introductory microeconomics (es10001) topic 2: consumer theory

Introductory Microeconomics (ES10001)

Topic 2: Consumer Theory

1. Introduction

We have seen how demand curves may be used to represent consumer behaviour.

But we said very little about the nature of the demand curve; why it slopes down for example.

Now we go ‘behind’ the demand curve

i.e. we investigate how buyers reconcile what they want with what they can get

1. Introduction

N.B. We can use this theory in many ways - not simply as household consumer buying goods.

For example:

Modelling decision of worker as regards his supply of labour (i.e. demand for leisure)

Allocation of income across time (saving and investment)

2. Theory of Consumer Choice

Four elements:

(i) Consumer’s income

(ii) Prices of goods

(iii) Consumer’s tastes

(iv) Rational Maximisation

3. The Budget Constraint

The first two elements define the budget constraint

The feasibility of the consumer’s desired consumption bundle depends upon two factors:

(i) Income

(ii) Prices

Note: We assume, for the time being, that both are exogenous (i.e. beyond consumer's control)

Example (N.B two goods)

Two goods - films and meals

Student grant = £50 per week (p.w.)

Price of meal = £5 Price of film = £10

Thus student can ‘consume’ maximum p.w. of 10 meals or 5 films by devoting all of his grant to the consumption of only one of these goods.

Alternatively, he can consume some combination of the two goods

For example, giving up one film a week (saving £10) enables student to buy two additional meals (costing £5 each)

qm £5*qm qf £10*qf M

0 0 5 50 50

2 10 4 40 50

4 20 3 30 50

6 30 2 20 50

8 40 1 10 50

10 50 0 0 50

Table 1: Affordable Consumption Bundles 8

0 Meals

Figure 1: Budget Constraint

2 8 10

The budget constraint defines the maximum affordable quantity of one good available to the consumer given the quantity of the other good that is being consumed.

N.B. Trade-off!

Trade-off is represented slope of budget constraint.

Intercepts

Determined by income divided by the appropriate price of the good

Define maximum quantity of a particular good available to an individual

Independent of income

Determined only by relative prices

If consumer is devoting all income to films (qf = £50/£10 = 5), then 1 meal can only be obtained by sacrificing consumption of some films.

How many films must consumer give up?

pm = £5; thus to obtain that £5, the consumer must give up 1/2 a film

The slope of the budget constraint in this example is thus:

0 Meals

Figure 2: Slope of Budget Constraint

Δqm = 1

Δqf = - 0.5

More generally:

Two goods (x,y), prices (px, py) and money income (m)

m = pxx + pyy

Slope of budget constraint: - px/py

Proof:

Such that

That is:

y = m/py - (px/py)x

Δy = -(px/py)Δx

Intuition:

If additional unit of x costs px

Then its purchase requires a change in consumption of y of –(px/py) (i.e. a sacrifice of y) in order to maintain the budget constraint.

4. Preferences

Consider now the consumer preferences Given what consumer can do, what would he like to

Four assumptions:

(i) Completeness

(ii) Consistency

(iii) Non-satiation

(iv) Diminishing Marginal Rate of Substitution

4. Preferences

Completeness

Consumers can rank alternative bundles according to the satisfaction or utility they provide

Thus given two bundles a and b, then , or

Preferences assumed only to be ordinal, not cardinal; i.e. consumer simply has to be able to say he prefers a to b, not to say by how much.

IV. Preferences

Consistency

Preferences are also assumed to be consistent

Thus if and , then we would infer that

We assume consumer is logically consistent

4. Preferences

Non-satiation

Consumers assumed to always prefer more ‘goods’ to less.

We can accommodate economics ‘bads’ (e.g. pollution) in this assumption by interpreting then as ‘negative’ goods

We can illustrate the first three assumptions graphically as follows

Figure 4a: Preferences

Figure 4b: Preferences

Figure 4c: Preferences

Figure 4d: Preferences

Indifference Curve

4. Preferences

Marginal Rate of Substitution (MRS)

The quantity of y (i.e. the ‘vertical’ good) the consumer must sacrifice to increase the quantity of x (i.e. ‘the horizontal’ good) by one unit without changing total utility.

We generally assume (smooth) diminishing MRS

To hold utility constant, diminishing quantities of one good must be sacrificed to obtain successive equal increases in the quantity of the other good.

4. Preferences

Diminishing MRS derives from underlying assumption of diminishing marginal utility

Marginal utility of a good is defined as the change in a consumer’s total utility from consuming the good divided by the change in his consumption of the good

Diminishing MRS assumes that the increase in utility from consuming additional units of a good is declining

4. Preferences

Non-satiation implies downward sloping indifference curves; increases in one good require sacrifices in the other good to hold total utility constant.

However, we can go further; diminishing MRS implies that indifference curves are convex to origin, becoming flatter as we move to the right.

Indeed, the MRS of x for y is simply the slope of the indifference curve

Figure 5: Indifference Curves

Δx = 1

4. Preferences

Diminishing MRS implies consumers prefer consumption bundles containing mixtures of goods rather than extremes

i.e. Bundle C = (5, 5) preferred to both Bundle A = (2, 8) and Bundle B = (8, 2)

Diminishing MRS (i.e. diminishing marginal utility)

2 8 38

4. Preferences

(i) Any point on the indifference map must lay on an indifference curve.

(ii) indifference curves cannot cross

Thus every point on the indifference map must lay on one and only one indifference curve.

Figure 8: Indifference Curves Cannot Cross

5. Utility Maximisation

Budget line shows the consumer’s affordable bundles given the market environment.

The indifference map shows the consumer’s desired bundles

To complete the model we assume rational maximisation - i.e. the consumer chooses the affordable bundle that maximises his utility.

This is a non-trivial point. We are implicitly assuming that the consumer only derives utility from the consumption of x and y.

Moreover, rational maximisation implies consumer processes huge amount of information before choosing his most preferred bundle

In reality, perhaps we ‘satisfice’

The optimal choice bundle will be that point at which an indifference curve just touches the budget line

That is, where an indifference curve is tangent to the budget line

In words, where the consumer’s marginal rate of substitution (MRS) and economic rate of substitution (ERS) are in accord

Marginal Rate of Substitution (MRS)

Amount of y consumer willing to sacrifice for one extra unit of x

Slope of indifference curve

Economic Rate of Substitution (ERS)

Amount of y the consumer is obliged to sacrifice for one extra unit of x

Slope of budget line

Figure 9: Equilibrium (MRS = ERS)

Figure 10: Disequlibrium (MRS ≠ ERS)

ΔyMRS

ΔyERS

Since preferences are unique, individuals will not choose identical bundles, even when confronted by same market environment

But they will all move to point where MRS = ERS

Even with different preferences, since ERS is the same for everyone (i.e. we all face same relative prices), it must be the case that in equilibrium:

MRS1 = ERS = MRS2

6. Comparative Statics

We now consider how the consumer responds to changes in his market environment

That is, to changes in:

(i) Endowment income;

(ii) Prices.

N.B, Comparative Statics / Dynamics

Changes in Income

An increase in endowment income causes a parallel shift out of the budget constraint

A decrease in endowment income causes a parallel shift in of the budget constraint

Figure 11: Increase in Income

x Normaly Normal

x Inferior y Normal

x Normaly Inferior

x Inferior y Normal

x Normaly Normal

x Normaly Inferior

Changes in Prices

An increase in price causes a pivot inwards of the budget constraint

An decrease price causes a pivot outwards of the budget constraint.

Figure 13: Fall in Price

Price changes affects the optimal choice bundle in two distinct ways:

First, there is a change in relative prices as represented by a change in the slope of the budget constraint.

Second, there is a change in purchasing power (i.e. real income). The same level of money income is now worth more to the consumer in terms of its ability to purchase both goods.

7. Income & Substitution Effects

Figure 13: Fall in Price

Figure 14: Effects of Fall in Price

Fall in price of good x reduces slope of budget constraint (ERS) - i.e. fall in the relative price of good x

Fall in price of good x increases consumer’s realincome - i.e. expansion of the budget set

Figure 15: Effects of a Fall in Price

Good x isNon-Giffen

Good xis Giffen

0 x0 x1 x

0 x1 x0 x

We decompose total effect of price change into:

(i) Income Effect

(ii) Substitution Effect

The income effect is the adjustment of demand to the change in real income.

The substitution effect is the adjustment of demand to the change in relative prices.

Figure 14: Income and Substitution Effects

(Fall in px)

We decompose the overall change in demand into income and substitution effects by (hypothetically) adjusting the consumer’s income to restore him to the level of real income he enjoyed before the price change

Given the fall in px and the subsequent increase in real income, we therefore reduce the consumer’s real income; mechanically, we drag the new budget line back until it is just tangent to the original indifference curve.

(Fall in px)

E0-E1: Total Effect (x0-x1)

E0-E2: Substitution Effect (x0-x2)

E2-E1: Income Effect (x2-x1)

x0 x2 x1

8. Inferior and Giffen Goods

In a two good model, a price change always induces a substitution effect in the opposite direction of the change in price

i.e: a rise (fall) in px induces a substitution away (towards) good x ceteris paribus

We usually say that ‘… the own price substitution effect is always negative.’

The income effect, however, can be positive (i.e. normal good) or negative (i.e. inferior good)

A rise in the price of a normal good induces a negative substitution effect and a negative income effect, both of which act to reduce the demand for good x

A rise in the price of an inferior good, however, induces a negative substitution effect but a positive income effect, thus the overall effect is ambiguous

If, when the price of an inferior good rises, the positive income effect dominates the negative substitution effect, we have the case of a Giffen Good

That is, a good for which demand rises (falls) when price rises (falls)

Giffen goods are very inferior good

Good x: Normal / Non-Giffen

Good x: Inferior / Non-Giffen

Good x: Inferior / Giffen

9. Measuring Real Income

When we decomposed the change in demand resulting from a change in price into an income and substitution effect, we did so by varying money income

Specifically, when the price of good x fell, we ‘varied’ the consumer’s money income to hold his real income constant, where real income was defined as the consumer’s ability to enjoy a particular level of utility

Varying money income is this way is known as a Hicks Compensating Variation in money income (HCV)

HCV allows consumer to enjoy original level of utility at the new relative price ratio

We ‘compensate’ the consumer for the change in price

Sounds odd in respect of a price fall.

Figure 16.1: Hicks Compensating Variation(Price Fall)

Figure 16.2: Hicks Compensating Variation(Price Rise)

An alternative definition of real income is the ability to consumer not a particular level of utility, but a particular bundle of goods

i.e. we vary the consumer’s money income following a change in price to permit him to consumer his original bundle of goods at the new relative price ratio

The is know as the Slutsky Compensating Variation (SCV) in money income.

Figure 16.3: Slutsky Compensating Variation(Price Fall)

Figure 16.4: Slutsky Compensating Variation(Price Rise)

Both Hicks and Slutsky compensating variations adjust the consumer’s new level of income (i.e. the level following the price change) such that he is able to enjoy either his original level of utility (Hicks) or his original consumption bundle (Slutsky)

An alternative approach is to adjust the consumer’s original level of income in such a way that he is able to enjoy the level of utility (Hicks) or the consumption bundle (Slutsky) that he would have been able to enjoy were he to face the change in prices

That is, we vary the consumer’s money income at the original relative price ratio to enable him to enjoy the level of real income (i.e. utility or consumption bundle) that he would have been able to enjoy from the price change

i.e. we provide the consumer with an Equivalent Variation in money income

A variation in money income that will adjust the consumer’s real income in a manner analogous to the price change

Figure 16.5: Hicks Equivalent Variation(Price Fall)

Figure 16.6: Hicks Equivalent Variation(Price Rise)

Figure 16.7: Slutsky Equivalent Variation(Price Fall)

Figure 16.8: Slutsky Equivalent Variation(Price Rise)

To summarise, we have eight cases

Hicks / Slutsky

Compensating Variation / Equivalent Variation

Price Rise / Price Fall

Figure 16.1: Hicks Compensating Variation(Price Fall)

Figure 16.2: Hicks Compensating Variation(Price Rise)

Figure 16.3: Slutsky Compensating Variation(Price Fall)

Figure 16.4: Slutsky Compensating Variation(Price Rise)

Figure 16.5: Hicks Equivalent Variation(Price Fall)

Figure 16.6: Hicks Equivalent Variation(Price Rise)

Figure 16.7: Slutsky Equivalent Variation(Price Fall)

Figure 16.8: Slutsky Equivalent Variation(Price Rise)

10. Applications

Two key areas:

(i) Labour Supply;

(ii) Intertemporal Choice.

10.1 Labour Supply

Consider individual’s role as a supplier of factor services

Individuals sell their labour to firms in return for a wage.

Individual makes a choice between income and leisure given the dual constraints of time and the wage

Figure 18: Preferences

Figure 21: Labour Market Equilibrium

Y1 = Y0 + w(T – L1)

Ymax = Y0 + wT

L1 L2 T

Figure 22: Increase in Unearned Income

Figure 23: Increase in Wage Rate

L3 L2 L1

10.1 Labour Supply

Note that the income and substitution effects work against one another

Because leisure is a normal good, the income effect from the increase in wage increases the demand for leisure

But the wage rate is the opportunity cost, or price, of leisure. Thus, an increase in the wage rate / price of leisure induces a substitution away from leisure

L3 L2 L1

E1-E2: Total Effect (L1-L2)E1-E3: Substitution Effect (L1-L3)E3-E2: Income Effect (L3-L2)

(T-L) 0

(T-L1) (T-L2) T

Figure 24: Labour Supply Curve

10.1 Labour Supply

If the income effect dominates the substitution effect, then we have a situation in which an increase in the wage (i.e. the price of leisure) leads to an increase in the demand for leisure

That is:

Leisure is Giffen …

… but Normal!

10.1 Labour Supply

This is possible because there is also an Endowment Effect in operation …

The Individual is entering the market with an endowment of leisure which he is selling to the firm

The presence of endowment effects complicates the relationship between inferiority and Gifffeness

L3 L1 L2 T

E1-E2: Total Effect (L1-L2)E1-E3: Substitution Effect (L1-L3)E3-E2: Income Effect (L3-L2)

(T-L) 0

(T-L2) (T-L1) T

10.1 Labour Supply

Empirically, we tend to see labour supply curves bending backwards at high wage rates

H = (T-L) 0

10.1 Labour Supply

Rather than at low wage rates

H = (T-L) 0

10.1 Labour Supply

Moreover, backward bending labour supply curves are usually observed for males but nor females

H = (T-L) 0

10.1 Labour Supply

Implications of backward bending labour supply curve

Multiple equilibria

Unstable equilibria

What happens to w if it is perturbed slightly above / below its equilibirum level, w*? Do forces of excess demand / excess supply force w back to w*

H = (T-L) 0

Unstable Equilibrium

Stable Equilibrium

10.2 Intertemporal Choice

Assume individual lives for two periods with a lifetime income endowment of y = (y1, y2)

Consumption over time is c = (c1, c2)

Now, £x saved today (i.e. period 1) will yield £(1+r)x tomorrow (i.e. period 2)

The future value of £x today is thus £(1+r)x

Conversely, the present value of £x received tomorrow (i.e. period 2) is:

Intuitively, if we receive £x tomorrow, can borrow £z today, where:

Thus, given an income endowment of:

Then the maximum period 1 income is:

And the maximum period 2 income is:

Figure 30: Intertemporal Budget Constraint

Assume individual consumes in both periods

If the value of consumption in period 1 is , then can save in period 1 for period 2 consumption in excess of period 2 income, :

c2, y2

0 c1, y1

c2, y2

0 c1, y1

slope = -(1+r)

c2, y2

0 c1, y1

c2, y2

0 c1, y1

Note the effects of changes in income endowment or interest rate

Change in income endowment shifts the inter-temporal budget constraint parallel

Changes in interest rate pivot the budget constraint around the initial income endowment

c2, y2

0 c1, y1

c2, y2

0 c1, y1

Increase in Rate of Interest

Consider a (period 1) borrower

That is:

(c1 - y1) > 0

How does he react to changes in interest rate?

c2, y2

0 c1, y1

Period 1 Borrowing

c2, y2

0 c1, y1

Borrower (Fall in Interest Rate)

Thus, if interest rate falls:

(i) (Period 1) Borrower remains a (period 1) borrower;

(ii) Is better-off;

(iii) Increases (period 1) borrowing if c1 a normal good

c2, y2

0 c1, y1

Borrower (Fall in Interest Rate):

(i) Substitution Effect E0-E2;

(ii) Income Effect E2-E1

If interest rate rises:

(i) Borrower is definitely worse off;

c2, y2

0 c1, y1

Borrower: Increase in Interest Rate:

Conversely, for savers (c1 - y1) <0:

Rise in interest rates: (i) Remain savers; (ii) Better off; (iii) Increase saving if c1 is an inferior good

Fall in interest rate: (i) Definitely worse off

c2, y2

0 c1, y1

Saver (Rise in Interest Rate)

c2, y2

0 c1, y1

Saver (Rise in Interest Rate)

introductory microeconomics (es10001) topic 2: consumer theory

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