# Verification of understanding of the substitution and income effect of normal, inferior and Giffen goods?

My understanding is as follows:

Normal Goods: Income and Substitution effects are both positive.

Inferior Goods: Income effect negative, substitution effect positive. Substitution effect outweighs income effect and so although when the price of an inferior good F decreases (real income increases) and leads to an increase in the quantity of F consumed, this increase is small relative to the decrease in its price due to the substitution effect's magnitude being bigger than that of the income effect.

Giffen Goods:Income effect negative, substitution effect positive. Unlike inferior goods, income effect outweighs the substitution effect.

Please verify whether my understanding, as described above, is accurate.

Additionally, is it correct to assert that the positivity/negativity of the substitution/income effect of a change in price of a good remains the same regardless of whether said good's price increases or a decreases, e.g. regardless of whether the price of a normal good N increases or decreases, its income and substitution effect will always be 'positive'?

• Convention is to think of income and substitution effects in terms of increases in prices and incomes (so they relate directly to partial derivatives in a standard utility maximisation problem) so substitution effects are always negative (higher prices make you substitute away from a good, decreasing its demand) and the income effect of a normal good is positive. – Theoretical Economist Mar 2 '17 at 0:57

[Edited: I think that Theoretical Economist is right in highlighting that I'm perpetuating the confusion between the mathematical formalism, and one way of getting to the intuitive understanding. It also comes down to language referring to the slope of the curve versus effects that are positive or negative depending on moving up or down that negatively-sloped curve. So I clarified the table and text consistently against a price rise and Slutsky.]

I think your intuition is correct, but the derivatives have slopes in the other direction in Slutsky's equation. And it's Slutsky's equation that's ultimately given us this theoretical framework, so let's stick with that here ;)

To be clearer, let's discuss for a Price RISE:

Normal Good:   Demand- = Substitution-- Income-  [Same direction]

Inferior Good: Demand- = Substitution-- Income+  [S > I]

Giffen Good:   Demand+ = Substitution-- Income++ [I > S, weirdly]


I start my understanding of this with the demand curve. Under the “usual” laws of supply and demand, the demand-curve is backward-sloping, so as the price rises, we demand less of it. This is the Ecos101 curve we're familiar with; and it applies both to normal and inferior goods. But for Giffen goods, the demand curve has a positive slope... As the price rises, we actually demand more of it. Usually, examples of luxury goods are given as Giffen goods. The argument runs that as price is an indicator of quality and wealth of the purchaser, people actually by more of these goods as the price rises. The actual empirical evidence for the existence of Giffen goods in the real world, though, is slim and hotly debated... Sorry Apple!

So we understand the demand curves are backwards for normal/inferior, but upwards for Giffens. Why?

It was Slutsky who best disentangled demand curves as comprising an income effect and a substitution effect through a synthesis Marshall and Hicks' respective demand curves. (These are the uncompensated and compensated curves per the comments below.)

Per Slutsky's equation, Theoretical Economist is correct: The substitution effect can only ever be negative / downward-sloping. That leaves only the income effect to explain the differences between the three types of goods.

The link is that as the price of a good rises, in effect income falls. For normal goods, as effective income falls, we demand less of the good. For inferior goods, as income falls, we demand more of the good. Typical examples of inferior goods include staple foods. The idea is that as we get poorer, we cannot afford “rich” foods like meats, exotic fruits, chocolate, and so on; but must "downgrade" to cheaper foods.

Giffen is where things can get counter-intuitive. As the price of a Giffen good rises, even though effectively our income falls, we demand the good so much more that it outweighs the (always-negatively-sloped) substitution effect to yield the total positive demand.

I hope that's both more formal and clearer to understand.

Regarding your final question, the intuitive understanding around the increase/decrease in substitutions based on price rises/falls can be confusing against the fact that the slope of the substitution term in Slutsky is always negative.

From a mathematical perspective, the slope of substitution is always negative, but we can move "up" or "down" that curve to produce "positive" or "negative" changes... More or less substitution of a good.

For the second part of your question about the constancy of these effects; goods can apparently change between being normal/inferior. So if we do as we typically do in economics classes and draw out demand curves and indifference curves as straight lines, it holds.

But in reality, we know that demand curves are not immutable, straight lines, but can (a) curve and (b) change under exogenous variables. Think of the example of an asset bubble. For a while, the asset may actually look like a Giffen good: The price rises, people demand more as they jump on the bandwagon. Suddenly, the bubble bursts, and that asset is “demoted” to being a normal good (just as everyone’s income is decreasing... oops!)

• How can the substitution effect be positive? This effect is meant to capture the idea that consumers substitute away from consuming a good when its price rises. Compensated demand functions (whether computed via Hicks or Slutsky compensation) are always downward sloping in their own price. – Theoretical Economist Mar 2 '17 at 15:11
• @TE: From the perspective of the Slutsky Equation I think you're absolutely correct. It's a little tricky for us to look at in SE comments... But dh/dp is downward sloping, and -x.dx/dw is +ive/-ive for inferior/normal. But the dx/dp in Slutsky is the inverse of the Marshallian demand, right? So when we start the discussion in Marshal demand curves, we fuzz a little and invert the signs of S/I to match that understanding. I'd put it down to a loose, non-mathematical common usage of "the substitution effect". Let me know if you agree. – richarddb Mar 2 '17 at 18:31
• Not sure what you mean by the inverse of Marshallian demand, but even when it comes to matching terminology to understanding, I find calling the substitution effect positive to be incongruous with the idea that a consumer substitutes away from consuming a good when faced with an increasing in price. That is, the substitution effect captures the decrease in demand due to the relative increase in the price of the good. Calling this effect 'positive' does match the intuition for it. I suppose you could be thinking of price decreases rather than price increases, but... (continued) – Theoretical Economist Mar 3 '17 at 2:50
• ...I think it makes more sense to stick with convention. Conventions are there for a reason, even if only for the value of coordination (though I would argue there are more reasons than just this). – Theoretical Economist Mar 3 '17 at 2:52
• Looks like I missed your edits. Downvote rescinded; have an upvote instead. – Theoretical Economist Mar 3 '17 at 10:54