feature of indifference curve

The characteristic feature of indifference curve is that it will not touch the X axis or Y axis. But as a special case it will touch the Y axis if the combination is between Money and Commodity. "If money is taken on Y-axis, then IC curve can touch oy-axis" here we have taken 'money' on Y-axis and 'commodity' on X-axis. Here my doubt is could we use indifference curve for one commodity? If so please explain me with an example.

• Indifference curves can touch the axis. In that case, preferences are not strictly convex. – Patricio Jan 8 at 12:20
• @Patricio Please post answers as answers so I can downvote them when they are incorrect. (I also like to upvote when they are correct.) – denesp Jan 8 at 14:27
• @denesp, I thought mine wasn't aproper answer, just a comment – Patricio Jan 8 at 17:49
• @Patricio: Your comment is incorrect in that convex preferences can generate indifference curves that intersect the axes. An example is the quasi-linear preference $u(x,y)=\sqrt x+y$. – Herr K. Jan 14 at 15:43
• @HerrK.I was under the impression that strict convexity guarantees an interior solution (one with $x>0,y>0$). That is not the case with quasi-linear preferences (in your example, income needs to exceed $\frac{p_y^2}{4p_x}$ in order for the consumer to be willing to consume some amount of good $y$) – Patricio Jan 16 at 9:08

An indifference curve can touch the axes, take for example the case of perfect substitutes, if the consumer his utility is given by U=x1+x2 then obviously he is indifferent between bundle (10,0) and (0,10). So not touching the axes is not a characteristic of indifference curves as such, even though in the case of Cobb-Douglas functions it holds.

As for your other concern, whether an indifference curve can take as input only one good, with the other input being money: this is perfectly possible, it is even a more general case than the indifference curve for two goods. In the case of the inputs x1= a good and m=money held by the consumer we can formalize the utility maximization problem in the following way: max U=u(x1,m) Subject to the constraint: b=p1x1+m As you see the standard form can be used with just one change: the price of a unit money held is of course 1.

And now the more general case, again let x1 be a good the consumtion of which we are interested in and now let y be the MONEY SPENT on all other goods. Now again we can use the modification of the budget constraint above. That is: price of y is 1. In short: anything can be an input in an utility function, just think about your own preferences: you dont just enjoy goods, you enjoy holding money and giving to charity etc. but also spending time with friends/family, with some modifications all this can be put in the form of a utility maximization problem and thus an indifference curve can be constructed for any two inputs, holding other inputs fixed.

As already mentioned by others indifference curves can touch the axes.

I think that here some confusion arises from the language that people usually use. When we say being indifferent between two goods we mean between holding or consuming two goods. And indifference curve gives you all bundles that satisfy this.

In the same manner you can be indifferent between goods and services, goods and leisure or as in your example goods and money.

To construct indifference curve you need just two alternatives. Here you don’t have indifference curve for one good with itself but an indifference curve for two alternatives, one holding money which you may like to do and second alternative is purchasing given good.