequantity combination for the monopolist. Also. calculate the monopolist's profits. b) Suppose that the cost structure would be unaffected by a change in the market structure. Derive the equilibrium if the market operated under conditions of perfect competition. c) Derive the consumer surplus in parts a) and b} and the deadweight loss 'om monopoly. 5. In the market for spicy salsa sauce; the market demand is given by Q = SUCH] IUDP. The salsa industry is currently perfectly competitive with a constant marginal cost of $25 and no fixed costs. An entrepreneurial salsa producer is trying to monopolize the market. If this were successiL her access to a superior production technology would decrease the constant marginal cost to 816 (there are still no fixed co sts). a) Find the equilibrium output and prices under perfect competition and monopoly. b) Calculate the change in consumer and producer surplus 'om the monopolization of the salsa market. 1Iii-"hat is the deadweight loss from monopolization'.' Draw a graph to explain your answer. s. A monopolist faces a demand curve that is given by Q{ p} = Jan"5. vt-here I; is equal to the absolute value of the ovvnprice elasticity of demand. This demand curve turns out to have a constant elasticity of demand. i.e.; the absolute value of the elasticity of demand is equal to I} for all levels of output (in general; and for linear demand in particular; this is not true). Suppose that marginal cost is constant and equal to 8113MB; that there are no fixed costs. and that I; = 2 . Derive the monopolist's profitmaximizing price and quantity. 7". Suppose a perfectly competitive industry can produce vvidgets at a constant marginal cost of 3113 per unit. If the industry is monopolized. marginal cost rises to $12 per unit because $2 per unit must he paid to lobbyists to retain the widget producers favored position. Suppose the market demand for widgets is given by Q 2 LEGO 5GP. a) Derive price and quantity in the vvidget market under perfect competition and monopoly. b) Derive the loss of consumer surplus 'om monopolization of vvidget production. c} lGraph your results and discuss hovv they differ from the standard welfare comparison betvaeen perfect competition and monopoly