Are100b-hw1 - ARE 1008 Spring 2008 M Whitney HOMEWORK l k ‘7 h ‘ wax Due[11 class Thursday April “t 0 W1 h To earn full credit show your work

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Unformatted text preview: ARE 1008 Spring 2008 M. Whitney HOMEWORK l k ‘7 h . . ‘ / wax Due [11 class Thursday, April “t. 0 W1 h To earn full credit, show your work! 61-, j 1 Emmpm, m rm 1 1 l. (33 pts) Suppose that monthly demand for wedding cakes in Valencia is Qd = 970 ~5P. A finn’s cost of producing this product is: Tci = $1280 + 50* q,- + .2* qi 2 a) (7) Suppose that, at present, there are 4 bakeries that supply this product under perfect competition. Find: the individual firm’s supply function; the market supply function; market price; market output; and individual firm output. Also, find each firm’s profit or loss, and industry profit or loss. Based on your results, is this market in long-run equilibrium? If not, what will happen next? b) (6) Now suppose that over time, the market above reaches long-run competitive equilibrium. Find the output produced by each firm; market price; total market output; and the number of firms. Now what is the profit per firm, and for the industry as a whole? c). (4) Suppose that, instead of reaching long run equilibrium as in part b, the 4 bakeries in part a had all been purchased by a single firm, and run as a multiplant monopoly. Find the quantity produced at each plant; total market quantity, price, and the monopolist’s profit or loss (from all 4plants combined). d) (3) Alternatively, suppose that the 4 firms in part a had been purchased by a monopolist, but the monopolist then shut down 3 of the 4 facilities, leaving only a single plant to operate. (So this leaves us with a standard, single-plant monopoly) Now how much is produced, and what is the price? What is the firm’s profit or loss in this scenario? e). (3) Using your answer to part (1, find the elasticity of demand at your solution point, and show that the monopolist’s MR = P(1+ l/Ep) = MC. 0 (10) Again using your answer to part d, graph your results. Label the following: The inverse demand function Marginal revenue function; Marginal cost fimction; The equilibrium price and quantity; The equilibrium level of marginal revenue and marginal cost; Total revenue (shaded in) ' Consumer surplus, producer surplus and total variable costs (label the areas). Now, using your graph, calculate the dollar values of consumer surplus, producer surplus, total variable costs and total social welfare for this market. What is the relationship between producer surplus and profit? 4 2. (4 pts) A California firm holds the copyright on a particular line of collectible trading cards. The total cost of producing packs of these cards is: T.C = 20,000 + .4 Q The market demand for this firm's output is: Qd = 200,000 P '1'2 a. (l) Prove that this demand fimction has a constant elasticity of - 1.2. b. (3) Given that this firm has a monopoly in its product market, what is the profit-maximizing price it should charge? How much output is sold? What is its profit or loss? 3. (8) Draco Industries owns the world’s only two known deposits of a rare gemstone. The two mines it operates have the following cost fimctions: Tcl Tc2 10q,+.lql2 Mine#1 15q2+.05q22 Mine#2 II M a. (4) Suppose demand for the firm’s gemstones is Qd = 400 - 2 P. Find the optimal output for each mine. What is the monopoly price for these gemstones? What is the firm’s profit? b. (4) Now repeat question a, but assume that demand is Qd = 140 .- 10 P. 4. (2) Cooper Park ski resort serves two types of customers: Visitors (V) and locals (L). The firm is the only resort in its area, thus can price as a monopolist. Visitors’ elasticity of demand is -2, while locals’ elasticity of demand is -3. The firm’s marginal cost per lift ticket is $20. The firm plans to attract more locals to its ski run by offering discount coupons in the local newspaper, which is not likely to be read by visitors. What is the optimal price of a lift ticket (the price paid by visitors)? What percent discount should be offered to locals? 5. (4) Donna Smythe runs a bridal shop in Chester City. As she is the only bridal consultant in the area and knows the local customers well, she is able to practice perfect price discrimination when selling custom-fitted wedding dresses. Inverse demand for wedding dresses is P= 8000 - 20 Q The bridal shop’s cost fimction is TC = $12000 + $400 Q How many dresses does Ms. Smythe sell? What is her profit? What range of prices does she charge her customers? Show your result on a graph. What is the deadweight loss of this monopoly? 6. (3) St. Helena Enology Club is a private club that offers fine wines to its members. The firm charges an annual membership fee, plus a fixed price per bottle of wine. The club’s marginal cost per bottle of wine is $12. Suppose a typical customer’s demand for wine is qd = 100 - 2P. What is the club’s optimal membership fee, and the price charged per bottle of wine? How many bottles does each customer buy per year? ...
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This note was uploaded on 05/03/2008 for the course ARE 100B taught by Professor Whitney during the Spring '08 term at UC Davis.

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Are100b-hw1 - ARE 1008 Spring 2008 M Whitney HOMEWORK l k ‘7 h ‘ wax Due[11 class Thursday April “t 0 W1 h To earn full credit show your work

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