Note 5

V. DEMAND

In this and the next several notes, we examine how markets coordinate the behavior of individuals, each with their own distinct and individual goals, achieving cooperation that no single individual planned. We will see how resources are moved from the production of one good to another to match shifts in the desires of individuals in the society. We will also see how consumption patterns will shift in response to changes in the opportunity costs of production. We will begin with a look at demand.

A. Quantity demanded

We have two terms that we will use distinctly for two different concepts that, in common language, are both referred to as demand. We use two different terms for these two commonнlanguage definitions so we do not slip from one definition to the next while attempting to reach a logical conclusion. Consider the following "logical" argument:

a) a tax on automobiles will cause the prices of automobiles to rise (perfectly true);

b) a rise in the price of automobiles will cause the demand for automobiles to fall (of course);

c) a drop in the demand for automobiles will cause the price of automobiles to fall, perhaps below the original price (of course).

But the three statements put together makes a silly argument. The reason for this problem is a slippage from one definition of demand to another, so we must be very careful to keep these two definitions separate by using two different terms.

Let us begin our look at supply and demand analysis by defining the term QUANTITY DEMANDED, instead of defining demand. After defining quantity demanded and explaining how it is affected by other factors, we will define DEMAND. Quantity demanded is the amount of some good (or service) a person or group of people PLAN to buy in a particular time period. Notice that quantity demanded is a FLOW variableннit is measured with respect to some time period. By "plan to buy", we mean that he (they) has (have) the wherewithal and the purpose to buy the good, that the purchase of the good is purposefully pursued.

There are several goods which will affect people's plan to purchase. For example, if one's income changes, a one's buying plans will certainly be altered. Let us take a look at the major categories of factors that affect buying plans by using FUNCTIONAL NOTATION. A function shows how one factor (the dependent variable) will change when other factors (independent variables) change. We can say that quantity demanded is a function of several other variables, such as the price of the good itself, a person's income, and the prices of other goods, but all we are really saying is that the factor we identify on the leftнhand side of the equation is affected by the factors listed on the rightнhand side:

1) QD_a = f(P_a, P_c, P_s, Y, T, K),

where:

QD_a: the quantity demanded of some specific good "a";

P_a: the price of good "a";

P_c: the prices of goods complementary with good "a", that is, goods which one would use along

with good "a", for example, sugar with coffee or beer with pizza;

P_s: the prices of goods that are substitutable (alternatives) for good "a", that is, goods which one

would use in place of good "a"; Y is the person's income;

T: the person's tastes, likes and dislikes, especially for good "a" and substitutes for good "a";

K: the consumer's knowledge of the characteristics of good "a", its alternatives, and where these

goods can be purchased.

What equation 1) above says is that these factors, P_a (the price of the good), Y (consumer's income), P_c (prices of complements), P_s (prices of substitutes), T (tastes), and K (consumer knowledge), affect how much of good "a" a person would like to buy in a particular time period. There may be other factors, such as weather, illness, etc., but these are the main ones we will study. Let us now turn to how we might expect these factors to affect quantity demanded.

As the price of a good goes up, the opportunity cost (remember, the benefits given up) of obtaining that good goes up. This means that a person will have to make ever greater sacrifices of other things in order to obtain that good. We can think of opportunity cost as a punishment for doing something, and from even limited knowledge of psychology, we know that increasing the penalty (if it is really a penalty to that person) for some type of behavior will reduce the amount of that behavior, so the higher the price of a good, the less of that good people will buy, as long as nothing else has changed. By the same token, a reduction in the price some good will encourage people to buy that good. We can say that the price of a good and quantity demanded of that good are inversely or negatively related, holding other factors constant, as they move in opposite directions. We will study this in much greater detail very soon.

Often we buy goods in order to use that good in the production of some further good at home. Coffee is purchased, along with water, sugar and cream, in order to make coffee with cream and sugar at home. An increase in the price of sugar will mean that there is an increase in the price of coffee with cream and sugar. People will then purchase less coffee with cream and sugar and so will purchase less coffee. When the price rises of some good that is used with a particular good "a," people will use less of both goods. That is, an increase (decrease) in the price of a complementary good will decrease (increase) the quantity demanded of its complement. We can say that price of a complementary good and quantity demanded are inversely or negatively related, holding other factors constant, as they move in opposite directions.

In contrast, an increase in the price of a substitute good will cause people to seek alternative means of satisfying a particular desire. If the price of air travel from New Orleans to Houston rises, some people will find other means to get to Houston (given that they wanted to go to Houston in the first place), by rail, by bus, by car, or even by sea. So an increase in the price of air travel will cause an increase in the quantity demanded for air travel substitutes. Likewise, a decrease in the price of a substitute will decrease the quantity demanded of that good. We can say that price of a substitute good and quantity demanded are directly or positively related, holding other factors constant, as they move in the same direction.

The way that income affects quantity demanded is not so clear cut. For some goods, a higher income means that one is able to afford more of a good, and so, will buy more. This is usually the case, and so, for goods that we buy more of when our incomes go up, we call normal goods. However, sometimes when income improves, we wish to buy a better class of goods, instead of the less expensive alternative we had been using. For instance, when our incomes go up we tend to buy new shoes as our old ones wear out, instead of getting the old ones repaired, and so, we buy less shoe repair services as income rises. The goods we buy less of as income rises, we call inferior goods. This does not mean that the good is of poor quality, as the shoe repair services may be of very high quality, but inferior to the more expensive alternative, if we have a preference for the more expensive alternative. So we see that if the good is like most goods, if it is normal, we tend to buy more as our incomes rise, but if it is an inferior good, we buy less as income increases. In other words, quantity demanded is positively related to income for normal goods, while negatively related to income for inferior goods, holding other factors constant.

For both tastes and knowledge, the relationships are more complex, yet these are things we tend to naturally understand. If we like a particular good more than we once did, we tend to buy more of it.

We can summarize the directions of effect by using "+" to denote a positive or direct relationship between quantity demanded and the independent variable, holding the other factors constant, and by using a "н" to denote a negative or inverse relationship between quantity demanded and the independent variable, holding other factors constant.

- - + + or -

2) QD_a = f ( P_a, P_c, P_s, Y, T, K)

Notice that we have used our understanding of human beings and how we act to deduce how one factor affects another, holding other factors constant, instead of using laboratory experiments, in which these "other factors" are kept constant by laboratory methods. As an aside, many economists are beginning to use laboratory experiments, to confirm (or possibly refute) current economic theory. Receiving the most attention has been supply and demand analysis, which has been strongly confirmed. In class, we have done this with our double-oral auction.

B. Demand

Now that we have defined quantity demanded and understand how certain basic factors affect it, we can turn our attention to defining demand: DEMAND is the relationship between the price of a good and quantity demanded of that good, holding other factors constant. Note that this relationship is a negative one, that is, that higher prices reduce consumption while lower prices encourage consumption. Keep in mind that quantity demanded is a variable, while demand is NOT a variable, but is instead, a relationship between two variables. We can show this relationship on a two dimensional diagram with price measured along one axis and quantity demanded measured along the other axis, as in FIGURE I.

FIG I

This can also be expressed by the equation

3) QD = 100 -н 2P.

If the price is $5, then quantity demanded would be 90 units per time period. If the price increases to $15, then quantity demanded would fall to 70 units per time period. But has demand, the relationship between price and quantity demanded dropped? The answer is no, demand is still

QD = 100 н- 2P. Quantity demanded has fallen, but demand has not.

Perhaps an analogy might be helpful. The equation, y = 10 + 2x, shows the relationship between x and y. If x = 1, then y = 12. If x = 2, then y = 14. When x changes from 1 to 2, y changes from 12 to 14, BUT THE RELATIONSHIP BETWEEN Y AND X IS NOT ALTERED, IT IS STILL y = 10 + 2x, EVEN THOUGH BOTH X AND Y TAKE ON NEW VALUES. Demand is a relationship (like an equation) and is not a variable (like y or x), and so cannot be expressed as a single value.

The horizontal axis in FIGURE I reads Quantity demanded, not Demand. Demand is then the whole relationship between price and quantity demanded, as shown by the line. If an increase in price from $5 to $15 brought about a change in demand itself, as from D₁ to D₂ as in FIGURE II, why draw either D₁ or D₂? Instead, why not draw D₃ and be done with it? The line does not move as price changes, so CHANGES IN THE PRICE OF A GOOD WILL NOT BRING ABOUT CHANGES IN DEMAND OF THAT GOOD, BUT WILL BRING ABOUT CHANGES IN THE QUANTITY DEMANDED OF THAT GOOD. This distinction between "demand" and "quantity demanded" is very important, a distinction that you must understand.

If changes in price do not cause changes in demand, then what does change demand? Remember how we defined demand: Demand is the relationship between the price of a good and quantity demanded of that good, holding other factors constant. If one of these other factors changes, then demand, the relationship between price and quantity demanded will change. For instance, suppose we rewrite equation 3) as

4) QD = .5Y -н 2P,

where Y, income per time period, is initially $200. Then we have the same demand as

3) QD = 100 н- 2P. Now we can see that for every dollar increase in income, this person buys half a unit more per time period. If income increases to $250 per time period, then demand will now be

5) QD = 125 н- 2P,

which we see as D₂ in FIGURE III. Now, the relationship between price and quantity demanded is no longer the same QD = 100 н- 2P, the relationship itself has changed. By the way, is this good a normal good or an inferior good?

An increase in a factor that is positively related to quantity demanded (other than price) will cause demand to increase, that is, to shift to the right. A decrease in a factor negatively related to quantity demanded (other than price) will also cause demand to increase, that is, to shift to the right. We refer to this as an increase in demand. Decreases in factors that are positively related to quantity demanded (other than price) or increases in factors negatively related to quantity demanded (other than price) will cause decreases in demand, that is for demand to shift to the left. Note that "up" on supply and demand diagrams is to the right, and "down" is to the left.

While it is true that a change in price causes a change in quantity demanded, not a change in demand, it is not correct to say that a change in a factor other than price causes a change in, demand but does not cause a change in quantity demanded. As we saw, an

FIG II

FIG III

increase in a factor, income, for example, will cause a different quantity demanded, holding all other factors, including price constant.

C. Demand of a group

So far, we have been looking at the behavior of a single individual and examining how that behavior is expected to change given a change in circumstances. Now let us see how we can move from examining the demand by an individual to the demand of a group. The simplest group we can examine is a group of two individuals, Smith and Jones. Their plans to buy good "a" at various prices of good "a" are listed in TABLE 2.

TABLE 2

If the price of good "a" is $1, Smith plans to buy 10 units of "a" per week, while Jones plans to buy 12 units per week, the two of them together plan to buy 22 units of "a" per week. If the price rises to $2, Smith plans only 8 units per week and Jones 11 units per week, so the two of them together plan to but 19 units per week at a price of $2, and so forth. TABLE 2 is diagrammed as FIGURE IV.