Econ 310 29508a Exam #1 Multiple Choice: (circle the correct letter) (5 points each) 1) Consider a consumer with Cobb-Douglas preferences characterized by the utility function 212)( xxXU = . For such a consumer 121xxMU = and 212xxMU =. The preferences of such a consumer: a. are such that 122,1xxMRS =. b. are monotonic. c. are not convex. d. are such that the bundle )12,2(=Y is preferred to the bundle )6,6(=Z . e. both (a) and (b) are correct. 2) The Law of Demand states: a. a rational consumer will always purchase a positive amount of more than one commodity. b. demand is a linear function of price. c. holding all other factors fixed, there is an inverse relation between price and quantity demanded. d. holding all other factors fixed, there is a positive relation between price and quantity demanded. e. None of the above answers are correct. 3) Consider the demand function 2100pQD= . For this demand function: a. the Law of Demand is NOT satisfied. b. price elasticity of demand is −−=qqpq100,ε. c. price elasticity of demand is 2,−=pqε. d. The choke price is 100. e. None of the above answers are correct.4) Consider a consumer with },2min{)(21xxXU=. For such a consumer: a. 122,1xxMRS =. b. the optimal bundle is such that Ixpxp=+2211. c. any bundle such that 212 xx= is optimal. d. any bundle such that 212xx= is optimal. e. the bundle )8,4(=X is optimal for a consumer with 12=I. f. More than one, but not all, of the above answers are correct. True or False: (circle TRUE or FALSE) (5 points each) 1) TRUE or FALSE: When monotonicity is satisfied, indifference curves are negatively sloped and the level of well-being is greater further from the origin. 2) TRUE or FALSE: A market is in equilibrium whenever quantity supplied is positively related to price. 3) TRUE or FALSE: If supply increases and demand decreases, then the equilibrium price can either increase or decrease. 4) TRUE or FALSE: If the income of a consumer decreases, holding prices constant, then the strict upper contour set to the bundle X must become smaller. 5) TRUE or FALSE: An endogenous variable is one whose value is taken as given in a model. Problems and/or short answer questions: 1) Qihong has utility for 1x and 2x given by 21)( xxXU=. As a result, 21xMU = and 12xMU = . i) Determine .2,1MRS (5 points)ii) Given a choice between )4,4(=Y and )3,6(=Z , which would Qihong prefer? Clearly explain. (6 points) iii) Suppose 11=p , 42=p , and 80=I . Determine the optimal consumption bundle for Qihong. (8 points) 2) Consider a market for which inverse demand is qqPD3100)(−= and inverse supply is given by qqPS2)(=. i) Determine the equilibrium price and quantity. (8 points) ii) If supply were to increase (with demand unchanged), how would the equilibrium price and quantity change? Explain. (4 points)iii) If supply were to decrease (with demand unchanged), how would the equilibrium price and quantity change? Explain. (4 points) iv) Suppose supply changes so that now inverse supply is qqPS=)(ˆ. Does this change correspond to an increase or decrease in supply? Explain. (4 points) v) Determine the equilibrium price and quantity when supply is given by the inverse function )(ˆqPS. (8 points) vi) Are your answers to parts (i) through (v) consistent with each other? Explain. (8
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