ECON 310 – Spring 2006 (ticket #16388) Name: _A. Key________________ Exam 1 - Version N Multiple Choice: (circle the letter of the best response; 4 points each) 1) Consider a market in which demand is given by the function ppD 2100)( −= . In this market, demand is c. elastic at all prices above 25=p . 2) Consider a consumer with an Engel curve for commodity one that is negatively sloped at the current level of income. It follows that b. commodity one is an inferior good. 3) Consider the market for lemons. Suppose demand in this market were to increase, with no change in supply. This change would result in a. an increase in both equilibrium price and equilibrium quantity. 4) Paula’s utility is given by 2132)( xxXU+=. It follows that d. the bundle )6,1(=A is preferred to the bundle )2,5(=B (that is, BA  ). 5) The value of Indirect Utility should e. All of the above answers are correct. 6) Retief is indifferent between )16,2(=A and )4,6(=B (that is, BA~). Which of the following must be true? d. “If his preferences are convex, then he prefers the bundle )10,4(=E to the bundle )16,2(=A (that is, EA ≺ ).” 7) By definition, good one is a Giffen good if a. an increase in 1p leads to increased consumption of good one. 8) Normative Analysis e. All of the above answers are correct. 9) The Cross-Price Elasticity of Demand for Coke with respect to the Price of Pepsi is (.48). This value implies that: b. A decrease in the price of Pepsi will lead to a decrease in demand for Coke. 10) Consider a market in which both the Law of Demand and Law of Supply hold, and further 20)8( =D and 50)8(=S . It must be that: a. there is “excess supply” at a price of 12=p .11) Hiring 40 units of labor and 10 units of capital a. would produce 800)10)(40(40 = units of output. 12) For this firm, the Marginal Product of Labor is c. “Diminishing,” since LKMPL20= becomes smaller as more labor is hired. 13) The Marginal Rate of Technical Substitution e. More than one of the above answers is correct. 14) This production process exhibits b. Constant Returns to Scale, since ),(),( KLSFSKSLF= for any 1>S . 15) Consider a market in which demand is given by the linear function ppD 4200)( −= . If price were to decrease from 40=p to 30=p , Consumers’ Surplus would c. increase by 600. 16) As the price of hotdogs decreases from 3=Hp to 2=Lp , Richard increases his consumption by 7 units as a result of the “Substitution Effect” and increases his consumption by 5 units as a result of the “Income Effect.” From this information, it follows that e. None of the above answers are correct. 17) The income elasticity of demand for “Fresh Peas” is 05.1=ε. This value suggests that c. “Fresh Peas” are a normal good, since 005.1 >=ε. 18) Gregory’s indirect utility is denoted by the function ()IppV ,,21. Suppose the price of good one were to decrease from 1p to 1ˆp (with I and 2p fixed). The Compensating Variation in Income for this price decrease, denoted CV , must satisfy d. ()()IppVCVIppV ,,,,ˆ2121=− . 19) The preferences of this consumer a. are “monotonic,” since each marginal utility is never negative. 20) If the consumer can afford the bundle )5,10(=A but cannot afford the bundle )10,5(=B it follows that e. All of the above answers are correct. 21) With income of 150=I , the bundle )25,25(=X c. does not maximize utility, since 214221=≠MUMU.“Short Answer” Question: 1. Ernie’s utility for =1x (wine) and =2x (steak) is given by 213)( xxXU=. It follows that 213xMU = and 123xMU=. Each unit of wine costs 1p ; each unit of steak costs 2p ; Ernie has income of I. a. Graphically illustrate the solution to Ernie’s “Utility Maximization Problem.” (3 points) b. State two equations that his “utility maximizing consumption bundle” must satisfy. (3 points) (i): Ixpxp=+2211 (ii): 212,1ppMRS = ⇒ 2112ppxx= c. Showing all work, derive the functional forms of ),,(21*1Ippx and ),,(21*2Ippx . (6 points) Rearranging Condition (ii) we see that 1212xppx =. Substituting this expression into Condition (i) for 2x , we have: Ixpppxp =+121211. This equation simplifies to Ixp=112 . It follows that 121*12),,(pIIppx = . Since 1212xppx =, this implies 221*22),,(pIIppx = . d. Determine the functional form of Ernie’s “Indirect Utility Function.” (4 points) 212*2*1*21433)(),,(ppIxxXUIppV ===. 2x1x00*2x*1xExtra Credit! Consider a consumer with utility given by the function {})(),(min)(4321xxxxXU ++=. Suppose: each unit of good one costs 51=p ; each unit of good two costs 22=p ; each unit of good three costs 43=p ; and each unit of good four costs 34=p . If this consumer wants to realize “10 units of happiness” (that is, 10)(=XU ) as inexpensively as possible, how much money would she have to spend? Clearly explain. (4 points) This consumer will want 104321=+=+xxxx . Further: 12pp < implies 01=x , from which it follows that 102=x and 34pp < implies 03=x , from which it follows that 104=x This consumption bundle ( 1042==xx and 031== xx) costs 50)32(10)(1042=+=+ pp . Thus, in order to achieve 10)( =XU, the consumer must spend