# marginal utility and Marginal rate of substitution

While studying for my microeconomics class, I realized that I could not fully understand the meanings of Marginal utilities and marginal rate of substitution. Can anyone explain to me the difference between these two and what they mean, briefly and with examples? thanks in advance

• These are standard concepts that should be covered in your textbook/class notes. Have you read those? Perhaps you can point out the specific aspects of those concepts that you couldn't understand? Was it a particular phrase/expression/formula in the definitions that's unclear? Nov 14, 2021 at 19:33

Marginal utility is the increase in utility per unit increase in a good. Marginal rate of substitution is like the exchange rate between two goods given a level of utility.

To Answer your question, suppose that you have the following utility function $$U ={U(x,y)}$$

Then the
marginal Utility of good x will be $$MU_x = \frac{\partial U}{\partial x}$$
and
marginal Utility of good y will be $$MU_y = \frac{\partial U}{\partial y}$$

The Marginal rate of substitution will be $$MRS = \frac{MU_x}{MU_y}$$

In summary Marginal utility shows how your utility changes when you consume more unit of a given good. Marginal rate of substitution shows how much you have to give up of one good if you want to consume more of another good keeping the utility at the same level.

• "Marginal rate of substitution shows how much you have to give up of one good if you want to consume more of another good." This is not well put, as the sentence does not contain any information about utility levels. Nov 14, 2021 at 22:01
• Thanks for pointing that, the answer has been updated Nov 15, 2021 at 10:31