Econ 310 29031c Exam #1 Multiple Choice: (circle the correct letter) (5 points each) 1) Consider a consumer with preferences characterized by the utility function 2132)( xxXU += . For such a consumer 21=MU and 32=MU . The preferences of such a consumer: a. are such that 322,1=MRS . b. are Cobb-Douglas. c. are not monotonic. d. are such that 2,1MRS is not constant. e. More than one, but not all, of the above answers are correct. f. None of the above answers are correct. 2) Consider the demand function 350pQD= . For this demand function: a. the Law of Demand is NOT satisfied. b. price elasticity of demand is −−=qqpq50,ε. c. price elasticity of demand is 3,−=pqε. d. The choke price is 50. e. None of the above answers are correct. 3) Suppose 31=p and 52=p . Consider a consumer with income 25=I . For such a consumer: a. are such that 122,1xxMRS =. b. the bundle )3,3(=Z is not feasible. c. the bundle )2,5(=Y is feasible. d. the bundle )2,5(=Y is optimal. e. both (c) and (d) are correct.4) Consider a market in which demand is given by )( pQD and supply is given by )( pQS. Suppose that both the Law of Demand and the Law of Supply are satisfied. Consider a price ∗p such that )()(∗∗= pQpQSD. In this market: a. the equilibrium price is ∗p . b. the equilibrium quantity is )(∗∗= pQqS. c. the equilibrium quantity is )(∗∗= pQqD. d. )()(∗∗> pQpQSD at any price below ∗p . e. there is excess supply at any price above ∗p . f. All of the above answers are correct. True or False: (circle TRUE or FALSE) (5 points each) 1) TRUE or FALSE: For the demand function pQD5100−=, demand is inelastic for all prices. 2) TRUE or FALSE: For a consumer with }2,min{)(21xxXU=, any bundle for which 212xx = is optimal. 3) TRUE or FALSE: If supply increases and demand decreases simultaneously, then the equilibrium price could either increase or decrease. 4) TRUE or FALSE: The Marginal Rate of Substitution must be diminishing for a consumer with convex preferences. 5) TRUE or FALSE: An exogenous variable is one whose value is taken as given in a model. Problems and/or short answer questions: 1) Wayne has utility },min{)(21xxXU=. Each unit of 1x costs 1p ; each unit of 2x costs 2p . Wayne’s income is I. Suppose Wayne wants to maximize his utility, while not spending more than his income. i) State Wayne’s objective function. (5 points)ii) State the constraint that Wayne faces. (5 points) iii) Which variables are exogenous and which are endogenous? (5 points) iv) Formally state the optimization problem that Wayne wishes to solve. (7 points) v) Suppose 21=p , 82=p , and 100=I . Determine the optimal consumption bundle for Wayne. (8 points)2) Consider a market in which demand is given by )( pQD and supply is given by )(pQS. Suppose demand were to increase to )(ˆpQD and supply were to decrease to )(ˆpQS simultaneously. Suppose that both demand functions satisfy the Law of Demand and that both supply functions satisfy the Law of Supply. Clearly explain how the equilibrium quantity and equilibrium price will change in this market. (25
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