As shown in the Calculus of Hedonism, economists derive the individual demand curve from individual utility maps. Normally this results in the desired downward-sloping demand function, but there is a fly in the ointment to dispose of, since it is possible, though difficult, to draw a utility map which results in an upward sloping demand curve, as in Figure 12.
Figure 2.12 Upward sloping demand curve with “inferior” good
This anomaly occurs because when the price of a commodity falls, the consumer’s real income in effect increases. This can be seen in our bananas and biscuits example: if the price of bananas falls while income and all other prices remain constant, then the consumer can buy more bananas without reducing her purchases of any other commodities. Therefore she is materially better off, even though her income hasn’t changed.
However, this can lead to perverse effects if one item in her shopping basket is relatively undesirable compared to more expensive alternatives–say, instant coffee rather than freshly ground beans–and plays a large role in her budget. If the price of this commodity falls, it is possible the consumer could respond to the effective increase in income by consuming less of this product, even though it has become cheaper.
The increase in material well-being due to the price of a commodity falling is known as the “income effect”. It can lead you to consume more of the product, or it can lead you to consume less–it depends on the commodity. The pure impact of a fall in price for a commodity is known as the “substitution effect”. So long as we are dealing with “goods”–things which increase the consumer’s utility, however slightly–then the substitution effect is always going to be in the opposite direction to the change in price.
There’s a catch for beginners coming up here (but don’t worry too much if trying to understand it makes your head spin, because it plays no role in the forthcoming critique). If the income effect for a commodity causes the consumer to consume more of a commodity, it’s described as being negative. The reason for this is that consumption has moved up in response to price moving down. Since consumption and price move in opposite directions, the effect is said to be negative. However, if the fall in price of a commodity causes you to consume less of it, then the income effect is said to be positive. Price and consumption have both moved in the same direction, therefore the effect is positive. If two effects are in the same direction, they are positively related; if they are in the opposite direction, they are negatively related.
The substitution effect is said to always be negative–consumption of a commodity due to the substitution effect always moves in the opposite direction to the price. Thus if the price of a commodity rises, the substitution effect always causes the consumer to consume less of this product.
Sometimes the substitution and the income effects will both be negative–this will apply when what you regard as a luxury becomes cheaper. So if the price of, say, chocolate falls, you will consume more, both because the fall in price has made you effectively wealthier (negative income effect), and because the fall induces you to substitute chocolate for other commodities in your shopping basket, which are now relatively more expensive compared to chocolate (negative substitution effect).
At other times, the substitution effect will be negative as always, but the income effect will be positive. Castor oil was once a popular example of this. If this unpalatable but common medicine became cheaper, the income effect could induce you to spend less on it–and to buy more of a more palatable medicine instead. However, it is still possible that the negative substitution effect could outweigh the positive income effect, so that the consumer would buy more castor oil and more of some other medicines.
But it is conceivable that the income effect of the price fall could be so positive, that it outweighs the negative substitution effect of the lower relative price, resulting in consumption of a commodity falling as its price falls. This results in the upward-sloping demand curve shown in Figure 12.
Economists thus found it necessary to search for a way to divide the impact of any change in price into the income effect and the substitution effect. If the income effect could be subtracted from a price change, this would leave the subtitution effect as the pure impact on consumption of a change in relative prices. The problem is, though, that neither the “income effect” nor the “substitution effect” is directly observable: all we actually see is a consumer’s purchases changing as the price of a commodity changes.
Economists dreamt up a way of at least notionally subtracting the income effect from a price change, using indifference curves. Since, to an economist, the real object of individual behaviour is utility maximisation, and since any point on a single indifference curve generates the same utility as any other point, then in utility terms the consumer’s “psychic income” is the same along this curve.
The substitution effect of a price fall could thus be isolated by “holding the consumer’s utility constant” by keeping him/her to the same indifference curve, and rotating the budget constraint to reflect the new relative price regime. This amounts to reducing the consumer’s income until such time as he/she can achieve the same level of satisfaction as before, but with a different combination of biscuits and bananas. Then the budget constraint is moved out to restore the consumer’s income to its actual level and voila, we have separated the impact of a price change into the substitution and income effects.
This convoluted procedure is illustrated in Figure 13. The initial position has the consumer’s income allowing him to choose A bananas, given that the budget line aa represents both his/her income and the initial price ratio of bananas to biscuits. Then the price of bananas drops, allowing the consumer to purchase B bananas along the budget line ab (since income and the price of biscuits have remained constant). This observable change (in that we could actually observe a consumer changing from A to B with a fall in the price of bananas) is then broken down into two unobservable components–since to observe the substitution effect we would actually have to know the consumer’s indifference curves, which are unobservable–by notionally moving the new budget constraint back until it is tangential to the original indifference curve. At this notional budget line, cc in Figure 13, the consumer would choose C bananas, and the move from A to C represents purely the substitution effect of bananas being cheaper than before. This pure subsitution effect necessarily results in the consumer consuming more bananas. The difference between C and the actual consumption level B thus represents the income effect of a lower price for bananas (which as I’ve drawn it is also positive–though it is possible for the income effect to be negative, as discussed earlier).
Figure 2.13 Separating the impact of a price change into the “income” and “substitution” effects
A demand curve constructed by “holding utility constant” in this fashion isolates the substitution effect, which is necessarily negative–in that a higher price results in a lower level of consumption, and vice versa–and therefore results in a demand curve which necessarily slopes downward in price. Economists describe this curve, shown in the lower half of Figure 14, as a “compensated” or “Hicksian” demand curve.
Figure 2.14 A “compensated” demand curve necessarily slopes downwards