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