# 3 Ways to Calculate Marginal Utility

In economics, the concept of marginal utility represents a means of measuring the amount of value or satisfaction a consumer gets from consuming something. As a general rule, this is the difference in total utility divided by the difference in the quantity of goods consumed. A common way of thinking about it is to imagine how useful someone is for each additional unit of good consumed.

## Steps

### Method 1 of 3: Using the Marginal Utility Equation

#### Step 1. Understand the economic concept of utility

It represents the "value" or "satisfaction" that the consumer gets from consuming a certain amount of products. A good way to look at it is to imagine how much money he would hypothetically pay for the satisfaction offered by a certain product.

• For example, suppose you are hungry and are buying fish to eat for dinner. Imagine that the total cost of the product is R$2{displaystyle {text{R}}\$\ 2}

. Se a sua fome é grande a ponto de fazê-lo pagar R$8{displaystyle {text{R}}\$\ 8}

por ele, diz-se que o peixe oferece R$8{displaystyle {text{R}}\$\ 8}

em utilidade. Em outras palavras, você está disposto a pagar R$8{displaystyle {text{R}}\$\ 8}

pelo peixe independente de qual será o custo verdadeiro.

#### Step 2. Calculate the total utility with the consumption of a specific amount

Total utility represents only the concept of utility applied to a quantity greater than one. If the consumption of a product brings a certain amount of utility, increasing that consumption will bring superior, inferior or equal results.

• For example, suppose you plan to eat two fish. However, after eating the first one, your hunger is no longer so intense. Now, you would only pay BRL 6{displaystyle {text{R}}\$\ 6} pela satisfação do segundo, ou seja, ele não vale mais tanto quando a sua barriga está cheia. Isso significa que os dois peixes trouxeram juntos R$ 6+R$8{displaystyle {text{R}}\$\ 6+{text{R}}\$\ 8} (primeiro peixe) =R$ 14{displaystyle ={text{R}}\$\ 14} #### Step 3. Calculate the total utility from the consumption of different amounts To determine marginal utility, you need to have two distinct measures of total utility. You will use the difference between them to make your calculation. • Suppose, in the example of Step 2, you've decided you're hungry enough to eat four whole fish. After the second one, it's already a little full, so I'd be willing to pay just R$ 3{displaystyle {text{R}}\$\ 3} pelo seguinte. Depois do terceiro, você já se sente quase satisfeito e pagaria apenas R$ 1{displaystyle {text{R}}\$\ 1} pelo último peixe. • A satisfação obtida seria quase superada pela sensação de se estar exageradamente cheio. Você poderia dizer que os quatro peixes trouxeram uma utilidade total de R$ 8+R$6+R$ 3+R$1=R$ 18{displaystyle {text{R}}\$\ 8+{text{R}}\$\ 6+{text{R}}\$\ 3+{text{R}}\$\ 1={text{R}}\$\ 18} #### Step 4. Calculate the marginal utility Divide the difference in total utility by the difference in units. The response obtained represents the marginal utility, or the utility that resulted from each additional unit consumed. In the example situation, you would perform the calculations as follows: • R$18−R$14 (Step 2)=R$44(fish)−2(fish)=2R$4R$2=R2{displaystyle {begin{aligned}{text{R}}\\ 18-{text{R}}\$\ 14\ \left({text{Step 2}}\right)&={text{R}}\$\ 4\4\left({ text{fish}}\right)-2\left({text{fish}}\right)&=2\{frac {{text{R}}\$\ 4}{{text{ R}}\$\ 2}}&={text{R}}\\ 2\end{aligned}}} • Em outras palavras, entre o segundo e o quarto peixes, cada novo peixe valerá apenas R 2{displaystyle {text{R}}\$\ 2} • em utilidade para você. Esse é um valor médio, apenas - o terceiro peixe valerá R$ 3{displaystyle {text{R}}\$\ 3} enquanto o quarto valerá apenas R$ 1{displaystyle {text{R}}\$\ 1} ### Método 2 de 3: Calculando a utilidade marginal de unidades adicionais #### Step 1. Use the equation to determine the marginal utility of each additional unit In the example above, it was possible to determine the average marginal utility of several products being consumed. However, the concept is more often applied to individual units, which results in the precise marginal utility of each one (rather than an average). • This is an easier calculation than it appears to be. Just use the normal equation to determine the marginal utility when the change in quantity equals a. • In the example, you already know the marginal utility of each unit. Before having consumed any fish, the marginal utility was equivalent to R$ 8{displaystyle {text{R}}\$\ 8} (sendo R$ 8{displaystyle {text{R}}\$\ 8} de utilidade total −R$ 0{displaystyle -{text{R}}\$\ 0} consumido antes ou em variação da unidade anterior), a utilidade marginal do segundo equivalia a R$ 6{displaystyle {text{R}}\$\ 6} (sendo R$ 14{displaystyle {text{R}}\$\ 14} de utilidade total −R$ 8{displaystyle -{text{R}}\$\ 8} consumido antes ou em variação da unidade anterior) e assim por diante. #### Step 2. Use the equation to maximize its utility In economic theory, consumers make decisions about their spending in an effort to maximize their utility. In other words, they want to extract as much satisfaction as possible from their money. This means that they tend to buy goods or products until the marginal utility of an additional purchase is less than the marginal cost (price of one more unit). #### Step 3. Determine lost utility Look at the example again. First, each fish cost R$ 2{displaystyle {text{R}}\$\ 2} . A seguir, foi determinado que o primeiro deles apresentava uma utilidade marginal de R$ 8{displaystyle {text{R}}\$\ 8} , o segundo de R$ 6{displaystyle {text{R}}\$\ 6} , o terceiro de R$ 3{displaystyle {text{R}}\$\ 3} e o quarto de R$ 1{displaystyle {text{R}}\$\ 1} • Com essa informação em mente, você acabaria não comprando o quarto peixe. Sua utilidade marginal (R$ 1{displaystyle {text{R}}\$\ 1} • ) se revelou inferior ao custo marginal (R$ 2{displaystyle {text{R}}\$\ 2} ). Basicamente, você está perdendo utilidade nessa transação, de modo que seguir adiante não está em seu melhor interesse. ### Método 3 de 3: Usando uma tabela de utilidade marginal Planilha de exemplo: Entradas para um festival de cinema Entradas compradas Utilidade total Utilidade marginal 1 10 10 2 18 8 3 24 6 4 28 4 5 30 2 6 30 0 7 28 -2 8 18 -10 #### Step 1. Define columns for quantity, total utility and marginal utility Most marginal utility tables have at least three columns. You can find a few with more, but these often display the most crucial information. It is customary to arrange them from left to right. • Note that the headings in each column will not always have an exact match. For example, the column "The amount" may be described as "purchased items", "Units purchased" or something similar. The most important thing is the information present in the column cells. #### Step 2. Look for a declining earnings trend A "classic" table is often used to demonstrate that as a consumer buys more of a certain product, the desire to buy even more diminishes. In other words, after a certain point the marginal utility of each additional purchase starts to decline. At a certain point, the consumer begins to derive less satisfaction than before when making new purchases. ### In the table above, the trend of diminished earnings starts almost immediately. The first ticket purchased for the film festival is of great marginal utility, but each additional ticket has a slightly lower value. After the sixth, each additional entry has a negative marginal utility, which decreases overall satisfaction. One of the explanations would be that, after six visits, the consumer starts to get tired of watching the same movies over and over again #### Step 3. Determine the maximum utility This is the point where marginal price trumps marginal utility. The table makes it easy to predict how many units of a product will be purchased by the consumer. As a reminder, it is customary for them to shop until the marginal price (cost of an additional unit) exceeds the marginal utility. If you know how much the products in the analyzed table cost, the point at which utility is maximum will be represented by the last row where marginal utility exceeds marginal cost. • Suppose the table entries cost BRL 3{displaystyle {text{R}}\$\ 3}

cada. Nesse caso, a utilidade será maximizada quando o consumidor adquirir quatro unidades. O seguinte, por sua vez, terá uma utilidade marginal de R$2{displaystyle {text{R}}\$\ 2}

, que é inferior ao custo marginal de R$3{displaystyle {text{R}}\$\ 3}

de utilidade marginal. Não se trata de um valor negativo, mas que ainda diminui a utilidade total por não valer o custo que foi pago.

#### Step 4. Use the data table to find additional information

Once you have found the three "core" columns above, it is easy to get more numerical data about the situation analyzed by the table. This is even more obvious when you make use of a spreadsheet application like Microsoft Excel, which can do all the calculations for you. Here are two types of data you might be able to enter in the additional columns to the right of the three examples:

• Average utility:

the total utility on each line divided by the quantity of products purchased;

• Consumer surplus:

the marginal utility on each line minus the marginal cost of the product. This value represents the "profit" in terms of utility that the consumer gets from the purchase of each unit. It can also be called "economic surplus".

## Tips

• It is important to understand that the exemplified situations represent mere hypothetical models. In other words, they represent imagined (and not real) scenarios. In everyday life, consumers are not perfectly rational and may, for example, fail to buy the necessary amount of a product to maximize the purchase's utility. Good economic models are great tools for predicting consumer behavior on a large scale, but they usually don't "emulate" real life accurately.
• If you want to insert the consumer surplus into a new column of your table (as described above), the point at which the utility is maximized will be the last row before the value becomes negative.