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Appendix to Chapter 3 Consumer Preferences and Demand 125

FIGURE 3A.3

The Consumer’s

Optimal Consumption

Bundle

The consumer attains

her highest level of

welfare at point B,

where her indifference

curve is tangent to the

budget line.

specific, MRS measures the slope of the indifference curve at any bundle, that

is, MRS Y/X along the indifference curve. In the present example, the

MRS at point B is 2.

Now we are ready to state a general result:

The consumer’s optimal consumption bundle is found where the marginal rate of

substitution is exactly equal to the ratio of the product prices, MRS PX/PY.

Another way of saying this is that the consumer’s preference trade-off between

the goods should exactly equal the price trade-off she faces. The MRS repre-

sents the valueof X in terms of Y, whereas PX/PYis the priceof X in terms of Y.

If the relative value of X were greater than its relative price (such as is the case

at point D), the consumer would shift to additional purchases of X and thereby

move to higher indifference curves. At point E, the situation is reversed. The

relative value of X falls short of its relative price, so the consumer would pur-

chase less of X. The consumer’s optimal purchase quantities (3 units of X and

Quantity of Good Y

Quantity of Good X

D

B

E

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