Question

Using the following information, calculate total utility and marginal utility. a. Plot the total utility curve. b. Plot marginal utility directly below total utility. c. At what marginal utility value does total utility reach a maximum? \(\begin{array}{lr}\text { Number of utils for the first unit } & 300 \\ \text { Number of utils for the second unit } & 250 \\ \text { Number of utils for the third unit } & 220 \\ \text { Number of utils for the fourth unit } & 160 \\\ \text { Number of utils for the fifth unit } & 100 \\ \text { Number of utils for the sixth unit } & 50 \\ \text { Number of utils for the seventh unit } & 20 \\ \text { Number of utils for the eighth unit } & 0 \\ \text { Number of utils for the ninth unit } & -250\end{array}\)

Short answer

Answer: The point on the marginal utility curve where the values start to decline signifies the maximum total utility. This indicates that the additional satisfaction a consumer gets from consuming the next unit begins to decrease, meaning that they have reached the highest level of satisfaction that the good can provide.

Step-by-step solution

Calculate Total Utility

To calculate total utility, add the utils for each unit of consumption. For example, total utility after consuming 1 unit will be 300, as there are 300 utils for the first unit. To find the total utility after consuming 2 units, add the utils for the second unit (250) to the previous total utility, and so on for the other units.

Calculate Marginal Utility

To calculate marginal utility, find the difference in total utility between each consecutive unit of consumption. For example, the marginal utility of the second unit is the difference in total utility between consuming 2 units and consuming 1 unit.

Create Total Utility Curve

Using the calculated total utility values, plot the total utility curve with the number of units consumed on the x-axis and the total utility on the y-axis.

Create Marginal Utility Curve

Using the calculated marginal utility values, plot the marginal utility curve with the number of units consumed on the x-axis and the marginal utility on the y-axis. Make sure this graph is directly below the total utility curve for easy comparison.

Identify Maximum Total Utility

To find the marginal utility value at which total utility reaches a maximum, look for the point on the marginal utility curve where the value starts declining. At this point, the additional satisfaction that a consumer gets from consuming the next unit (marginal utility) begins to decrease. This point corresponds to the maximum total utility.

Key concepts

Total Utility Calculation

To understand total utility, simply imagine it as the sum of satisfaction or benefit that a consumer obtains from consuming goods and services. Whenever you indulge in a slice of your favorite pizza or buy that new pair of shoes, you're experiencing utility.

Calculating total utility entails summing up the utilities from each unit of consumption. So, in our exercise example, you begin with the first unit providing 300 utils, indicating a high level of satisfaction from the initial consumption. As more units are consumed, you continue to add each additional unit's utils to the previous total.

Here's a simplified illustration: after consuming two units, your total utility would be 300 (from the first unit) plus 250 (from the second unit) for a total of 550 utils. As you consume more, it progressively adds up, painting a picture of overall satisfaction across the span of consumption.

Visualize this process with a shopping spree. The first item brings a burst of happiness, and as you add items to your cart, your happiness accumulates—up to a certain point, that is.

Utility Curves in Economics

Now take this concept into the visual realm—with utility curves. In economics, these curves are essential graphical representations that show the relationship between the quantity of a good or service consumed and the utility derived from that consumption.

For the total utility curve, you plot the cumulative satisfaction on the vertical axis (y-axis), against the quantity consumed on the horizontal axis (x-axis). As more items are consumed, the total utility generally increases, but the rate may vary—it's like watching your joy soar with each slice of pizza consumed at your party.

Comparing Curves

What's equally telling is considering the marginal utility curve alongside the total utility curve. This secondary curve represents the additional utility gained from each extra unit consumed. By plotting both, you can visually parse out how satisfaction evolves—not just in total, but at the margin with each bite, or each unit consumed.

Law of Diminishing Marginal Utility

Ah, the law of diminishing marginal utility, a pivotal principle in economics—it's like the bittersweet realization that your third slice of pizza doesn't taste as divine as the first. This law states that as a consumer consumes more units of a good or service, the utility gained from each additional unit tends to decrease.

The exercise amps up the reality of this concept: you start off with a high marginal utility (those first few slices are heavenly), but with each additional unit consumed (slice after slice), the added satisfaction diminishes.

• First unit: Total utility of 300 utils.
• Second unit: Adds only 250 utils (not as impactful as the first).
• By the eighth unit, no additional satisfaction is gained—it's at zero utils, possibly indicating fullness or even displeasure at overindulgence.

In essence, the principle guides consumers on when to stop consuming in order to maximize overall satisfaction and helps businesses price their goods effectively. It is this very law that tells us why we can't just keep consuming endlessly and expect to maintain the same levels of joy.