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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!

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    $\begingroup$ Have you studied differential calculus? $\endgroup$ – Dan Dec 2 '18 at 13:19
  • $\begingroup$ I know how to find the derivative of a single-variable function, but I've never done it with two variables $\endgroup$ – alkazam Dec 2 '18 at 13:26
  • $\begingroup$ 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. $\endgroup$ – Dan Dec 2 '18 at 17:19
  • $\begingroup$ Take a look at partial derivative. $\endgroup$ – Herr K. Dec 2 '18 at 20:55
  • $\begingroup$ It was quite easy then. Thank you very much! $\endgroup$ – alkazam Dec 2 '18 at 21:14
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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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