Understanding the Equal Marginal Benefit Principle

Note: This post is going into my teaching archive to help students who miss this particular class. For my fellow econ teachers, you might find it an alternate way of teaching EMBP.

The equal marginal benefit principle says that consumers will chose their consumption bundle in such a way that the Marginal Utility (MU) per dollar will be equal across all goods. In other words, the last commodity they purchase will yield the same level of marginal utility per dollar spent. Mathematically, it is expressed across N goods as:
It is important to understand that this condition is referring to an outcome of a process, that is, it is something consumers are moving towards. The intuition can be illustrated with a simple example.

Suppose a consumer is at a football game with $10 of income he plans to spend. With this $10, he can purchase different quantities of pretzels, beers, and nachos, which are each $1 in price. The Table below illustrates the marginal utility experienced with each unit of consumption:

Marginal Utility per Unit by Item

Notice that with each item, they experience diminishing marginal utility (the more they have, the less they want a little bit more).

Based on the above table, how will the consumer spend the first of their $10? It makes sense that they would get "the most bang for their buck" and buy the first beer, which yields 100 marginal utils (as opposed to 50 or 28 for pretzels and nachos, respectively).
Now, how does the consumer spend their 2nd dollar? They could buy their first pretzel (50 more utils), their second beer (60 more utils), or their first nacho (28 utils). Since the second beer adds to their utility at the greatest rate, they will have the second beer.
How about the third dollar? They can buy their first pretzel (50 more utils), their third beer (45 more utils), or their first nacho (28 more utils). With their third dollar, they will purchase their first pretzel. This process continues, of course, so that we can see a break down of how each dollar of spending will occur:
As you can see, with the first $9 they purchased 4 pretzels, 4 beers, and 1 nacho, and are now indifferent on the 10th dollar of spending. On the 10th dollar, the marginal utility is equal across all goods.

See Also: The EMBP in One Picture