Question

The total utilities associated with the first 5 units of consumption of good \(X\) are \(15,30,40,47,\) and \(50,\) respectively. What is the marginal utility associated with the third unit? a. 15 b. 70 c. 85 d. 10 e. 45

Short answer

The marginal utility associated with the third unit is 10.

Step-by-step solution

Understand the concept of marginal utility

Marginal utility is the additional satisfaction (utility) gained from consuming an additional unit of a good. To calculate the marginal utility, we need to find the increase in total utility from consuming each additional unit.

List the total utilities

We are given the total utilities (TU) for the first 5 units: Unit 1: TU = 15 Unit 2: TU = 30 Unit 3: TU = 40 Unit 4: TU = 47 Unit 5: TU = 50

Calculate the marginal utilities

To find the marginal utility (MU) for each unit, we will subtract the total utility of the previous unit from the total utility of the current unit. Unit 1: MU = (TU_1 - 0) = 15 Unit 2: MU = (TU_2 - TU_1) = (30 - 15) = 15 Unit 3: MU = (TU_3 - TU_2) = (40 - 30) = 10 Unit 4: MU = (TU_4 - TU_3) = (47 - 40) = 7 Unit 5: MU = (TU_5 - TU_4) = (50 - 47) = 3

Identify the marginal utility for the third unit

From our calculations in Step 3, the marginal utility of the third unit is 10. So, the correct answer is option d. 10.

Key concepts

Total Utility

Total utility represents the overall satisfaction or happiness that a consumer derives from consuming a set number of units of a good or service. This concept is significant because it helps us understand the maximum satisfaction level one can achieve with given quantities of goods consumed. For instance, if you consume 5 units of a product, you might be interested in knowing the overall satisfaction gained from these 5 units. In the given exercise, the total utility values associated with consuming the first to the fifth units of good X are 15, 30, 40, 47, and 50, respectively.
Each value represents the cumulative satisfaction up to that point. Understanding total utility is crucial because it sets the stage for calculating marginal utility, helping us identify the point of diminishing returns to consumption.

Consumption Units

Consumption units refer to individual quantities of goods consumed. Understanding consumption units is vital because it allows us to break down the consumption process into smaller parts, making it easier to analyze the utility gained from each additional unit. In our exercise, we're dealing with consumption units of a good labeled as X. You consume one unit at a time, which leads you to experience different total utilities at each stage. The process of analyzing consumption units helps explain granular changes in utility, allowing a detailed look into how each level of consumption affects satisfaction derived from the good.
Such information supports better decision-making regarding how much of a good to consume and when to stop, to get the most satisfaction while using resources wisely.

Utility Calculation

To effectively calculate utility, one needs to determine both total utility and marginal utility. When calculating total utility, you simply account for the cumulative satisfaction from all units of a good consumed. However, calculating marginal utility requires subtracting the total utility of the previous consumption unit from the total utility of the current unit. This step highlights the additional satisfaction gained from consuming one more unit. For instance, to find the marginal utility of the third unit in our exercise:

• Total utility for 3 units: 40
• Total utility for 2 units: 30
• Marginal utility for third unit = 40 - 30 = 10

Such calculations reveal diminishing returns, as seen in the reducing marginal utility values with each unit consumed.

Additional Satisfaction

Additional satisfaction, synonymous with marginal utility, signifies the extra benefit derived from consuming an additional unit of a product. Understanding this concept is essential because it helps consumers decide how much of a good to consume. In economic terms, it guides you to understand when your satisfaction from consuming an extra unit starts to decrease. In our exercise, the additional satisfaction decreases with each unit of good X consumed:
- First unit provides 15 units of additional satisfaction - Second unit also provides 15 units - Third unit provides only 10 units This diminishing pattern is typical and aligns with the law of diminishing marginal utility, illustrating why consumers stop consuming after a certain point.