3. CONSUMER BEHAVIOUR (THEORY OF CONSUMER CHOICE)

focuses on how consumers choose goods with limited recourses (constrained optimization)

Consumer preferences and the concept of utility

Consumer preferences describe how an individual would rank (i.e. compare the desirability of) any two baskets (bundles), assuming the baskets were available at no cost.

Assumptions about consumer preferences taking for granted that consumers behave rationally under most circumstances:

1. preferences are complete (consumer is able to rank any two baskets)

2. preferences are transitive (consumer makes choices that are consistent with each other, i.e. if consumer prefers basket A to basket B and B to basket C it means that basket A is preferred to basket C. Transitivity in algebraic notation can be represented as follows: if A
   B and if B
   C, then A
   C

3. more is better (having more is better for the consumer).

There are two types of rankings:

1. ordinal ranking gives information about the order in which a consumer ranks baskets (the consumer prefers A to B, because in A there is e.g., twice as much any good as in basket B - much is better), but the ranking does not answer: how much more A is preferred to B

2. cardinal ranking contains more information as it gives information about the intensity of a consumer's preferences (both are known preferences of baskets and the strength of the consumer's preferences).

In theory it is not important to measure the amount of utility (satisfaction, pleasure) a consumer receives from a basket. However, a cardinal ranking is often used to facilitate exposition, an ordinal ranking explains sufficiently consumer's decisions.

Utility functions - preferences with a single good

To illustrate the concept of a utility function, an assumption of only one good purchased is relevant. If x denotes the number of cola tins per day and U(x) - the level of utility derived from their consumption then having enough information to write down the utility function, it is possible to assign values of each basket, satisfy the assumption that more is better and compare (rank) intensities of various baskets.

Quantity consumed (x - cola tins)	Total utility U(x) = 22x - x^2	Marginal utility MUx= 22 - 2x
1	21	20
2	40	18
3	57	16
4	72	14
5	85	12
6	96	10

TU

U(x) = 22x - x²

72 A

58

(a)

0 1 2 3 4 5 6 7 8 9 10 tins of cola

MU

20

(b)

14

MU_x = 22 - 2x

0 1 2 3 4 5 6 7 8 9 10 tins of cola

The ratio
is marginal utility (MU), it is the rate at which total utility changes as the level of consumption changes (rises).

The example in the table and in the figures indicates that marginal utility declines as the consumer drinks more cola tins. This trend illustrates the principle of diminishing marginal utility (the I^st Gossen's law - the more something is consumed the less additional satisfaction is obtained from additional consumption holding all else fixed).

Drawing total utility and marginal utility curves one should keep the following points in mind:

1. total utility and marginal utility should not be plotted on the same graph (different dimensions on vertical coordinates)

2. marginal utility is the slope of the total utility function (e.g. at point A in panel a) the slope of the utility function is 14 while the value of U(4) = 72 and in panel (b) MU₄ = 14 per cola tin

3. the relationship between total and marginal functions holds for other measures in economics

4. the more is not always better, i.e. marginal utility may be negative (the marginal utility for 11^th cola tin equals zero, so the next tin brings dissatisfaction or discomfort).

Preferences with multiple goods

In real life consumers may choose among a great deal of goods. To study the trade offs a consumer must make in choosing his/her optimal basket, it is necessary to examine the nature of consumer utility with multiple products.

A consumer faces a choice between two types of commodities e.g. food and clothing

clothing

c₂ A

c₁ B

U₄

C E

D U₃

U₂

U₁

0 f₁ f₂ f₃ f₄ f₅ food

Each contour is called indifference curve because the consumer would be equally satisfied with (or indifferent in choosing among) all baskets on the indifference curve. A set of indifference curves is an indifference map.

Indifference curves on an indifference map share the following properties:

1. the further the curve's position from the origin of coordinate system is, the higher utility level it represents (more is better if only there is more of one commodity in the basket (basket E
   C)

2. when a consumer likes both goods (MU_food and MU_clothing are both positive), the indifference curves will have a negative slope

3. indifference curves cannot intersect

4. every consumption basket lies on one and only one indifference curve

5. indifference curves are not “thick”.

The slope of the indifference curve is a tool describing consumer's willingness to substitute one good for another. In economics, the term that describes the willingness to substitute is the marginal rate of substitution (MRS_f,c). Specifically, the marginal rate of substitution of food for clothing (in general of x for y) is the rate at which the consumer will give up clothing to get more food, holding the level of utility constant.

MRS for any basket can be expressed as a ratio of the marginal utilities of the goods in that basket. Suppose the consumer changed the level of consumption of x and y by Δx and Δy, respectively. The corresponding impact on utility ΔU would be

ΔU = MU_x(Δx) + MU_y (Δy)

Changes in x and y that move the consumer along the indifference curve U₀ must keep utility unchanged, so that ΔU = 0:

MU_x(Δx) +MU_y(Δy) = 0

which can be rewritten - MU_y(Δy) = MU_x(Δx)

and solved for the slope of the indifference curve

Moving downward along the indifference curve MRS of x for y is lower and lower since the consumer would be willing to forgo the fewer and fewer portions of y to get additional unit of x. In that case the consumer's preferences exhibit a diminishing marginal rate of substitution of x for y. In other words, the MRS of x for y declines as the consumer increases his/her consumption of x along an indifference curve.

Since shape, slope and position of indifference curves reflect consumer's preferences so they represent a subjective approach to consumer behaviour.

Special utility functions

y y

U₃

U₂

U₁

U₁ U₂ U₃

x x

U = x + 2y MRS_x,y = - 1/2 U = (x,y) = a min (x,y) MRS_x,y = 0

perfect substitutes perfect complements

The goods are perfect substitutes when the MRS of one for the another is constant, but not necessarily equal to - 1. Perfect complements are goods the consumer always wants to consume in fixed proportion to each other, so MRS = 0.

Budget constraint

Consumer's choice becomes objective in respect to income and market terms (prices).

The budget constraint defines the set of baskets that a consumer can purchase with a limited amount of income, so the budget line indicates all of the combinations of food and clothing that can be bought if the consumer spends all of his/her available income on the two goods. If the consumer does not save any income it means that all total expenditures equal his/her income:

I = P_f·F + P_c·C

Budget line can be expressed and plotted as:

. Its slope =

If income (I) is constant in nominal terms and

P_C = constant P_F ↑ P_F ↓

in real terms

I↓ I↑

C I C

C=I/P_C

I₃ I₂ I/P_F

0 F₃ F₂ F₁ F 0 F₁ F₂ F₃ F

P_F = constant P_C↑ P_C↓

C₁ C₃

C₂ C₂

C₃ C₁

0 F 0 F

P_C↑ P_F↓ P_C↓ P_F↑

real income ?

C C

C₂

C₁ I₂

I₁

C₂ C₁

I₁

I₂

0 F₁ F₂ 0 F₂ F₁ F

P_C and P_F are constant

I↑ I↓

C C

I₁ I₂ I₂ I₁

0 F 0 F

Optimal choice

Assuming that a consumer makes a choice rationally means he/she chooses a basket of goods that:

• maximizes his/her utility while

• allowing him/her to live within his/her budget constraint in a given time.

The optimal choice problem for the consumer is expressed like this:

If the consumer likes more of both goods, the marginal utilities of both goods are positive. At an optimal basket all income will be spent, so the consumer maximizes utility by reaching the highest indifference curve while being on the budget line. This means that the slope of the budget line and the slope of indifference curve are equal.

Therefore, at the optimal basket (E), the tangency condition requires that

In optimal basket the marginal utility per a spent unit of money (dollar, euro or zloty) must be equal for all goods (the II^nd Gossen's law).

Y

Y_E E

U₃

U₂

U₁

I

0 X_E X

The notation „min” means “take the minimum value of the two numbers in parentheses” and “a” is a constant indicating the minimum utility level of the function.

Prof. Teresa Kamińska Microeconomics

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