# Chapter 4 Principles and Preferences

 Sana 14.01.2018 Hajmi 447 b.

• ## Differences in tastes

• Preferences for one good over another affect the slope of an indifference curve (weights attached to each good in the utility function)
• Implications for MRS
• ## Starting point on the indifference curve

• People like variety so most indifference curves get flatter as we move from top left to bottom right
• Link between slope and MRS implies that MRS declines; the amount of Y required to compensate for a given change in X decreases

• ## For example assume preferences are described by the following utility function:

• U = X1/2Y1/2
• To plot an indifference curve for this utility function, first isolate Y:
• U2 = XY
• Y = U2 /X
• Then pick some level of utility. Let’s set U = 25

• ## Thus, Y = 5/X

• When X = 1, Y = 25
• When X = 2, Y = 12.5
• When X = 3, Y = 8.33
• When X = 4, Y = 6.25
• When X = 5, Y = 5
• And so on…
• ## Describe the indifference curves for the following utility functions:

• U = X + Y
• U = min(X,Y)

• ## Let’s find the MRS for each of the following utility functions:

• U = X1/2Y1/2;
• MUX=(1/2)X-1/2Y1/2 and MUY =(1/2) X1/2Y-1/2
• U = X1/3Y2/3
• MUX=(1/3)X-2/3Y2/3 and MUY =(2/3) X1/3Y-1/3
• U = X + Y
• MUX = Y and MUY = X

• ## Latanya likes to talk on the telephone. We can represent her preferences with the utility function U(B,J) = 18B + 20J, where B and J are minutes of conversation per month with Bill and Jackie, respectively. If Latanya plans to use the phone for one hour to talk with only one person, with whom would she rather speak? Why? What is the formula for her indifference curves?

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