How to Calculate Marginal Utility

Understand the economic concept of utility. Utility refers to the "value" or "satisfaction" a consumer gains from consuming a certain quantity of goods. It can be thought of as the amount a consumer is willing to pay for the satisfaction provided by the goods.

• For example, suppose you are hungry and buy fish for dinner. A fish costs 40,000 VND. If you are so hungry that you would pay 160,000 VND for a fish, the utility provided by the fish is equivalent to 160,000 VND. In other words, you are willing to pay 160,000 VND for the satisfaction the fish brings, regardless of its actual price.

Calculate total utility from consuming a specific quantity of goods. Total utility is the concept of utility applied to more than one unit of goods. Consuming one unit of a good provides a certain level of utility, while consuming more units may result in higher, lower, or equivalent utility.

• For example, suppose you plan to eat two fish. However, after finishing the first one, you no longer feel as hungry as before. Now, you are only willing to pay 120,000 VND for the additional satisfaction from the second fish. As you start feeling full, the fish becomes less valuable to you. This means the two fish together provide 120,000 VND + 160,000 VND (the first fish) = 280,000 VND in "total utility."
• Note that whether you actually buy the second fish or not is irrelevant. MU only concerns how much you are willing to pay for it. In practice, economists use complex mathematical models to predict what consumers are willing to pay for certain products or services.

Determine total utility from consuming different quantities of goods. To find MU, you need two different levels of total utility and use the difference between them to calculate MU.

• Suppose in the example scenario from Step 2, you decide you are hungry enough to eat four fish. After consuming the second fish, you are relatively full and only willing to pay 60,000 VND for the next fish. After the third fish, you are almost completely full, so you only pay 20,000 VND for the last one.
• The satisfaction from consuming the fish is almost negated by the discomfort of being full. You could say the four fish provide a total utility of 160,000 VND + 120,000 VND + 60,000 VND + 20,000 VND = 360,000 VND.

Calculate MU. Divide the change in total utility by the change in the quantity of goods. The result is the marginal utility, or the utility gained from consuming an additional unit of the good. In the example scenario, you calculate MU as follows:

• 360,000 VND – 280,000 VND (example from Step 2) = 80,000 VND
• 4 (fish) - 2 (fish) = 2
• 80,000 VND / 2 = 40,000 VND
• This means, for you, between the second and fourth fish, each additional fish provides a utility equivalent to 40,000 VND. This is an average value; in reality, the third fish is worth 60,000 VND, and the last one is worth 20,000 VND.

Use the equation to determine MU for each additional unit of goods. In the example above, we calculated the average MU for several goods consumed. This is one way to use MU. However, in practice, MU is often applied to each individual unit of goods consumed. This gives us the specific MU that each additional unit provides (rather than an average value).

• Calculating MU for each additional unit is not difficult. Simply use the standard equation to find MU when the change in the quantity of goods consumed is one.
• In the example scenario, you already know the MU for each unit. When you haven't eaten anything, the MU of the first fish is 160,000 VND (160,000 VND total utility - 0 VND before / 1 unit change), the MU of the second fish is 120,000 VND (280,000 VND total utility – 160,000 VND before / 1 unit change). The same applies to the remaining fish.

Use the equation to optimize your utility level. According to economic theory, consumers make purchasing decisions based on their effort to maximize utility. In other words, consumers aim to achieve the highest possible satisfaction from their available budget. This means they tend to buy products or goods until the marginal utility of purchasing additional units is less than the marginal cost (the price of adding one more unit).

Identify the level of utility loss. Let’s revisit the example scenario once more. Initially, the price of each fish is 40,000 VND. We then determine that the first fish has an MU of 160,000 VND, the second 120,000 VND, the third 60,000 VND, and the last fish has an MU of 20,000 VND.

• With this information, you ultimately wouldn’t buy the fourth fish. Its marginal utility (20,000 VND) is lower than the marginal cost (40,000 VND). Essentially, your utility level suffers a loss in this transaction, making it unfavorable for you.

Create columns for quantity, total utility, and marginal utility. Most MU charts include at least these three columns. Sometimes, MU charts may have additional columns, but these three represent the most critical information. Typically, these columns are arranged from left to right.

• Note that column headers may not always match exactly. For example, the "Quantity" column might be labeled as "Items Purchased," "Units Bought," or something similar. What matters is the information presented in the column.

You may notice the trend of diminishing marginal utility. A "classic" MU chart often illustrates this, where as a consumer buys more of a specific good, the desire to purchase additional units decreases.

• In other words, at some point, the marginal utility of each additional unit purchased begins to decline. Eventually, the consumer becomes less satisfied with each additional purchase.

Identifying Maximum Utility. This is the point where the marginal price exceeds MU. The marginal utility chart makes it easier to predict the quantity of goods a consumer will purchase. It's important to reiterate that consumers tend to buy goods until the marginal price (the cost of adding one more unit of goods) is greater than MU. If you know the price of the goods analyzed on the chart, maximum utility is achieved at the last line where MU is higher than the marginal cost.

• Note that utility does not necessarily reach its maximum when MU starts to go negative. The goods may still benefit the consumer even if they are no longer "worth it."
• MU here is not negative, but it still reduces total utility because it does not justify the cost.

Using Chart Data to Find Additional Information. Once you have the three "key" columns, finding additional numerical information about the model scenario the chart is analyzing becomes much easier. This is especially true when using spreadsheet software like Microsoft Excel, which can perform calculations for you. Here are two types of data you might want to input into additional columns to the right of the three main columns:

• Average Utility: Total utility at each line divided by the quantity of goods purchased.
• Consumer Surplus: Marginal utility at each line minus the marginal cost of the product. This figure represents the "profit" in terms of utility that the consumer gains from purchasing each product. It is also known as "economic surplus."

• Understanding that the scenarios in the example are model scenarios is crucial. Here, they represent hypothetical consumers (rather than actual consumers). In real life, consumers are not perfectly rational; for example, they may not buy exactly the amount of products they need to maximize utility. Good economic models are excellent tools for predicting consumer behavior on a broad scale, but they are often not entirely "accurate" in real-life situations.
• If you add a consumer surplus column to the chart (as mentioned above), utility will reach its maximum at the last line before the consumer surplus becomes negative.