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in the economics book that I'm reading right now it is written that this utility function: $$u(x_1,x_2) = 2x_1 + x_2$$ yields indifference curves with a slope of $−2$. Could someone please explain me how they found the $-2$?

Initially, I was thinking that they derivated the utility function in respect of $x_1$ and $x_2$ but this would give $2$ instead of $-2$. Thank you very much for your help

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Hint: First find the total derivative of $u(x_1,x_2)$, set it to zero as utility does not change along an indifference curve, then solve for $dx_2/dx_1$

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The easy way is to set utility constant $u_0$,

Now, $u_0 = 2x_1+x_2$

$x_2$ as a function of $x_1$ is $u_0-2x_1 = x_2$, this is the indifference curve for a given level of utility.

As you can see the indifference curve is linear with slope -2.

Regards

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