# 1.6 Marginal Analysis and Consumer Choice

#marginalanalysis

#consumerchoice

#dimininishingmarginalutility

written by

jeanne stansak

September 12, 2020

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.

## Sample Questions

### Question 1 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

Explanation

1. 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.
2. 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.
3. 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.
4. 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.

### Question 2 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

Explanation

1. 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.

2. 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.

3. 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.

4. 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.

### Question 3

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 