# UCLA STATS 100C - Midterm1_2014_Solution (10 pages)

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## Midterm1_2014_Solution

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

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UCLA Economics 11 Fall 2014 Professor Mazzocco MIDTERM 1 Version 1 NAME ID TA Part I Multiple Choice Questions 3 5 points each 1 John likes 2 sugar packets S in his coffee C Which utility function would best represent his preferences a U S C min 1 2 S C b U S C min S 2C c U S C min 2S 4C d All of the above Solution d 2 Robert s preferences are described by the following utility function U x y 2x y If px 2py then the optimal consumption for good x is given by a x I px b x I 2px c x 0 d x I py Solution c 1 3 Suppose we have the following equations for the M RS of a utility function U x y Which of the following corresponds to a homothetic utility function a M RS x y xy x2 y c M RS x y 2 x y b M RS x y d M RS x y x2 y 2 xy Solution d 4 Suppose a consumer s utility function U x y is given by max 2x y Suppose you know that when the price of x is 1 the consumer s demand for x is 4 What is the consumer s income a 2 b 4 c 8 d None of the above Solution b 5 Pizza and pepsi are complements Suppose that at current consumption level of 4 pizzas and 3 pepsis an individual s marginal utility of consuming an extra pizza is 12 whereas the marginal utility of consuming an extra pepsi is 3 Then the MRS of pepsi for pizza that is the number of pizzas the individual is willing to give up to get one more pepsi is a 3 b 4 c 1 3 d 1 4 Solution d 2 6 Andy is indifferent between consuming M units of x or N units of y Which of the following utility functions of x and y can represent Andy s preference a U x y Mx Ny b U x y ln N x M y c All of the above d None of the above Solution b If Andy views M units of x to be the same thing as N units of y then they are perfect substitutes The usual form for perfect substitutes is U x y N x M y And since b is a monotonic transformation of N x M y b represents the same preferences Note that this is the correct form of the utility function since U M 0 U 0 N ln N M One can also check this by calculating M RSx y N M 7 If the preferences of an individual are represented by the utility function U x y x y and the consumption bundle x1 y1 lies on a higher indifference curve than x2 y2 it must be that a x1 x2 and y1 y2 b

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