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Unformatted text preview: Econ 1, Fall 2010 Problem Set 4 Solutions University of California, Berkeley Page 1 of 13 Problem Set #4 Solutions Consider an economy with three types of workers—Dharmas, Egberts, and Gregs—who produce yoga lessons, ceramic plates, and cups of coffee respectively. In this economy the prices of yoga lessons and ceramic plates are expressed in cups of coffee. Questions 1 through 5 focus on the supply and demand for plates. Suppose that Egberts are willing to produce plates according to the following rule: at a price of zero, they will make zero plates, for every 1-cup-of-coffee increase in the price of plates, they are willing to make ten additional plates. Note that questions 1 through 5 did not request graphs, and indeed graphs are not needed to solve them. The graphs that appear in these solutions are not necessary, but help to illustrate the respective markets, their equilibria, and attendant consumer and producer surpluses. Note that in the markets described in questions 1 through 5 price (the vertical dimension in the graph) is expressed in cups of coffee per plate, and quantity (the horizontal dimension) is given in plates. Thus any product of price and quantity (represented by an area on the graph) is measured in units of cups of coffee. 1. Suppose that demand for plates follows this rule: if plates cost 10-cups-of-coffee, nobody wants to buy any. Each 1-cup-of-coffee reduction in the price of plates leads consumers to want to buy an additional ten plates. 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 70 80 90 100 price quantity CS PS Econ 1, Fall 2010 Problem Set 4 Solutions University of California, Berkeley Page 2 of 13 a. What is the market equilibrium price of plates in this market? The quantity supplied is given by the equation: Q S = 10 P The quantity demanded is given by the equation: Q D = 100 – 10 P The equilibrium price, P *, is the price at which the quantity supplied equals the quantity demanded—where Q S = Q D . Thus: 10 P * = 100 – 10 P * ⇒ 20 P * = 100 ⇒ P * = 5 The equilibrium price of plates in this market is 5 cups of coffee. b. What is the market equilibrium quantity of plates exchanged in this market? At the equilibrium price, the equilibrium quantity of plates exchanged is given by either the quantity supplied or the quantity demanded: by definition the market equilibrium occurs where these two are the same. Given the equilibrium price found in part a, we have: Q S = 10(5) = 50 Q D = 100 – 10(5) = 100 – 50 = 50 The equilibrium quantity of plates exchanged in this market is 50. c. What is the consumer surplus in this market, in units of cups of coffee? The consumer surplus (CS) is equal to the area of below the demand curve and above the equilibrium price. That is, in this case it is equal to the area of a triangle with height 5 and base 50. The consumer surplus is thus: g∙gG ¡ = ¢¡g _ The consumer surplus is equal to 125 cups of coffee....
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This note was uploaded on 10/04/2011 for the course ECON 1 taught by Professor Martholney during the Fall '08 term at Berkeley.
- Fall '08