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Economic Principles:
How the Market Works

Economic Principles: How the Market Works

Chapter 5: The Demand for a Product

The demand function
Income elasticity of demand
Price elasticity of demand
The law of demand: income and substitution effects
Cross-price elasticity
From individual demand to market demand

To be remembered:

• Law of demand

• Substitutability and complementarities

• Price elasticity

• Income elasticity

• Difficulties to aggregate demands

Bibliography:

. Adam Smith: Wealth of Nations

. Kirzner: Competition and Entrepreneurship

. Knight: Risk, Uncertainty and Profit

. Hayek: The Use of Knowledge in Society

The demand function

In the previous chapter, we have introduced concepts that should help us to organize our understanding of individuals choose; concepts such as those of marginal utility, marginal rate of substitution, budget constraint, relative price, complementarities, substitution, rationality, and so on. We were also able to derive some general principles concerning that choice. We saw, for instance, the law of decreasing marginal utility , or the necessity, in order to make a rational choice (the one that gives you the maximum satisfaction) to equalize the marginal rate of substitution and the ratio of relative prices .

In that chapter we will build on that model and derive further economic principles regarding consumer's choice.

We explained previously that the basket that will be chosen by the consumer depends on many parameters. It is therefore clear that the composition of the basket will change with those parameters. In this chapter we will focus on three parameters: the revenue, the price of good x, the price of good y.

• It will be useful to use some formula. To recall that the quantity x of good x chosen by Mila is function, among other things, of R , p x and p y , we will write:

x = x ( R , p x , p y )

This function is called the demand function .

The box below summarizes the construction we have done so far.

In this chapter we will look firstly, at how the demand changes when the revenue changes; secondly, how the demand changes when the price of the good change, and finally, how the demand change when the price of the other good changes. We will end up saying a few words on how we can aggregate the demands of millions of consumers.

Income Elasticity of Demand

That our behaviour as consumer changes when our revenue changes is obvious. The structure of our consumption is greatly modified by such changes. Indeed, if your revenue doubles, you will not consume twice more of everything. Some consumption will increase (like buying more sport goods, going more often to the restaurant), but other consumption will be droped altogether (like giving up public transportation, low quality wine, or buying parts to fix the car, etc.)
Similar observations can be made when comparing the structure of consumption in countries with levels of economic development which are far apart. Education, retirement plans or environmental protections are usually big issues in developed countries and not a top priority in less advanced one.
In the 19 th century, Ernst Engel (1821-1896), a German statistician, looked at the consumption pattern of 153 Belgian families and found that with rising incomes the share of expenditures for food products declines. This result has come to be known as Engel's Law . It is important to notice that this law is empirical , it is a regularity found in the evolution of consumption. It does not follow directly from logic. Nonetheless, it makes sense that when your income is low, most of it goes to food expenditures, because this satisfies an essential need. Then, as you get wealthier, you start to spend a higher share of your revenue on less essential needs such as leisure goods, travelling, and so on.
In the language of modern economics, Engel's law is stated using the concept of income elasticity .
Income elasticity is a measure of the sensibility of your demand to a variation in your income. Assume your income increase by 10%, how much that will affect your demand for good x ? We see that four possibilities have to be considered:

i. The demand for x increases by more than 10%

ii. The demand for x increases by less than 10%

iii. The demand for x remains unchanged

iv. The demand for x decreases.

The income elasticity is a ratio of relative changes, it compares the relative change in the demand that follows a relative change in income. The formula is (N.B.: here D R means the change in R, so that if your income change from 100 leva to 150 leva, D R = 50 and D R/R = ½ or 50%. Same thing for D x/x):

Goods for which that ratio is greater than 1 are often labelled superior (normal) goods . 1 Empirically, education goods, health goods, leisure goods seem to belong to that category. Those for which the income elasticity is smaller than one are called inferior goods . According to Engel's findings, such is the case for food. We also have some goods which share in total expenditure tends to remain constant as income increases. Housing and clothes usually belong to that category; as I get wealthier, I move to a nicer apartment and buy more and nicer clothes, so that I end up spending the same share of my revenue on those items. Finally, we should remember for what follows, that the income elasticity might be negative . This will be the case, for instance, for low quality wine: as my income increases, I consume less of that good.

Price elasticity of demand

Just as we can measure the sensibility of the demand to a change in income, one can measure the sensibility of the demand to a change in price. The price elasticity of the demand function will be defined as was defined the income elasticity:

Contrarily to what was the case for the income elasticity, our intuition tells us that this elasticity will in general be negative, that it is to say, and increase in the price of good x should induce the consumer to decrease his demand of good x . We will discuss in a moment whether this is always the case. But before, let us introduce some more terminology.
A demand with a high response (again, a priori negative) to a change in price would be said to be elastic . One can easily imagine cases in which a 30% percent increase in price is followed with a 60% fall in demand (the price elasticity is then equal to -2). Inversely, a demand which shows little sensibility to a change in its price will be qualified as inelastic .
The concept of price elasticity is very useful to analyze economic phenomena. Let us take an example. Assume you are the government and you want to tax some goods (excise taxes). What type of good will you choose? If you tax a good with a highly elastic demand you will raise little money. The reason is of course that to impose a tax amounts to increasing the price of the good; and if the demand is elastic, consumers will not purchase the taxed good. This is why excise taxes are always on goods with inelastic demands like tobacco and gas. If the government taxes potatoes, you will eat more pasta and fewer potatoes. But if it taxes gas, you will not necessarily switch to horse riding, or public transportation, and a cigarette smoker will not easily switch to chewing.
Another illustration of the use of the concept of price elasticity is in marketing. If you produce a good with a very elastic demand, then you have little margin left. In particular you must be careful when setting price; an increase in price might have a disastrous effect on the volume of your sells. If, at the opposite, the demand for your product is inelastic, then you enjoy more freedom in your pricing strategy. More generally, the degree of price elasticity is important to identify the market power of a producer.

The law of demand: income and substitution effects

Let us come back now on the sign of the price elasticity. We suggested earlier that its sign should be negative. Will that always be the case? Because prices and quantities are always positive (i.e., in the formula above, x and p x are always positive), the sign of the elasticity will depend entirely on the sign of the ratio D x/ D p x , that is on the whether demand and price tend to move in opposite or identical directions.
To answer that question it is useful to split up the effect of price on demand into two effects: the income effect and the substitution effect.
When the price of a good, let us say, housing, increases, this makes me in a sense poorer. As a matter of fact, if my revenue has not changed and if other prices have not changed, that increase in the price of housing will force me to modify my consumption plan. I can no longer afford the basket I was buying before that increase took place. Economists say that, although my nominal income has not changed, my real income has decreased. My salary has not changed, but the purchasing power of that salary has changed. So, an increase in price will have the same effect has a decrease of my income. This is why we say that when a price changes, there is an income effect .
Now, we saw in the previous paragraph that the income elasticity of demand (the way demand reacts to a variation of income) is usually positive: less income is followed by less consumption, and higher income is followed by higher consumption. So, in most cases that part of the price effect that we call the income effect, will be negative. But we cannot rule out the possibility that, because my income is lower, I consume more of one good (think about public transportation for instance).
The other thing going on when the price of a good is increasing is that it makes other goods relatively more attracting. To the extant that those other goods can satisfy the same need, the consumer will tend to substitute those goods to the good which price has increased. If housing is becoming more expensive, I might decide to move to a smaller apartment and use my money for other purposes. This is the substitution effect . The magnitude of that effect will of course depend of whether or not there exist substitutes to that good. But, as general principle, the substitution effect will be negative in the sense that an increase in the price of good x can only lead, through substitution, to a fall in the consumption of good x .
Summing up, the effect of a price increase can be split up in two effects: the substitution effect which leads to a lower consumption of that good, and an income effect which also leads in most cases but not always to a decrease in consumption. Hence, almost surely, an increase in price will lead the consumer to reduce his or her consumption. This is the substance of the law of demand.

For goods with negative income elasticity (i.e., goods such that the demand increase when the revenue fall), the sign of the price effect is unknown a priori. If the substitution effect is stronger than the income effect, then the law of demand still holds. But if the income effect is stronger, then the demand for that good will increase when its price increase . A name is given to such goods; we call them Giffen goods , after the name of an economist who has studied that possibility. But you should not worry too much about it because empirically it is almost impossible to find such a good.
Now, our efforts can be rewarded. We are indeed in a position to draw the famous demand curve since we have shown and explained that in most cases the demand curve will slope downward, that is, will decrease when its price increases.
Needless to say, that demand curve has been drawn in a totally arbitrary way, except the slope that was purposefully chosen to be negative. The exact shape of the demand curve will depend on many things among which we found the preferences of the consumer and whether that consumer finds substitute to that good.
A last word about that result is necessary. It should not be forgotten that the law of demand, as all economic laws, holds under certain conditions. Some of those conditions have been implicit so far. In particular it was implicit that we were studying the change in demand produced by a change in price assuming that everything else was remaining unchanged . If the price of good x is not the only thing that changes, if, for instance, we have simultaneously an increase of your income, or if all the prices are changing at the same time, then the law of demand does not apply. The analysis becomes more complex and we cannot tell without further analysis whether the consumer will choose to reduce, increase, or leave unchanged his demand for good x . Now, some of you may wonder what is the use of a law which does not apply in many real life cases, since in real life, you often have more than one price moving at the same time. The answer to that legitimate question can be double. First, even if the law does not apply perfectly, it may nonetheless indicate a tendency. Ask a salesman whether he believes the tendency depicted by the law to be exact! Second, we can tell the sceptical that this law is like the gravitation law. Jean-Baptiste Say, a famous French economist of the first part of the 19 th century, would ask the sceptical: do you stop believing in the law of gravitation just because a feather don't fall like a stone, and enjoys dancing for a while in the air before hitting the ground ?

Cross price elasticity

Most western economies have developed a special set of regulations known as competition law . Competition law regulates the behaviour of market participants, especially producers. It controls mergers and acquisitions, price strategies, and agreements between companies. For reasons we will explain in a later chapter, the judges who have to apply those laws often have to decide whether two goods produced by two different companies are �on the same market�. For instance, can you say that Coca Cola and Orangina are on the same market? As we will see, the question is not without ambiguity. But ask yourself: How will I go answering such a question?

One way is to look at cross-price elasticity . As the name indicates, it is elasticity, that is, a ratio of relative variation. We will look at a change in the demand of good x which follows a change in the price of good y . To come back to our example, we will measure the impact of a change in the price of Orangina on the consumption of Coca-Cola. If a 10% increase in the price of Orangina is followed with a 5% increase in the demand for Coca-Cola, this means that, in the eyes of the consumer, the two goods are good substitutes and, in a sense, �belong to the same market�. If the demand for Coca-Cola does not change, it means that they don't belong to the same market.

From individual demand to the market demand

Let us see if you are smart. What is the difference between the two graphs below?

Mila's demand curve Market's demand curve

Apparently there is no difference. But in fact there is one. The one on the left is the one we have been talking about since the beginning; it informs us about how Mila will modify her demand for good x as the price of that good is modified. In other words, the graph on the left is an individual's demand curve. The graph on the right is supposed to represent the market's demand curve. For a given price, the curve indicates the sum of thousands of individual demands at that price.

The market demand curve is usually drawn that way, namely, downward sloping, just at the individual demand curve was drawn. The intuition is that if the law of demand applies to each individual taken separately, then it will surely apply to the aggregate demand curve.
Well, at the risk of confusing you, let me show through an example that your intuition is to a large extent misleading you. 2 Assume an economy with two goods, x and y , and two consumers, Mila and Milko. Both have an income of 1000. The table below gives you the baskets they choose when the prices are 10 and 10 and when the prices are p x = 15, and p y = 5.

	Mila's choice	Milko's choice	Market's demands
p x =10 p y = 10	(25 of x and 75 of y )	(75 of x and 25 of y )	(100 of x , 100 of y )
p x = 15 p y = 5	(40 of x and 80 of y )	(64 of x and 8 of y )	(104 of x , 88 of y )

Obviously Mila is someone who likes good y a lot. When the price of good y decreases, she therefore buys more of it. Note that with the first set of prices (10, 10) she could not have afforded the basket she chooses with the second set of prices. The case of Milko is similar, except that Milko likes good x . So when its price increases he is forced to reduce his consumption of x , even if he does sacrify a lot of good y . Like Mila, Milko is rational, he prefers the basket (75, 25) but cannot afford it with the second set of prices (it would cost him 1125).
Now, let us look at the market's demands for good x and good y . What we see is surprising. When the price of good x increases from 10 to 15, the market demand for x increases from 100 to 104! And when the price for good y decreases from 10 to 5, the market demand for good y decreases from 100 to 88!
Of course, one cannot deduce from that example that the law of demand does not hold at the market level, because, here, two prices are moving at the same time (and we saw above that the law of demand assumes implicitly that only one price is changing). But this shows how much careful we must be.
But that's not all. Another observation makes us understand that the logic of consumer's choice does not generalize to what we would be tempted to call the logic of the market. More precisely, there is no such a thing as �market preferences�. To see that, note that �the market� could have chosen the basket (100, 100) when prices are (15, 5). Since �the market� chooses (104, 88), we must deduce that �if the market is rational�, he reveals through that choice that he prefers the basket (104, 88) to the basket (100, 100). But! How can you then explain that when the prices are (10, 10) he chooses the basket (100, 100), knowing that, at that price, the other basket, that he is supposed to prefer, was affordable, and would even have cost him less money (precisely, 1920) ???
The lesson to be drawn from this example is that one must be very careful in generalizing to �the market� what is true at the level of individual choice. When thinking about economic phenomena, we use introspection a lot. We look at the way we choose, and we build generally theories on that basis. This reminds us that intuition based on introspection is not always a safe guide.

1Such expressions as �superior� and �inferior� goods are somehow ambiguous. After all, there is nothing �inferior� about potatoes, or pasta, even though the income elasticity of their demand is probably inferior to 1 for most consumers.

2 The example is taken from David M. Kreps, A course in Microeconomic Theory , Princeton University Press, 1990. By the way, this textbook is probably the best among intermediary level textbook in microeconomics. It has also a nice introduction to game theory and choice in a context of uncertainty.