numbers, the marginal utilities from the last dollar spent on X and Y are
equal.
The condition required for a consumer to be maximizing utility, for any
pair of products, is
This equation says that a utility-maximizing consumer will allocate
expenditure so that the utility gained from the last dollar spent on one
product is equal to the utility gained from the last dollar spent on any
other product.
This is the fundamental equation of marginal utility theory. With only a
given amount of income to spend, a consumer demands each product up
to the point at which the marginal utility per dollar spent on it is the same
as the marginal utility per dollar spent on every other product. When this
condition is met for all products, the consumer cannot increase utility
further by reallocating expenditure. That is, utility will be maximized. (Of
course, if she gets more income to spend, she can raise her total utility by
buying more of each product.)
An Alternative Interpretation
MpUXX = MpUYY