In Economics, utility means the...
Strand 1 · Consumers’ Rational Decision-Making
Economics Year 2 Learner Material, Section 3: Utility
Learner, welcome to Section 3 of Year 2 Economics. In this section, you will focus your attention on another interesting concept in Economics. One of the core ideas in Economics is the concept of utility. This is the satisfaction or benefit a consumer derives from consuming goods and services. In Ghana, whether it is deciding how much kenkey to buy at a food joint or how many minutes to top-up on a mobile phone, consumers are constantly balancing their resources to maximise their satisfaction. But how do you recognise when a consumer is fully satisfied? In Economics this state of full satisfaction is called equilibrium. This section helps you to understand this the idea of equilibrium in utility, and explores different types of utility, Total Utility, Marginal Utility, and Average Utility). You will learn how to draw the utility curves, what they mean and how they help to explain consumer behaviour.
KEY IDEAS
• Equilibrium in utility refers to a state in which a consumer has allocated their resources (usually income) in such a way that gives them the highest satisfaction for each commodity they consume.
• In Economics, utility refers to the satisfaction or pleasure that a consumer derives from consuming goods and services. It is a measure of the happiness or benefit those results from making specific choices in the marketplace.
• The consumption pattern of a consumer can be expressed in the form of Total Utility, Marginal Utility and Average Utility.
• The utility of the consumer can further be explained using Total, Marginal and Average utility curves.
A consumer always aims to make the best possible choices with their limited income to maximise satisfaction. The consumer is at equilibrium when the satisfaction (or utility) gained from consuming a good is equal to the amount of money spent on it. In economic terms, this means that the marginal utility of the good must be equal to its price.
In Economics utility is measures in UTILS. They are theoretical units which make comparisons easier when analysing how consumers use their resources to give them satisfaction. This can be expressed mathematically in terms of a single commodity and multiple commodities as:
For a single commodity, the consumer is in equilibrium when:
MUₓ = Pₓ Where, MUₓ is Marginal Utility of commodity X and Pₓ is price of commodity X
Example
A rider bought a bottle of water for GHC10 after riding for 30 minutes because they were very thirsty. The rider thought that the satisfaction he gained from drinking the water was the highest it could be. This meant that the satisfaction of drinking the water was the same as the price so its marginal utility must be 10 utils. This demonstrates the equilibrium state because the price paid is equal to the marginal utility.
For multiple commodities, the consumer is in equilibrium when the marginal utility per cedi spent on Commodity X is equal to the marginal utility per cedi spent on Commodity Y. In other words, it is the ratio of the marginal utility of Commodity X to the Price of Commodity X and the ratio of the marginal utility of Commodity Y to the Price of Commodity Y.
MUx MUy
Px Py
= MU_(X) is the marginal utility of Commodity X, Pₓ is the price of Commodity X, MU_(Y) is the marginal utility of Commodity Y and P_(Y) is the price of Commodity Y.
Total Utility
Total utility is the total satisfaction a consumer derives from consuming a certain amount of goods or services. The total utility tells how much satisfaction that is derived from the total amount of a good consumed. It can also be expressed as the addition of all the marginal utilities to the last unit of a commodity consumed.
If ‘n’ units of a good is consumed, the total utility can be expressed mathematically as:
Total Utility (TU) = U₁ + U₂ + U ₃+...+Uₙ Where:
• U₁ is the utility from the first unit consumed,
• U₂ is the utility from the second unit consumed,
• U₃ is the utility from the third unit consumed,
• and so on, up to Uₙ which is the utility derived from the n-th unit consumed.
Marginal Utility
Marginal utility is the additional satisfaction derived from consuming one more unit of a good or service. It helps to understand how much more satisfaction you derive from consuming one more unit of a commodity. Marginal utility decreases as you consume more and more of the same commodity. This leads to the idea of diminishing marginal utility.
Marginal utility is calculated as the change in total utility divided by the change in the units of the commodity consumed. This can be expressed mathematically as:
ΔTU ΔQ
MU= ΔTU is the change in total utility ΔQ is the change in quantity Where ΔTU= TU₂ - TU₁ - represents the change in total utility after consuming another unit of a good.
and ΔQ= Q₂ - Q₁ – represents the change in quantity after consuming another unit of a good.
By replacing ΔTU and ΔQ in the original equation above you get ΔTU TU₂ - TU₁ ΔQ Q₂ -Q₁ MU= = The Law of Diminishing Marginal Utility The law of diminishing marginal utility states that ‘as more and more units of a commodity are consumed, the additional satisfaction derived from each additional unit consumed decreases.’
Example: Imagine yourself eating Kenkey, as you consume more and more of the Kenkey, your marginal utility will decrease. After you consume the first ball, any additional consumption decreases the satisfaction gained after eating the previous one.
Average Utility
This is the amount of satisfaction a person derives from consuming each unit of a good or service. It shows how much satisfaction a person derives per unit of a good consumed. It is calculated by dividing the total utility by the number of units consumed.
It is expressed mathematically as:
TU Q AU= Where, TU = Total Utility, and Q = Quantity For example, Kudus Mohammed, after playing a football match drank some bottles of water and realised the following total utilities.
After the 1ˢᵗbottle 8 utils After the 2ⁿᵈbottle 15 utils After the 3ʳᵈbottle 21 utils After the 4ᵗʰbottle 25 utils After the 5ᵗʰbottle 27 utils After the 6ᵗʰbottle 27 utils The marginal utilities are calculated as follows 1ˢᵗbottle: 8 utils 2ⁿᵈbottle: 15-8 2-1 =7 utils 4ᵗʰbottle: 25-21 4-3 = 4 utils Can you calculate the marginal utility for the 3ʳᵈ, 5ᵗʰand 6ᵗʰbottles?
Average utilities are calculated as follows 1ˢᵗbottle: 8 utils 2ⁿᵈbottle: utils 3ʳᵈbottle: utils Can you calculate the average utility for the 4ᵗʰ5ᵗʰand 6ᵗʰbottles?
Have a look at this table which gives you the total utility and ALL the marginal and average utilities for Kudos’ water drinking:
Table 3.1: Total utility, marginal and average utilities Bottle number Total Utility (utils) Marginal Utility (utils) Average Utility (utils) 1 8 8 8.00 2 15 7 7.50 3 21 6 7.00 4 25 4 6.25 5 27 2 5.40 6 27 0 4.50 This table shows that as more of the commodity is consumed, the total utility increases but the marginal utility falls continuously. This explains the law of diminishing marginal utility. If Kudus had bought each bottle of water at GHC4, he would be in equilibrium at the level of consuming the 4th bottle. This is because the marginal utility at the 4ᵗʰbottle is 4 utils.
You should notice that in the first line of the table, Total, Marginal and Average Utility are all the same. This is because only ONE bottle of water has been consumed. So, the first unit of consumption (1) is setting the initial values. Total Utility is 8 after consuming one bottle, Marginal Utility is calculated by TU/Q which is 8/1 = 8 utils.
For Average Utility there are no previous values to compare with, so it is simply a case of MU=TU₁−TU₀/Q1-Q0 =8−0/1-0=8 utils If you check the infographic below then you will see that all three graphs start at the same point.
Activity 3.1 Calculating Total Utility, Marginal Utility and Average Utility For this activity you should work with a friend either in class or at home.
Materials needed:
• A notebook and pen
• A list of specific food items (e.g., apples, biscuits, or chocolates)
• A calculator Instructions Follow these steps to explore utility concepts and carry out calculations with your friend. Take turns in completing each part of the task. Discuss your findings at each stage.
Step 1: Understanding Utility Concepts
Before starting the activity, discuss with your partner what the following terms mean:
1. Total Utility (TU)
2. Marginal Utility (MU)
3. Average Utility (AU)
Write down these definitions in your notebook so that you can refer to them later.
Think of a few examples where you feel satisfied after consuming something (e.g., food, drinks, haircut, bus ride).
Step 2: Choosing a good and creating your table Now, you will carry out a simple experiment.
1. Choose one good (e.g., apples, biscuits, or chocolates) that you will imagine consuming.
2. Create a table in your notebook like the one below to record your results. Use a scale from 1 to 10 to show how much satisfaction you will get after eating each unit. For example, after eating one apple, you might feel 8 out of 10 satisfied, but after eating more, your satisfaction could change.
3. Assuming that at unit six, your satisfaction score is -2.
Number of Units
Consumed (e.g.
Apples) Satisfaction
(Utility) Score (utils) Total Utility (TU)
(TU = Running total of satisfaction scores – add next satisfaction to last total) utils Average Utility (AU) (AU = TU ÷ Number of Units)utils Marginal Utility (MU) (MU₁ = TU₂ -TU₁/ Q₂-Q₁) utils 1 2 3 4 5 6 -2
Step 3: Recording your satisfaction (Utility) score in the table drawn With your partner, take turns to complete the following:
1. Imagine eating the first unit of the good (e.g., one apple). How satisfied do you feel? Both of you should agree on a score (e.g., 8 out of 10) and record it under “Satisfaction (Utility) Score” for 1st unit.
2. Repeat this for the 2nd, 3rd, 4th, and 5th units (consider the law of diminishing marginal utility.) The sixth satisfaction score is done for you to give you an idea of what to work towards. A negative utility score shows the consumer experiences displeasure, dissatisfaction, or even discomfort from consuming any more of that good!
Step 4: Calculate the Total Utility (TU) for all levels of units consumed.
Step 5: Calculate the Marginal Utility (MU) and Average Utility for each level of unit consumed.
Step 6: Observing and Discussing Results: Discuss the following questions with your partner and write your thoughts and answers in your notebook.
1. What happened to your Marginal Utility as you consumed more and more of the unit? Did it increase or decrease?
2. How did your Average Utility change as you consumed more and more units?
3. Why do you think your Marginal Utility might have decreased? Is there a point where you stop enjoying the extra units that you consumed?
Step 7. Reflecting on Real-Life Examples
Finally, think of a real-life situation where you experienced diminishing satisfaction after consuming more and more of the same product (e.g., food, drinks, entertainment). Discuss this example with your partner and each of you should write down your thoughts.
Compare your work with another group of friends. You can also show your work to your teacher if you are not sure of your answers.
Remember to respect and tolerate each other.
The infographic illustrations that show how utility or satisfaction changes with the consumption of additional units of a good or service are known as utility curves (Total, Marginal and Average utilities).
Total Utility curve The total utility curve shows the total satisfaction that the consumer gets as a result of consuming a certain amount of a good or service. The total utility curve starts at the origin (at point 0,0) because zero consumption yields zero results or utility. As the consumer consumes more and more of the commodity or service, total utility rises at an increasing rate, then a decreasing rate to a maximum and eventually declines when the utility becomes negative (dissatisfaction).
Marginal Utility curve The marginal utility curve shows the level of utility the consumer gets as a result of consuming an additional unit of a good or service. The marginal utility curve starts at 0 because the consumer has not consumed the good. It rises to the point where the first good is consumed and is equal to the total utility. It then slopes downwards to the right, starting following the law of diminishing marginal utility which says that the consumption of additional units results in a decrease in marginal utility. The marginal utility becomes negative when the marginal utility curve cuts the X-axis.
Average Utility curve The average utility curve shows the utility per unit of consumption of the commodity.
It is the ratio of the total utility to the units of the commodity consumed. The pattern of the average utility curve is similar to that of the total utility, and it is determined by the quantity of the commodity consumed.
It rises initially showing the influence of utility and finally falls as a result of the impact of diminishing marginal utility.
The quantity consumed of the commodity is on the horizontal or x-axis of the graph while the average utility is on the vertical or y-axis. Figure 3.1 shows how the total utility, marginal utility, average utility curves look on an infographic.
Figure 3.1: Total utility, marginal utility and average utility curves on infographics
Activity 3.2 Drawing the TU, AU and MU Curves Number of Units Consumed (Apples) Total Utility (TU) Average Utility (AU) (AU = TU ÷ Number of Units consumed) Marginal Utility (MU) (MU₁ = TU₂ -TU₁ /Q₂-Q₁) 1 8 8 8 2 14 7 6 3 18 6 4 4 21 5.25 3 5 23 4.6 2 6 22 3.6 -1 Instructions
1. You will need a piece of graph paper, a sharp pencil, ruler and some coloured pencils to draw each curve.
2. Review the information in the table which is based in the consumption of apples.
3. Use the information in the table to draw the Total Utility Curve (TU), Average Utility Curve (AU) and Marginal Utility Curve (MU) on the same graph axes or you can use MS Excel if you know how to draw three graphs on the same axes using the software.
Step 1: Plot the TU, MU, and AU values on the y-axis (scale: 1cm to 4 units) against the values of the units consumed on the x-axis (scale: 1cm to 1 unit).
Step 2: Using a pencil and your free hand, join the points you have plotted for each utility concept to reveal the TU, MU, and AU curves. Describe your curves.
Step 3: Given the price of one apple as Ghc 4.00, determine the equilibrium of the consumer from your graph. Do you remember the formula for equilibrium in the utility of a single commodity consumed?
In Economics, utility means the...
Yaw buys a plate of rice for GH¢12. If Yaw is in utility equilibrium, what is the marginal utility of the rice?
Adwoa's total utility from consuming 2 oranges is 18 utils. When she consumes 3 oranges, her total utility becomes 24 utils. What is the marginal utility of the third orange?
Kwame consumes 4 bottles of water. His total utility is 36 utils. What is his average utility?
Akosua spends her income on kenkey and fish. The marginal utility of kenkey is 20 utils and its price is GH¢4. The marginal utility of fish is 12 utils and its price is GH¢3. What should Akosua do to maximise satisfaction?
Kojo sells bottled water at Madina Market. Ama records the total utility she gets from drinking bottles of water on a hot afternoon. The price of one bottle is GH¢4.00. Use the table below to answer the questions that follow.
| Quantity of bottled water (bottles) | Total utility (utils) |
|---|---|
| 1 | 10 |
| 2 | 18 |
| 3 | 24 |
| 4 | 28 |
| 5 | 30 |
| 6 | 28 |
Define utility and marginal utility.
Calculate the average utility and marginal utility for each quantity of bottled water. Present your answers in a table.
Identify the quantity at which diminishing marginal utility sets in. Explain your answer.
Determine Ama's equilibrium quantity if the price of a bottle is GH¢4.00. Explain your answer.
Suppose the price of a bottle falls to GH¢2.00. Determine Ama's new equilibrium quantity and calculate her total expenditure.
Suggest two ways Ama can use the idea of marginal utility to make rational buying decisions.
Mr. Mensah gives his daughter, Akosua, GH¢50 each month to spend on two goods: kenkey and mobile data. Akosua wants to get the highest possible satisfaction from the money. Use the ideas of utility to answer the following questions.
Define the following terms: utility, total utility, marginal utility, average utility.
State the law of diminishing marginal utility and explain how it affects total utility as more units of a good are consumed.
Explain the condition for consumer equilibrium: (i) for a single commodity; (ii) for two commodities.
Akosua's last ball of kenkey gives her 15 utils and costs GH¢3. Her last mobile data bundle gives her 16 utils and costs GH¢4. (i) Determine whether Akosua is in equilibrium. Show your working. (ii) If she is not in equilibrium, advise her on how to adjust her spending to maximise satisfaction.