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The market demand for consumer goods: theory of the rational consumer

Indice

In this lesson you’ll understand why the demand for goods has the decreasing trend seen in the previous lesson.

The budget constraint

In the previous sections, we have seen how the market equilibrium for a good is reached. Now we deepen the economic theories that lie behind the construction of a curve and in particular of the slope of that curve.

Let’s start with the market demand for consumer goods. In the following lessons we will instead examine the supply curve in that same market, and then focus on supply and demand within the input market (for e.g. the labor market).

The theory which explains the demand for consumption goods, but above all its downward trend (as price increases the amount demanded by consumers decreases and vice versa) is called theory of the rational consumer, i.e. the consumer buys goods in the market following a logical behavior.

The first constraint that shapes the decisions of the consumer is his ability to spend. Indeed, the quantity of goods that he will ask on the market can never exceed, in terms of expenditure, his available income.We can thus hypothesize that for the average consumer this equality always applies:

Total expenditure = Disposable income

Where, for the sake of simplicity we are ignoring the possibility to save. Since total expenditure is given by the summation, for all the goods purchased, of the price times the quantity, we can write the following expression in which, for simplicity, we suppose that the basket of our rational consumer is reduced to only 2 goods (good A and good B):

Disposable income = (PA x QA) + (PB x QB)

This equality is the budget constraint of the consumer. content_the budget constraint

The line expresses (similar to the production frontier of a country, see lesson 1) the consumer’s possibility of spending, given his available monetary income. He has the ability to buy a combination of the two goods offered (or he can just buy one of them, i.e. 25 units of good A or 50 units of good B). However, he cannot afford a combination of A and B represented by any point lying above the budget constraint (e.g. E), lacking the money needed. Further, although feasible, any combination of the two goods represented by points below the constraint (e.g.  E’) is an inefficient allocation of financial resources, because the consumer has the monetary means to ensure a greater consumption of both commodities.

The conclusion – similar to that seen for the production frontier of an economic system – is that the best consumption choices of an average buyer will always be represented by  points along the budget constraint (e.g. Q’ or Q ). In fact, in any of these points he acquires a combination of the two goods A and B which is the best possible given the available income.

But which of the many points along the budget constraint will be chosen by the consumer? To learn more about this last point we need to draw into our graph another curve representing the preferences of the buyer. The latter, called indifference curve, will enable us to determine the optimal allocation of the buyer’s resources.

However, before proceeding in the study of this new feature, we need to spend a few words on the mathematical expression describing the budget constraint.Since the quantities on the axes are the quantities of the two goods, the function underlying the chart is the following:

QB = PA / PB x QA

Note that the slope of the constraint is PA/PB, i.e. the ratio of the two prices.This conclusion is important because it allows us to understand the consequences of price changes affecting the two goods. content_the consequences of price changes

Ifthe price of good B (Pb) increased, the constraint would rotate counterclockwise such that the intercept on the ordinate would no longer be point B, but a lower value, B’. This is so because given that the price for good A is fixed, the resources now available to acquire good B can only buy a lower amount of the latter. Conversely, in case of a price reduction (again for good B) the constraint rotates clockwise pivoting around the intercept on the horizontal axis (i.e. the price of A does not vary).

The same shifts will occur at the other summit of the budget line, in the case of changes affecting the price of good A.

Marginal utility and indifference curves

In his purchasing decisions the consumer is guided, by the budget constraint, but also by personal preferences for products on the market. He will purchase those goods to which he assigns a higher utility value, which are thus better able of meeting his needs.

Assuming, for simplicity, that the choice must be made among only two goods (A and B), the value attributed to different amounts of these two goods could be the following:

Amount of good A

Amount of good B

Total utility of the basket

0

5

0

1

5

2.24

3

5

3.87

6

5

5.48

9

5

6.71

12

5

7.76

 

From the table we can infer a first important economic law: the total utility of a basket of goods increases together with quantity, even though only the amount of one good increases while that of the other stays the same.

content_the total utility of a basket of goods increases together with quantity

This concept is easily understandable and straightforward as the higher consumption of a good (or of both) is usually associated with higher levels of wealth (hence utility), at least within a capitalist society.

Besides utility, which must take into account: marginal utility. The latter is defined as the utility an individual receives from consuming an additional (marginal) amount of a good.

From a mathematical point of view marginal utility is the ratio between the increase of total utility and that of the amount of a good, with the quantity of all the other goods staying fixed (Mu = delta Tu / delta Q).

The following table shows the variations of the values for our example:

Variation of good A

Variation of good B

Total utility variation

1

0

2.24

2

0

1.63

3

0

1.61

3

0

1.23

3

0

1.05

 

By applying the above formula we obtain the following table:

Basket of origin

Marginal utility of good A

(0.5)

2.24

(1.5)

0.82

(3.5)

0.54

(6.5)

0.41

(9.5)

0.35

 

We can now state a second important economic law: the marginal utility of a product tends to decrease as the amount of that good increases. content_the marginal utility of a product tends to decrease as the amount of that good increases

The latter, seemingly in contradiction with previous statements, is explained by the fact that we are not speaking of total utility (which indeed continues to grow) but rather of marginal utility. The absolute value of the latter will be initially high, when we start consuming, then, as consumption of that same good continues to grows it will start to decrease since it refers to the utility derived from additional units of consumption after that already other units have been consumed, i.e. the agent might already be partially satisfied. Therefore, we generally attach great importance and value to amounts of goods consumed initially, and much less to increasing amounts as we become overwhelmed by that product. (Think of water and compare what would somebody lost in a desert be willing to pay for a glass to what would a regular person going to work in Rome be willing to pay for that same glass).

The third and final law regarding the usefulness of goods. A rational consumer, having to allocate his spending between a basket of goods, will purchase the quantities of these goods (Q1, Q2, Q3, … , Qn) that ensure that the equality between the marginal utility values of those goods is reached (UM1= UM2 = UM3 = … = Um for n goods).It can be shown that, in doing so, total utility is maximized.Any departure from the equality of the marginal utility of goods decreases total utility and therefore involves a sub optimal combination (in terms of utility) of the quantities of goods purchased.

Looking back at the graph presented in the section on the budget constraint, where the basket was composed of only two goods (A and B), and omitting for the moment the budget constraint, we now introduce indifference curves in order to find the consumer’s equilibrium allocation, i.e. the quantity of the two goods that maximizes his total utility:

Marginal utility of good A = Marginal utility of good B

(MuA) = (MuB)

 content_Marginal utility of good A = Marginal utility of good B

In order to construct an indifference curve we keep total utility fixed and thus obtain all the combinations of the two goods that provide that same level of aggregate utility.

Quantity of good A

Necessary quantity of good B

 Costant utility level

1

14.98

3.87

3

4.99

3.87

6

2.50

3.87

9

1.66

3.87

12

1.25

3.87

 

The points on the curve represent all the combinations of A and B which satisfy the equation with a degree of total utility equal to 3.87.

content_satisfy the equation with a degree of total utility equal to 3.87

So rather than talking of a single indifference curve, we must speak of infinite indifference curves, each related to a specific level of total utility. Note that the curve corresponding to the highest utility level will also be the farthest away from the origin of the axis. This is so because the combined absolute quantity of the two goods increases as the curve shifts to the right and upward and we have assumed that higher levels of total utility derive from higher levels of consumption.

We now have all the tools to determine the consumer equilibrium, the point which describes his consumption choices in terms of the two goods A and B that form his basket.

We need only to put together in the same graph, the budget constraint and the indifference curves map of our rational consumer.

content_The equilibrium point is point E

The equilibrium point is point E, where the indifference curve with utility value U2 is tangent to budget constraint. So why is E the equilibrium point and what does it represent?

And because the point is the budget constraint, and then, as we said in the previous paragraph, expresses a choice efficient in terms of financial resources for the consumer. Moreover, this is the point on the budget constraint that ensures the highest total utility achievable by the consumer given his resources. In fact, although the indifference curve labeled U3 would provide a higher utility level the points along that curve are not obtainable due to the consumer’s insufficient income.Thus, of all the possible expenditure combinations our buyer will choose the quantity QA* for good A and QB* for good B. This is the only feasible combination of goods that ensures the maximization of utility given the available disposable income.

In mathematical terms the equilibrium is reached when MuB = MuB, hence when marginal utilities equalize.

Finally, we see how we can express the equilibrium point if we consider the mathematical functions that are “below” the curves in the previous figure.

We said that the slope of the budget constraint is the ratio Pa/Pb whereas that of the indifference curves is (increase QB) / (increase QA). This ratio is called the marginal rate of substitution (MRS) and it represents the degree of substitutability of good A with good B, and vice versa. Accordingly, the equilibrium point is the point where the following condition holds:

MRS = PA/PB

Price effect

So, we have developed a consumer’s theory that tells us where the equilibrium is reached within a market, but we have not yet established a relation between this equilibrium and the market demand curve seen in the previous chapter.

How do we get from consumer theory to a negatively sloped demand function?

To answer this question and demonstrate that the demand curve is negatively sloped (an inverse relationship between P and Q exists) we need to undertake an experiment. The experiment consists in varying the price of goods and seeing if the new equilibrium, resulting from this change, leads to a higher or lower expenditure for the goods subject to the price change. If consumption of the good whose price has increased lowers (or, which is the same, if the consumption of the alternative good increases), we have evidence of the inverse relation between price and quantity which ultimately leads to negatively sloped demand schedules.

Assume a price increase for good B. As it is clear from the following graph (and from our previous discussions) the budget constraint rotates as follows: content_Assume a price increase for good B

From the figure it is clear that the maximum affordable amount of good B shrinks from B to B’. In fact, the price increase, given a fixed amount of disposable income, decreases the quantity of good B that can be purchased on the market by the consumer. Further, note that the price increase of B does not affect the maximum affordable amount of good A, since we have assumed that the price of A remains fixed.

Where will the new equilibrium be located?

The new equilibrium point will now lye on the new budget constraint, and in particular where the constraint is tangent to a lower indifference curve. The total utility (represented by the new indifference curve) of the consumer will thus necessarily shrink as the price increase for good B reduces the acquirable amount of that good. This new equilibrium point is characterized by a combination of A and B, in which the equilibrium amount of B is less than the previous one.

Therefore, we can show that the price increase of a good leads to a re-composition of the best equilibrium combination in which the expenditure for the consumption of that good is lower. Here, then checked the relation according to which an increase of P causes the reduction of Q demanded. Conclusion: The demand schedule will have to be negatively slopped to highlight the inverse relationship between the quantity demanded of a good (Q) and its price (P).

However, our experiment highlights also other aspects.

Indeed, the price effect on the quantity actually demanded of a good can be broken down into two components: a substitution effect and an income effect. In particular, the relation between these effects is as follows:

price effect = substitution effect + income effect

The decrease of demand following the increase in price P is due to the summation of two consumer behaviors.

The first one, the substitution effect, is the tendency of consumers to substitute the good that has encountered a price increase with the one whose price has remained unchanged.

The other, the income effectis the consumer’s tendency to reduce spending on both goods, because the increase in the price for one good, given a fixed available income, makes him feel poorer (the purchasing power of his income is lower).

The combination of these two behaviors, while on the one hand certainly reduces the quantity demanded of the good whose price has increased, on the other hand affects the quantity demanded of the good whose price has remained unchanged in ways which are not so straightforward. Hence, in the new consumption equilibrium, the quantity demanded of that good can either be higher or lower than it had been before the price for the other good had increased.

There exists a case (perhaps hypothetical) in which the demand for a good increases together with its market price.

We have seen (previous lesson) that in economics there are what are called inferior goods which are those for which demand increases as income decreases (and vice versa). Hence, if we ran the previous experiment on 2 goods, one of which (whose price increases) is an inferior good, the result could be the opposite of what we have seen in the previous section, so that demand could, instead, actually increase as a consequence of the price increase.

Thus, the income reduction in terms of purchasing power (caused by the price increase) would generate an income effect on the inferior good opposite to the one seen previously in the case with a normal good. In other words, the income effect would lead to an increase in the consumption of the good that has experienced the price increase. If this increase in consumption of the inferior good were so large, in absolute terms, to overcome the decline in consumption due to the substitution effect (which does not change sign in presence of an inferior good), the end result would precisely be the growth of demand for the inferior good, even though its price has risen. Goods that have a stronger income effect than a substitution effect, in absolute terms, are called Giffen goods.

The consumer surplus

To conclude this chapter we provide a definition of the concept of consumer surplus.

The need to define consumer surplus stems from the fact that price changes determine gains or losses for sellers and buyers. But while for vendors the amount of profit or loss can be more easily measured in monetary terms (as we shall see in the next lesson) because it gives rise to a business profit or loss, for buyers/consumers the quantification of such gains or losses (as a consequence of prices changes) is not so straightforward. The concept of consumer surplus is thus needed to determine whether, following the readjustment of the consumer’s portfolio, he actually gains or loses money.

The surplus is the difference between the maximum amount that the buyer would be willing to pay for a certain amount of the good he has requested and the amount he is actually charged for that same amount.Using a chart makes it a bit easier.

content_The consumer surplus

The maximum amount is the whole area under the demand curve D, whereas the amount actually paid is the area under the price P line (because the sum paid is price times quantity, P x Q).

The difference between these two areas is constituted by the dashed area EPA, which represents the consumer surplus. So, if after the price change, the surplus area increases it means that the buyer is actually gaining, which implies he loses when the former shrinks.

Autore: Carlo

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