I. Show your workings for the following questions.

6. Consider a monopolist which faces an inverse demand curve p(y) = 12-y. The cost function of the monopoly is given by c(y) = y?. (a) What is the monopolist's profit maximizing level of output yM? (b) What price arises when the monopolist chooses quantity yo? (c) Draw a graph of the monopolist's Marginal Cost and Marginal Revenue functions, along with the demand curve. (d) Suppose the government decides to put a tax on this monopolist so that for each unit it sells it has to pay the government $2. What will be the monopolist's output?QUESTION 3 Snow Security Services is a monopolist in the market for freeze-resistant wall-top security cameras. The rm has xed costs of 20 and a constant marginal cost of 5 at all levels of output. The demand function for the market is given by D (p) = 12.5 0.25p. (a) Rewrite demand as the inverse demand function. (h) Set up the monopolist's problem and solve for the optimal price and quantity. (c) Calculate the maximized prot for Snowr Security Services. 9 QUESTION 4 Suppose that the inverse demand function for a monopolist's product is p (q) = 9 0.05q while the rm's total cost function is C(q) = 10+ 10g- 4g2 + 3:13. (3) Plot or sketch carefully the demand curve, marginal revenue curve, and marginal cost curve. ([1) At what volume of output does marginal revenue equal marginal cost? (c) What are the prot- maximizing output and price? (Note: you should check the second-order condition to verify that your answer is a maximum). A) shows that the individual firm can increase sales by lowering the price of output. 43) A perfectly elastic demand function Bj occurs because a perfectly competitive firm can sell all it wishes at the market price, () has a marginal revenue which is always decreasing. DJ shows that a consumer is willing to pay any amount for the product. Table 9-1 Output Total Cost Output Total Cost $527 100 $500 101 501 107 556 102 504 103 506 109 SAD 104 510 110 615 105 518 111 44) Table 9-1 shows the total cost function for a firm operating in a perfectly competitive market. If the market price is $10, then a profit maximizing firm would produce A) 104 units. B) 110 units. C) 109 units. D) 106 units 45) Assume that a firm in a perfectly competitive industry faces the following cost and revenue conditions: ATC -$6; AVC - $3; MR - MC = $5. The firm is A) experiencing economic losses. B) experiencing zero profits. ( earning economic profits, DJ in a position in which it should shut down. 46) In a perfectly competitive market, demand and supply curves intersect at a price of 58. From this we know that, in equilibrium A) the firm is making a positive economic profit at a price of $8 or more. B) the average total cost of producing the good is $8. C) the marginal cost of producing the good is $8. Dj the average variable cost of producing the good is $8. Table 9-2 Output Total Costs Output Total Costs 100 5400 106 101 $427 402 107 102 435 405 108 103 409 445 104 109 414 454 105 110 420 466 111 480 47) In Table 9-2, if price is initially $3.50 and then increases to $7.95, a perfect competitor will A) increase output by 10 units. C) increase output by 4 units. B) increase output by 5 units. D) increase output by 8 units