UCLA STATS 100C - Midterm1_Version2 (5 pages)

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Midterm1_Version2



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Midterm1_Version2

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5
School:
University of California, Los Angeles
Course:
Stats 100c - Linear Models
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UCLA Economics 11 Fall 2016 Professor Mazzocco MIDTERM 1 Version 2 NAME ID TA Part I Multiple Choice Questions 3 5 points each 1 If U X1 X2 X13 23X2 the MRS a depends on the values of X1 and X2 b depends only on the values of X1 c depends only on the values of X2 d is always constant 2 If U z r 4z 6r then the bundle 4 2 provides the same utility as a 4 3 b 3 2 c 2 5 3 d 3 5 1 3 If a function f x y is homogeneous of degree 3 then which of the following is true a f 2x 2y 9f x y b f 2x 2y 6f x y c f 2x 2y 8f x y d None of the above 1 4 What does the transitivity assumption on preferences imply a Indifference curves never cross b Indifference curves are convex c Indifference curves have diminishing M RS d All of the above 5 Suppose Peter s MRS of cake for tofu is 2 That is at the current consumption bundle he is willing to give up 2 pounds of tofu to get an extra piece of cake Suppose also that the price of a pound of tofu is 6 and a piece of cake is 3 Then in order to increase his utility Peter should a Buy more tofu and less cake b Buy more cake and less tofu c Continue with the current bundle d None of the above 6 An individual has a utility function for tennis rackets x and tennis balls y of the form U x y min x y She wants to achieve the utility level U Then her expenditure function is given by a E px py U px py U U b E px py U px py c E px py U 2px 3py U d E px py U px py U 7 Which of the following utility functions represent the same preferences as U x y ln x ln y a U x y xy b U x y ln x ln y c U x y x y x d U x y ln y 2 8 Suppose that an individual has a constant MRS of shoes for sneakers of 3 4 that is he or she is always willing to give up 3 pairs of sneakers to get 4 pairs of shoes Then if sneakers cost twice as much as shoes he or she will a buy only sneakers b buy only shoes c spend his or her income equally on sneakers and shoes d wear sneakers only 3 4 of the time 9 Bob spends his income buying tomatoes T and juices J The price of each pound of tomatoes is 8 dollars the price of each juice is 4 dollars His utility is given by U lnT lnJ What is the minimum income Bob needs to obtain a utility level equal to ln 8 a 40 b 32 c 64 d 100 10 An individual has a utility function for skis x and ski boots y of the form U x y min 2x y His or her indirect utility function is given by a V I px py b V 2px py I c V 2px py I d V 2I px 2py 3 Part II Essay Questions Question 1 34 Points 1 Janet loves eating large salads S while drinking Odwalla juices J Drinking the juices improves the taste of salads Therefore her utility function has the following form U S J JS 3S a For a given income I and prices ps and pj find Janet s Marshallian demands for S and J 8 Points b Find the indirect utility function 8 Points c Suppose Janet has 50 dollars of income to spend on salads and juices and the prices of these goods are ps 4 and pj 2 What is her optimal consumption bundle What is her utility at that consumption bundle 5 Points Janet s mother is really proud of her daughter s healthy diet She therefore wants to find a way to improve her daughter s happiness utility To do this she comes up with two possible plans i The first plan is to increase Janet s income by 10 from its current value of 50 ii The second plan is to subsidize Janet s consumption of juices by paying 20 of the price of each juice she buys d Which of the two plans should Janet s mother choose if she wants to maximize Janet s utility To obtain the points show the calculation that enables you to choose the plan 8 points e How much money does Janet s mother have to spend to implement each plan 5 points 4 Question 2 31 Points 1 Janet got tired of eating salads and drinking juices and she decides that from now on she will only eat steaks s and drink red wine w Her preferences for those two goods are such that she always wants to eat one steak with 4 glasses of wine Her utility is therefore U s w min 4s w The prices of steak and wine are ps and pw a Find Janet s Hicksian demand functions for s and w 7 Points b Find her expenditure function 7 Points c Suppose that ps 10 pw 5 How much income does Janet needs to achieve the utility level U 200 4 Points A new scientific article has provided evidence that excessive consumption of red meat reduces life expectancy As a consequence the government has decided to impose a sale tax of 20 on steaks d If Janet wants to stay at the same utility level U 200 how much income does she need to spend after the introduction of the tax 6 Points e Janet realizes that she cannot afford to spend that much and decides to spend the same amount she was spending before the introduction of the tax What will her new level of utility be after the introduction of the tax Hint use the expenditure function and its economic meaning definition but if you prefer you can use other methods 7 Points 5


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