AP_Krugman_Textbook

module 80 Appendix 795

Section 14 Appendix
The flattening of indifference curves as you slide down them to the right—which re-
flects the same logic as the principle of diminishing marginal utility—is known as the
principle of diminishing marginal rate of substitution.It says that an individual
who consumes only a little bit of good Aand a lot of good Bwill be willing to trade off
a lot of good Bin return for one more unit of good A,and an individual who already
consumes a lot of good Aand not much of good Bwill be less willing to make that
trade-off.
We can illustrate this point by referring back to Figure 80.5. At point V,a bundle
with a high proportion of restaurant meals to rooms, Ingrid is willing to forgo 10
restaurant meals in return for 1 room. But at point Y,a bundle with a low proportion
of restaurant meals to rooms, she is willing to forgo only 2 restaurant meals in return
for 1 room.
From this example we can see that, in Ingrid’s utility function, rooms and restau-
rant meals possess the two additional properties that characterize ordinary goods. In-
grid requires additional rooms to compensate her for the loss of a meal, and vice versa;
so her indifference curves for these two goods slope downward. And her indifference
curves are convex: the slope of her indifference curve—the negative ofthe marginal rate
of substitution—becomes flatter as we move down it. In fact, an indifference curve is
convex only when it has a diminishing marginal rate of substitution—these two condi-
tions are equivalent.
With this information, we can define ordinary goods,which account for the great
majority of goods in any consumer’s utility function. A pair of goods are ordinary goods
in a consumer’s utility function if they possess two properties: the consumer requires
more of one good to compensate for less of the other, and the consumer experiences a
diminishing marginal rate of substitution when substituting one good for the other.
Next we will see how to determine Ingrid’s optimal consumption bundle using in-
difference curves.

The Tangency Condition

Now let’s put some of Ingrid’s indifference curves on the same diagram as her budget
line to illustrate an alternative way of representing her optimal consumption choice.
Figure 80.6 shows Ingrid’s budget line, BL,when her income is $2,400 per month,

The principle of diminishing marginal

rate of substitutionstates that the more

of good Ra person consumes in proportion

to good M,the less Mhe or she is willing

to substitute for another unit of R.

Two goods, Rand M,are ordinary goods

in a consumer’s utility function when (1) the

consumer requires additional units of Rto

compensate for fewer units of M,and vice

versa; and (2) the consumer experiences a

diminishing marginal rate of substitution

when substituting one good for another.

figure 80.6

The Optimal Consumption

Bundle

The budget line, BL,shows Ingrid’s possible con-

sumption bundles, given an income of $2,400 per

month, when rooms cost $150 per month and

restaurant meals cost $30 each. I 1 , I 2 , and I 3 are

indifference curves. Consumption bundles such

as Band Care not optimal because Ingrid can

move to a higher indifference curve. The optimal

consumption bundle is A,where the budget line

is just tangent to the highest possible indiffer-

ence curve.

A

B

0 2468 141210 16

80

70

60

50

40

30

20

10

Quantity of rooms

Quantity of

restaurant

meals

I 2

I 3

I 1

BL

Optimal

consumption

bundle

C