Post on 07-Feb-2016
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Marginal Utility and Indifference Curves
APPENDIX 8APPENDIX
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
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.
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.
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.
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.
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.
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 .
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 .
Maximizing Utility is Choosing the Best Affordable Point
But –QS /QM—rise over run—is 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.
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 person’s utility schedule and the marginal utilities at each quantity combination.
THE END