Marginal analysis allows us to explain how consumers make choices about what goods and services to purchase. As consumers, we want to maximize our satisfaction, which is known as utility maximization. In economics, utility is defined as satisfaction. Marginal utility is essentially the same thing as marginal benefit.
Rules for Utility Maximization
- The consumer will spend all of their income.
- The consumer will buy only two goods.
- When choosing which good to buy next, the consumer will always choose the good with the greatest MU/P (Marginal Utility per dollar).
- When a consumer stops buying, the MU/P of the last unit of each good should equal each other.
Steps for working these problems
- If you are given total utility (TU), you must first calculate marginal utility (MU). To calculate the MU, you subtract the TU going from one unit to another. Sometimes, the problems will give you marginal utility (MU); in this case, you can jump right to the second step!
- Once you have marginal utility (MU), calculate marginal utility per dollar (MU/P). This is done by dividing your marginal utility (MU) by the price of the product.
- Once you have calculated all these values, the consumer will look to buy the good that has the greatest MU/P first. Then, subtract the cost of that good from your budget.
- You continue this process until you have spent all of your budget.
If the budget given to Sam at the local county fair for food is $18, what would be the combination of hamburgers and soft pretzels that would maximize his utility?
3 hamburgers 4 soft pretzels
- He would first buy ONE soft pretzel because the MU/P of 1 soft pretzel is 8 and the MU/P of one hamburger is 6. He will be left over with $15.
- Next, he will buy a SECOND soft pretzel (MU/P = 6) and a FIRST hamburger (MU/P = 6). He will have $10 at this point.
- Then, he will buy a SECOND hamburger (MU/P = 4) and a THIRD soft pretzel (MU/P = 4). He will end up with $5 after this.
- Finally, to use the last of his budget, he would buy his THIRD hamburger (MU/P = 3) and the FOURTH soft pretzel (MU/P = 3)
The ideal combination would be 3 hamburgers and 4 soft pretzels. MU/P of 3 hamburgers = MU/P of 4 soft pretzels (3 = 3), while still staying in budget.
If Heather has a budget of $21 to purchase packs of pencils and composition books for the upcoming school year. What would be the combination of packs of pencils and composition books she could purchase in order to maximize her utility?
3 packs of pencils 3 composition books
She would first buy ONE composition book because the MU/P of 1 composition book is 7 and the MU/P of one pack of pencils is 6. She would be left with $17.
Next, she will buy her FIRST pack of pencils (MU/P = 6) instead of a second composition book (MU/P = 5). Since 6 is greater than 5, this is the best decision. She will have $14 left over at this point.
She will then purchase a SECOND pack of pencils (MU/P = 5) and a SECOND composition book (MU/P = 5). Since the MU/P for both these items is 5, she will purchase both items. She will still have $7 remaining.
Finally, she will purchase both a THIRD pack of pencils (MU/P = 4) and a THIRD composition book (MU/P = 4).
The ideal combination would be 3 pack of pencils and 3 composition books. MU/P of 3 packs of pencils = MU/P of 3 composition books (4 = 4), while staying in budget.
On the AP Microeconomics exam, they may just give you the MU and price of each good and ask if it is the ideal combination. Here is an example:
The table below shows the per-unit prices and marginal utility for the last unit of popcorn buckets and large sodas that Donna purchased. Donna spent all of her allocated budget on buckets of popcorn and large sodas at the movies. To maximize her utility, Donna should have purchased:
(A) more buckets of popcorn and fewer large sodas
(B) fewer buckets of popcorn and more large sodas
(C) fewer of both goods
(D) equal amounts of both goods
(E) more of both goods
Donna should purchase more large sodas and less popcorn buckets because the MU/P of large sodas is greater than the MU/P of buckets of popcorn (MU/P of large sodas is 18/3, which is 6, and the MU/P of buckets of popcorn is 25/5, which is 5). Since 6 > 5, large soda has a greater utility-per-dollar value than popcorn buckets.
The rule of thumb is: if the MU/P for the two goods are not equal, then you buy more of the higher value good and less of the lower value good.
Law of Diminishing Marginal Utility
The Law of Diminishing Marginal Utility essentially says that as you consume more and more of a good or service, the additional satisfaction you get from that product decreases more and more. Let's say you were eating cake. For the first slice you eat, you get a lot of utility or satisfaction. For the second slice you eat, you get about the same amount of utility. But as you eat the third, fourth, and fifth slices, you start to gain less satisfaction. By the sixth slice, the marginal utility may actually become negative (which means that your total utility is actually decreasing) because you feel sick from all that sugar.