<p>This is quite simple to answer given you know a bit of multivariable differential calculus. You're looking for <em>partial</em> derivatives of the utility function. </p>

<p>So, given <span class="math-container">$$U(x,y) = x(y+1)$$</span> we have <span class="math-container">$$\frac{\partial U}{\partial x} = y+1$$</span> and <span class="math-container">$$\frac{\partial U}{\partial y} = x$$</span>. </p>

<p>These are the goods' marginal utilities.</p>

CC BY-SA 4.0
2018-12-02T22:46:07.387Z
2018-12-02T22:46:07.387Z
Pedro Cavalcante
<p>I'm just getting started as an amateur into microeconomics and I really can't understand this thing about marginal utility when more than one good is involved:</p>

<p>Let's say I have the utility function <strong><em>U = x(y+1)</em></strong>. </p>

<p>Now, from what I've studied, I  think that the marginal utilities for x and y should be:</p>

<p><em>MU<sub>x</sub> = y+1<br>
MU<sub>y</sub> = x</em></p>

<p>I just don't get how to arrive there "mathematically", and I fear I wouldn't be able to find the marginal utilities of a more complex function, for example <strong><em>U = x(x+y)</em></strong> </p>

<p>Could you help me?<br>
Thank you!</p>

CC BY-SA 4.0
2018-12-02T13:19:29.763Z
Have you studied differential calculus?
Dan
CC BY-SA 4.0
2018-12-02T13:26:05.873Z
I know how to find the derivative of a single-variable function, but I've never done it with two variables
alkazam
CC BY-SA 4.0
2018-12-02T17:19:40.993Z
It's basically the same, but called a partial derivative.  The marginal utility of $x$ is just $dU/dx$, treating $y$ as if it's a constant.  This is exactly what you've already done for your first utility function.
Dan
CC BY-SA 4.0
2018-12-02T20:55:38.477Z
Take a look at [**partial derivative**](https://en.wikipedia.org/wiki/Partial_derivative).
Herr K.
CC BY-SA 4.0
2018-12-02T21:14:08.507Z
It was quite easy then. Thank you very much!
alkazam
<microeconomics><utility><marginal>
How to calculate marginal utility with two goods?
alkazam
# How to calculate marginal utility with two goods?

(Asked by: username_0 on 2018-12-02)

I'm just getting started as an amateur into microeconomics and I really can't understand this thing about marginal utility when more than one good is involved:

Let's say I have the utility function ***U = x(y+1)***.

Now, from what I've studied, I think that the marginal utilities for x and y should be:

*MUx = y+1  
MUy = x*

I just don't get how to arrive there "mathematically", and I fear I wouldn't be able to find the marginal utilities of a more complex function, for example ***U = x(x+y)***

Could you help me?  
Thank you!

**Tags:** microeconomics, utility, marginal

> **Comments:**
> **username_1**: Have you studied differential calculus?  
> **username_0**: I know how to find the derivative of a single-variable function, but I've never done it with two variables  
> **username_1**: It's basically the same, but called a partial derivative.  The marginal utility of $x$ is just $dU/dx$, treating $y$ as if it's a constant.  This is exactly what you've already done for your first utility function.  
> **username_2**: Take a look at [**partial derivative**](https://en.wikipedia.org/wiki/Partial_derivative).  
> **username_0**: It was quite easy then. Thank you very much!  

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## 1 answers

### Answer by username_3 on 2018-12-02. Score: 1 | Accepted answer

This is quite simple to answer given you know a bit of multivariable differential calculus. You're looking for *partial* derivatives of the utility function.

So, given $$U(x,y) = x(y+1)$$ we have $$\frac{\partial U}{\partial x} = y+1$$ and $$\frac{\partial U}{\partial y} = x$$.

These are the goods' marginal utilities.


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