# indifference curve slope from utility function

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

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 $$dx_2/dx_1$$

• What do you mean by total derivative? Feb 6 '19 at 10:33
• See: en.m.wikipedia.org/wiki/Total_derivative and look for the differential form. Feb 6 '19 at 10:41

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