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Marginal rate of substitution – the quantity of one good that a consumer is willing to sacrifice in<br />

order to obtain a unit of another good.<br />

A consumer will attempt to maximize the total utility that they receive from their limited income.<br />

We used utility theory to examine utility maximization in Examples 8A-8E earlier in the chapter.<br />

Now we will use indifference curves and budget constraints.<br />

Budget constraint – a curve showing the different combinations of two goods that a consumer<br />

can purchase with a certain amount of income.<br />

A consumer’s budget constraint depends on the consumer’s income and the prices of the two<br />

goods under consideration.<br />

Example 12A: Refer back to Example 8C. Consumer A has $10 of income and Good X and<br />

Good Y each cost $1 each. The graph below illustrates the budget constraint for Consumer A.<br />

Units of<br />

Good Y<br />

10 -<br />

9-<br />

8-<br />

7-<br />

6-<br />

5-<br />

4-<br />

3-<br />

Example 12B<br />

budget constraint2-<br />

1-<br />

.<br />

130<br />

Example 12A<br />

budget constraint<br />

.<br />

.<br />

180<br />

.<br />

.<br />

.<br />

.<br />

.<br />

.<br />

.<br />

.<br />

0 <br />

0 1 2 3 4 5 6 7 8 9 10<br />

.<br />

. .<br />

.<br />

..<br />

.<br />

Units of Good X<br />

.<br />

.<br />

.<br />

.<br />

. 270<br />

.<br />

. 250 255<br />

. 205<br />

Consumer A can afford various combinations of Good X and Good Y. Which combination will<br />

Consumer A choose? Consumer A will attempt to choose the combination that maximizes A’s<br />

total utility. This will be the combination on the indifference curve that is tangent to (has the same<br />

slope as) the budget constraint. For the utility-maximizing combination of units, the marginal rate<br />

of substitution will be the same as the slope of the budget constraint.<br />

In this case (as in Example 8C), the utility-maximizing combination is six units of Good X and four<br />

units of Good Y. The marginal utility of the sixth unit of Good X is 15 utils. The marginal utility of<br />

the fourth unit of Good Y is also 15 utils. So the marginal rate of substitution will be 1 unit of Good<br />

X for 1 unit of Good Y. This is also the slope of the budget constraint (since the price of both<br />

Good X and Good Y is $1).<br />

FOR REVIEW ONLY - NOT FOR DISTRIBUTION<br />

Example 12B: Refer back to Example 8D. The price of Good Y increases to $3. The graph above<br />

illustrates the new budget constraint for Consumer A.<br />

18 - 7 Utility

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