Hello, this is Frank.

Today, I’m going to explain how to calculate **marginal utility** using **partial differentiation**, a method that frequently appears in economics. Many of you have probably heard the phrase **“law of diminishing marginal utility.”** Back in my university days, I remember feeling a little proud when I first learned it.

■ Understanding the Basics of Economics

As written in my profile, I majored in Economics at Hyogo Prefectural Kobe University of Commerce.
Marginal utility represents the increase in satisfaction (utility) gained by consuming one additional unit of a good or service, and it plays a key role in consumer theory in microeconomics.

Today, let’s calculate marginal utility using partial derivatives.

【Problem】

For the utility function \(u = x^{0.2}y^{0.5}\), find the marginal utilities \(MU_{x}\) and \(MU_{y}\).

Partial differentiation means taking the derivative with respect to one variable while keeping all other variables constant.

Now, let’s solve it.

【Solution】

\(MU_{x} = \frac{du}{dx} = 0.2x^{0.2 – 1}y^{0.5} = 0.2x^{-0.8}y^{0.5}\)

Next,

\(MU_{y} = \frac{du}{dy} = 0.5x^{0.2}y^{0.5 – 1} = 0.5x^{0.2}y^{-0.5}\)

Although the topic may feel challenging—especially for those of us from a humanities background—understanding it is incredibly rewarding.

Let’s continue deepening our learning step by step.

Stay tuned for the next article!

---

Learn more in Mathematics for Global Business：Click here!
【Reference Book】“High School Mathematics Once Again” by Kazuo Takahashi / Japan Jitsugyo Publishing
【Lessons】For online English lessons, please see this page.
【Content Notice】We strive for accuracy, but we do not guarantee completeness. We assume no responsibility for any errors contained on this site.

---

For those curious about my publications, please visit my Amazon Author Page.

Back to Genre：>Here

---

Need a break? Why not check out my daughter’s YouTube channel, asobifantasia.
We’d be so happy if you subscribed!

Currently, I’m participating in the popular blog rankings.
Today’s ranking for [masona｜Top Blog Digest] is?