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Microeconomics
Course: Microeconomics > Unit 5
Lesson 1: Introduction to consumer theory: total utility and marginal utility- Marginal utility and total utility
- Visualizing marginal utility MU and total utility TU functions
- Total Utility and Marginal Utility
- Utility maximization: equalizing marginal utility per dollar
- Deriving demand curve from tweaking marginal utility per dollar
- Lesson overview - Total utility and marginal utility
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Lesson overview - Total utility and marginal utility
One of the questions that economists are interested in is how people decide to spend their money, a field of economics known as consumer theory. This study of how people decide to allocate their income to spending on goods has a few key assumptions that lead to some important conclusions about how a consumer will decide to allocate their income to spending on goods and services.
Key assumptions about consumer motivation:
- A rational consumer is a utility maximizer. A consumer will seek to have as much benefit or satisfaction as possible. In economics, the term utility refers to the happiness, benefit or value a consumer gets from a good or service. In other words, consumers are not satisficers who will settle for "good enough". This happiness or satisfaction is measured in a unit called a util.
- Most goods provide diminishing marginal utility. According to the law of diminishing marginal utility, as the consumption of good increases the additional amount of happiness the good provides the consumer decreases. So while having three scoops of ice cream makes you happier than two scoops, the second scoop doesn't make you as happy as the first one did, and the third one doesn't make you as happy as the second one did.
These assumptions lead us to several conclusions about how consumers go about deciding how to spend their money. Consumers will therefore consider
- the marginal utility of another unit of a good they are considering buying
- the prices of a good and alternative goods they are considering buying
- their budget for consuming goods and services
Because consumers derive less satisfaction from consuming additional units of a good, they will only be willing to buy more of a particular good if the good's price decreases. In this way, the law of diminishing marginal utility helps explain the law of demand.
Total utility
If we consider how an individual experiences utility when consuming ice cream, we can make some important observations how total utility changes as the consumption of a good increases.
To express utility, we will use a unit called the util, which is simply a measure of how happy someone is. For instance, we might say that the first scoop of ice cream provides Axel with 7 utils of happiness. The table below shows how Axel's utility changes as he consumes additional scoops of ice cream.
| Quantity consumed | Total utility | |
|---|---|---|
| 0, start text, s, c, o, o, p, s, end text | 0 utils | |
| 1, start text, s, c, o, o, p, end text | 7 utils | |
| 2, start text, s, c, o, o, p, s, end text | 12 utils | |
| 3, start text, s, c, o, o, p, s, end text | 15 utils | |
| 4, start text, s, c, o, o, p, s, end text | 16 utils | |
| 5, start text, s, c, o, o, p, s, end text | 15 utils | |
| 6, start text, s, c, o, o, p, s, end text | 12 utils |
Notice that additional scoops provide Axel with more utility up until the 4, start superscript, t, h, end superscript scoop, at which point Axel's utility is maximized. Beyond 4 scoops we can see that Axel is actually experiencing less and less total happiness.
Axel's total utility from ice cream can be graphed in a utility function, as seen in start text, F, i, g, u, r, e, space, 1, end text:
Marginal utility
If we look more closely at Axel's total utility we can observe how it changes as he consumes more ice cream. The change in a consumer's total utility when he consumes one additional unit is the marginal utility.
| Quantity consumed | Total utility | Marginal utility |
|---|---|---|
| 0, start text, s, c, o, o, p, s, end text | 0 utils | minus |
| 1, start text, s, c, o, o, p, end text | 7 utils | 7 utils |
| 2, start text, s, c, o, o, p, s, end text | 12 utils | 5 utils |
| 3, start text, s, c, o, o, p, s, end text | 15 utils | 3 utils |
| 4, start text, s, c, o, o, p, s, end text | 16 utils | 1 utils |
| 5, start text, s, c, o, o, p, s, end text | 15 utils | minus, 1 utils |
| 6, start text, s, c, o, o, p, s, end text | 12 utils | minus, 3 utils |
Notice that Axel's marginal utility decreases as he consumes more ice cream. This is explained by the fact that the second, third and fourth scoops of ice cream were less satisfying to him than the first scoop.
Notice also that beyond 4 scoops his marginal utility is negative, meaning that Axel is actually made worse off by the fifth and sixth scoops of ice cream.
Axel's marginal utility function can be added to his total utility function, as shown in start text, F, i, g, u, r, e, space, 2, end text
Note that the marginal utility for a particular quantity of consumption is actually in between two quantities. For instance, the marginal utility of the 1, start superscript, s, t, end superscript scoop is actually his change in total utility between 0 and 1 scoops, which explains why M, U, equals, 7 between 0 and 1 scoops in start text, F, i, g, u, r, e, space, 2, end text.
Marginal utility per dollar spent
A good first step in determining how a consumer will decide to allocate their income is knowing the satisfaction they get from a good. But before the optimal amount to buy of any good the price must also be considered. In other words, what is the "bang per buck" that a buyer will get from the good?
We can determine the "bang per buck" a buyer gets using the marginal utility per dollar spent, or M, U, slash, dollar sign. To determine the M, U, slash, dollar sign we divide the marginal utility a consumer gets at a particular level of consumption by the price of the good.
Assume ice cream costs dollar sign, 0, point, 50 per scoop. The marginal utility per dollar can then be calculated by dividing the M, U at each level of consumption by the price of dollar sign, 0, point, 50.
| Quantity consumed | Marginal utility | Marginal utility per dollar spent |
|---|---|---|
| 1, start text, s, c, o, o, p, end text | 7utils | 14, u, slash, dollar sign |
| 2, start text, s, c, o, o, p, s, end text | 5 utils | 10, u, slash, dollar sign |
| 3, start text, s, c, o, o, p, s, end text | 3 utils | 6, u, slash, dollar sign |
| 4, start text, s, c, o, o, p, s, end text | 1 utils | 2, u, slash, dollar sign |
| 5, start text, s, c, o, o, p, s, end text | minus, 1 utils | minus, 2, u, slash, dollar sign |
| 6, start text, s, c, o, o, p, s, end text | minus, 3 utils | minus, 6, u, slash, dollar sign |
The use of the marginal utility per dollar spent in making decisions is fairly straightforward. Suppose Axel is currently consuming two scoops of ice cream and is thinking about getting a third scoop of ice cream or a soda. Suppose he knew that his bang per buck for a soda was 10, start text, space, u, t, i, l, s, end text, slash, dollar sign. He would only get 6, start text, space, u, t, i, l, s, end text, slash, dollar sign on a third scoop of ice cream. Since he would be getting a better "bang per buck" from a soda, he would purchase the soda and not a third scoop of ice cream.
Considering the marginal utility per dollar spent on a good will help consumers spend their limited budgets in a way that maximizing their total utility, as we will develop further in the next lesson.
Diminishing marginal utility and the law of demand
The law of diminishing marginal utility helps us understand the law of demand. Because consumers will derive less happiness or benefit from additional units of a good, they will only be willing to buy a larger quantity if the price decreases.
This is true on an individual level, as with Axel's utility schedule for ice cream, but will be true on a market-wide level as well. Society as a whole's marginal utility diminishes as more of a good or service is provide, therefore in order for more units to be sold the price society must pay has to decrease. In other words, there is an inverse relationship between a good's price and the quantity society is willing and able to buy.
Key terms
| Term | Definition |
|---|---|
| consumer theory | the study of how buyers decide to allocate income toward consumption |
| utility maximizer | someone who seeks to achieve the highest possible satisfaction or happiness |
| utility | the happiness or benefit consumers derive from a good's consumption |
| util | an imaginary unit of measurement representing the amount of utility a good provides |
| total utility | the total amount of happiness a consumer derives from a good at any particular level of consumption |
| marginal utility | the change in total utility that a consumer experiences when one more unit of a good is consumed |
| law of diminishing marginal utility | the observation that as more units of a good are consumed the amount of happiness derived from each additional unit decreases as consumption increases |
| marginal utility per dollar spent M, U, slash, dollar sign | the "bang per buck" that a consumer gets from consuming a particular quantity of a good at a given price. |
Key models
A consumer's or society's utility schedule can be graphed using total and marginal utility functions.
Notice that at a quantity of 4, total utility is maximized at 15 units. Notice also that at a quantity of 4, marginal utlity is equal to zero. According to this graph, once this person has consumed 4 units of this good they no longer get additional enjoyment from the good. Consuming the 5, start superscript, t, h, end superscript unit actually makes them worse off.
Key calculations
Marginal Utility
equals, start fraction, delta, T, U, divided by, delta, Q, end fraction
Marginal Utility per dollar equals, start fraction, M, U, divided by, dollar sign, end fraction
Want to join the conversation?
Is the total utility always given in a question? or is there a specific formula to determine the total utility?(3 votes)- They can give you either MU or TU and ask you to calculate any one of the two at once.(2 votes)
- I have an exercise where the utility function is given (U(x,y)= x*y). Having in mind that the income is 8 and that the price of x is 2 and that the price of y is 0,5, how can we find the optimal consumption bundle?
Thank you for your time.(2 votes) - Hi, I'm wondering why is the marginal utility per dollar spent on the second scoop is 10 u/$?
Isn't it supposed to be 5 u/$?
5 utils /(2 scoop x $0.5) = 5/1 = 5?(1 vote)
We are considering marginal utility, meaning that we are ignoring the first scoop for the moment and asking how much more utility the consumer gained from only that second scoop of ice cream.
The second scoop provided 5 utils, meaning that the consumer gained 5 utils (units representing utility) whilst paying $0.50. Scaling upward, we see that this is equivalent to 10 utils/$.(2 votes)