Marginal Utility and Indifference Curves

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APPENDIX
APPENDIX
Marginal Utility and Indifference Curves
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After studying this chapter you will be able to

• Explain the connection between utility and
  indifference curves
• Explain why maximizing utility is the same as
  choosing the best affordable point
• Explain why utility exists

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Two Ways of Describing Preferences

• The marginal utility model describes preferences
  by using the concept of utility.
• The indifference curve model describes
  preferences by using the concepts of preference
  and indifference.
• Figure A8.1 on the next slide illustrates the
  connection between these two ways of describing
  preferences.

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Two Ways of Describing Preferences

• In part (a), you can see the levels of utility
  derived from each quantity of movies and soda.
• Three combinations generate 331 units of utility
  and two combinations generate 313 units of
  utility.
• Indifference curves pass through these points.

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Maximizing Utility is Choosing the Best
Affordable Point

• Call the marginal utility of movies MUM .
• Call the marginal utility of soda MUS .
• Call the price of movies PM .
• Call the price of soda PS .
• The marginal utility per dollar from movies is
  MUM/PM .
• The marginal utility per dollar from soda is
  MUS/PS.
• Utility is maximized when
• MUM/PM MUS/PS.

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Maximizing Utility is Choosing the Best
Affordable Point

• Call the marginal rate of substitution of movies
  for soda MRS.
• The consumer is at the best affordable point on
  the budget line when
• MRS PM/PS.

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Maximizing Utility is Choosing the Best
Affordable Point

• To see that maximizing utility is the same as
  choosing the best affordable point, begin with
• MUM/PM MUS/PS
• and multiply both sides of this equation by PM
  and divide both sides by MUS to get
• MUM/MUS PM/PS.

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Maximizing Utility is Choosing the Best
Affordable Point

• Because the best affordable point is when MRS
  PM/PS, it must be the case that
• MUM/MUS MRS.
• To see that this proposition is true, note first
  that
• ?U MUM ? ?QM MUS ? ?QS .
• But along an indifference curve, which is where
  we measure MRS, ?U 0, so
• 0 MUM ? ?QM MUS ? ?QS .

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Maximizing Utility is Choosing the Best
Affordable Point

• Because
• 0 MUM ? ?QM MUS ? ?QS
• we know that
• MUM ? ?QM MUS ? ?QS .
• Now divide both sides of this equation by MUS
  and by ?QM to obtain
• MUM / MUS ?QS /?QM .

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Maximizing Utility is Choosing the Best
Affordable Point

• But ?QS /?QMrise over runis the slope of the
  indifference curve and removing the minus sign,
  it is the marginal rate of substitution.
• So
• MRS MUM / MUS ?QS /?QM .
• The two models of consumer choice give the same
  answer.
• One implies the other.

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Utility Exists!

• The indifference curve model is powerful because
  it enables us to derive the downward-sloping
  demand curve from the assumption of diminishing
  marginal rate of substitution.
• The model is also powerful because it implies
  that utility exists.
• By observing incomes and prices and the
  quantities bought at those prices, we can infer a
  persons utility schedule and the marginal
  utilities at each quantity combination.

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THE END