# Ambiguous definition of Substitution and Income effect?

Consider the (schematic) indifference curve diagram of two good-quantities Q1, Q2: According to Wikipedia we call the vector AB' the substitution effect and the vector B'B as the income effect.

I now wonder why I could not, instead of translating the tangent through B onto the lower indifference curve, translate the tangent through A to the higher indifference curve, thus denoting AA' as the income effect and A'B as the substitution effect.

Note that these two definitions do not coincide for (sufficiently) different shaped indifference curves.

First, you can make any definition you want as long as you use it consistently, but it's usually better to adopt the standard definition if you want to avoid confusion. Similarly you could ask why we don't call a garage a dogpound and a dogpound a garage. We perfectly well could, but it's better if we all use words the same way.

Second, assuming we agree to adopt the standard definition, your picture doesn't give enough information to determine a substitution and an income effect. That depends on where you started and what changed, which you haven't told us.

IF you started at $A$ and the price dropped, then, according to the standard definition, the substitution effect is from $A$ to $B'$ and the income effect is from $B'$ to $B$.

If you started at $B$ and the price rose, then, according to the standard definition, the substitution effect is from $B$ to $A'$ and the income effect is from $A'$ to $A$.

Third, if you want to adopt your alternate definition, you will find that your definition and the standard definition agree arbitrarily closely for sufficiently small changes. So if you imagine an infinitesimal price change, it doesn't matter which definition you adopt. But for finite price changes, what matters is not that one definition is better than another, but that we find a definition we can all agree to use.

• Thank you for the detailed answer. You are right, I should have stated that I assumed considering a price drop of Q1, starting at A. Actually, as I just started diving into economics, I don't yet know what these definitions are important for. But if indeed we just use the handwavy property "the one denotes change in income, the other in substitution of products" as a motivation, this might be misleading as there are actually different changes satisfying this property (i.e. BB' != AA' respectively AB' != A'B). – axsk Dec 3 '14 at 16:45
• The third part indeed confuses me. As long as I take any continious definition (both indeed are here, assuming constant utility functions) they all lead to infinitesimal changes under infinitesimal changes, so if we are interested in infinitesimal changes we would have to use the derivative(s). But there the definitions differ again. So this argument doesn't save us. – axsk Dec 3 '14 at 16:50
• If none of the definitions is better, and they are not equivalent, won't this in the end result in two differing models/theories/policys, both justified by the same argumentation? I think it would be wrong to agree on one of them and ignore the other... – axsk Dec 3 '14 at 16:55
• Regarding your last comment: Very often in economics, the question we're asking is "Do we currently have too much of activity X or too little of activity X?" This is equivalent to asking "Would a tiny bit more of activity X make us better off or worse off?". So for policy questions, we generally find ourselves focusing on the effects of infinitesimal changes. – Steven Landsburg Dec 4 '14 at 5:03