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Unformatted text preview: ARE 1008 Spring 2008
HOMEWORK l k ‘7 h
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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.
- Spring '08