# UCLA STATS 100C - Midterm1_2015_Solution (7 pages)

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## Midterm1_2015_Solution

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- Pages:
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- School:
- University of California, Los Angeles
- Course:
- Stats 100c - Linear Models

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UCLA Economics 11 Fall 2015 Professor Mazzocco MIDTERM 1 Version 1 NAME ID TA Part I Multiple Choice Questions 3 5 points each 1 If all prices and income double the Marshallian demands for goods X and Y will a both increase since the consumer has more income b both decrease since the two goods are now more expensive c remain unchanged because the prices and income increase by the same proportion Answer d the demand for X might increase or decrease depending on the preference of the consumer 2 If Angelina s utility function is given by U x y min 2x 4y and she is considering the two consumption bundles A x 100 y 25 and B x 50 y 50 then we can say that the consumer a is indifferent between A and B Answer b prefers A relative to B c prefers B relative to A d can t compare A and B because preferences are not complete 3 Alice s utility function is such that she is always indifferent between 1 unit of x and 3 units of y Suppose initially px 2 py 1 and I 10 Alice chooses x and y to maximize her utility Then the government imposes a 100 sale tax on x the price of x doubles How much MORE does the person have to earn in order to achieve the same level of utility as before Find the increase in income required to achieve the same utility level 1 a 0 b 5 Answer c 10 d 18 4 Suppose the good x is graphed on the x axis and the good y is graphed on the y axis The slope of the budget constraint is a px py b ppxy Answer c ppxy d py px 5 Suppose that the price of champagne is pc 70 and that the price of cheap wine from Trader Joe s is pt 10 and Alessio has income I 210 Alessio s M RS of cheap wine Uc is equal to 8 for any consumption bundle for each point for champagne that is M M Ut of the indifference curves If he spends his income optimally then Alessio will a Buy only champagne Answer b Buy 8 units of champagne and 2 units of wine c Buy a 4 1 ratio of champagne to wine we don t know exactly how much he can afford d There is not enough information to answer the question 6 Which of the following functions is not a homothetic function a U x y x2 y 2 b U x y x y 1 c U x y x y 1 d U x y xy x y Answer 7 Which of the following utility functions represent the same preferences as U x y xy a U x y 10 xy 2 b U x y xy c U x y ln x ln y d All of the above represent the same preferences Answer 8

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