Problem 2: Brian wants to use his recent knowledge of utility to develop his own utility functionfor how many hours he should study for future tests. He mainly cares about two attributes: thenumber of hours he studies (x), and the mark (out of 100) that he gets (y). His research of utilityfunctions shows that when a decision maker has to decide based on more than one attribute, amulti-linear multi-attribute utility function can be developed. This function follows the formU(x, y) = kxUx(x) + kyUy(y) + (1 − kx-ky)Ux(x)Uy(y), where Ux(x) and Uy(y), areindependent utility functions for attribute x and attribute y, and kx and ky are constants.If Brian just considers the number of hours he studies, he believes his utility function for thenumber of hours he studies is: Ux(x) := 1x²-where 0 ≤ x ≤ 4. If Brian just considers the16=mark he gets, his utility function is: Uy(y) :)y, where 0 ≤ y ≤ 100. Brian is indifferentJ100between (i) studying 0 hours and getting a mark of 49 and (ii) studying 4 hours and getting amark of 100. Brian is also indifferent between (iii) studying for 2 hours and getting a mark of 64and (iv) studying for 3 hours and getting a mark of 81.a) Determine Brian's utility function as a function of the number of hours he studies (x) andthe mark he gets (y).ii.b) Using Brian's utility function, which of the following two situations would he prefer:i.Studying 2.5 hours and getting a mark of 78Studying 3.5 hours and getting a mark of 83

A utility function is a mathematical representation of an individual's preferences or satisfaction…

Problem 2: Brian wants to use his recent knowledge of utility to develop his own utility function for how many hours he should study for future tests. He mainly cares about two attributes: the number of hours he studies (x), and the mark (out of 100) that he gets (y). His research of utility functions shows that when a decision maker has to decide based on more than one attribute, a multi-linear multi-attribute utility function can be developed. This function follows the form U(x, y) = kxUx(x) + kyUy(y) + (1 − k¸-ky)Ux(x)Uy(y), where Ux(x) and Uy(y), are independent utility functions for attribute x and attribute y, and kx and ky are constants. If Brian just considers the number of hours he studies, he believes his utility function for the x² number of hours he studies is: Ux(x): = 1-: where 0 ≤ x ≤ 4. If Brian just considers the 16 mark he gets, his utility function is: Uy(y) = where 0 ≤ y ≤ 100. Brian is indifferent between (i) studying 0 hours and getting a mark of 49 and (ii) studying 4 hours and getting a y 100'

Problem 2: Brian wants to use his recent knowledge of utility to develop his own utility function for how many hours he should study for future tests. He mainly cares about two attributes: the number of hours he studies (x), and the mark (out of 100) that he gets (y). His research of utility functions shows that when a decision maker has to decide based on more than one attribute, a multi-linear multi-attribute utility function can be developed. This function follows the form U(x, y) = kxUx(x) + kyUy(y) + (1 − k¸-ky)Ux(x)Uy(y), where Ux(x) and Uy(y), are independent utility functions for attribute x and attribute y, and kx and ky are constants. If Brian just considers the number of hours he studies, he believes his utility function for the x² number of hours he studies is: Ux(x): = 1-: where 0 ≤ x ≤ 4. If Brian just considers the 16 mark he gets, his utility function is: Uy(y) = where 0 ≤ y ≤ 100. Brian is indifferent between (i) studying 0 hours and getting a mark of 49 and (ii) studying 4 hours and getting a y 100'

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.14P

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