introductory microeconomics (es10001) topic 2: consumer theory
TRANSCRIPT
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Introductory Microeconomics (ES10001)
Topic 2: Consumer Theory
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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
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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)
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2. Theory of Consumer Choice
Four elements:
(i) Consumer’s income
(ii) Prices of goods
(iii) Consumer’s tastes
(iv) Rational Maximisation
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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)
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3. The Budget Constraint
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
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3. The Budget Constraint
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)
.
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3. The Budget Constraint
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
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Films
0 Meals
A
B
Figure 1: Budget Constraint
2 8 10
1
4
5
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3. The Budget Constraint
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.
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3. The 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
Slope
Independent of income
Determined only by relative prices
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3. The Budget Constraint
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
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3. The Budget Constraint
The slope of the budget constraint in this example is thus:
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Films
0 Meals
Figure 2: Slope of Budget Constraint
1 10
4.5
5
Δqm = 1
Δqf = - 0.5
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3. The Budget Constraint
More generally:
Two goods (x,y), prices (px, py) and money income (m)
m = pxx + pyy
Slope of budget constraint: - px/py
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3. The Budget Constraint
Proof:
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3. The Budget Constraint
Thus:
Such that
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3. The Budget Constraint
That is:
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y
0 x
A
B
Figure 3: Budget Constraint
y = m/py - (px/py)x
m/px
m/py
Δy = -(px/py)Δx
Δx
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3. The Budget Constraint
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.
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4. Preferences
Consider now the consumer preferences Given what consumer can do, what would he like to
do?
Four assumptions:
(i) Completeness
(ii) Consistency
(iii) Non-satiation
(iv) Diminishing Marginal Rate of Substitution
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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.
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IV. Preferences
Consistency
Preferences are also assumed to be consistent
Thus if and , then we would infer that
We assume consumer is logically consistent
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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
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y
0 x
a
Figure 4a: Preferences
c
b
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y
0 x
a
Figure 4b: Preferences
c
f
d
egb
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y
0 x
a
Figure 4c: Preferences
b
c
f
d
eg
h
i
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y
0 x
a
Figure 4d: Preferences
b
c
f
d
eg
h
i
Indifference Curve
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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.
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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
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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
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y
x0
I0
Figure 5: Indifference Curves
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y
x0
Figure 5: Indifference Curves
A
BI0
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y
x0
I0
Figure 5: Indifference Curves
A
B
A´
B´
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y
x0
I0
Figure 5: Indifference Curves
A
B
Δx = 1
Δx = 1
Δy
Δy
A´
B´
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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)
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y
x0
I0
Figure 6: Indifference Curves
A
B
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y
x0
I0
Figure 6: Indifference Curves
A
B
8
2
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y
x0
I0
Figure 6: Indifference Curves
A
B
8
2
2 5 8
5C
I1
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4. Preferences
Note:
(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.
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y
x0
I0
I1
I2
Figure 7: Indifference Curves
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y
x0
I1
I0
Figure 8: Indifference Curves Cannot Cross
a
b
c
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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.
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5. Utility Maximisation
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’
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5. Utility Maximisation
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
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5. Utility Maximisation
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
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y
x0
I0
I1
I2
Figure 9: Equilibrium (MRS = ERS)
E1
y1
x1 47
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y
x0
I0
Figure 10: Disequlibrium (MRS ≠ ERS)
E0
ΔyMRS
ΔyERS
Δx
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5. Utility Maximisation
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
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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
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6. Comparative Statics
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
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y
0 x
Figure 11: Increase in Income
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y
0 x
Figure 12: Increase in Income
A
C
B
D
E0
I0
x Normaly Normal
I1
E1
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y
0 x
Figure 12: Increase in Income
A
C
B
D
E0
I0
x Inferior y Normal
I1
E1
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y
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Figure 12: Increase in Income
A
C
B
D
E0
I1
x Normaly Inferior
E1
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y
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Figure 12: Increase in Income
A
C
B
D
E0
I0
x Inferior y Normal
x Normaly Normal
x Normaly Inferior
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6. Comparative Statics
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.
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y
0 x
Figure 13: Fall in Price
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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
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y
0 x
Figure 13: Fall in Price
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y
0 x
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
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y
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Figure 15: Effects of a Fall in Price
E0
E1
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y
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Figure 15: Effects of a Fall in Price
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y
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Figure 15: Effects of a Fall in Price
E0
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y
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Figure 15: Effects of a Fall in Price
E0
A
B
C
Good x isNon-Giffen
Good xis Giffen
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y
0 x
0 x0 x1 x
Figure 15: Effects of a Fall in Price
E0
E1
E0
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y
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Figure 15: Effects of a Fall in Price
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y
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Figure 15: Effects of a Fall in Price
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7. Income & Substitution Effects
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.
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y
0 x
E0
I0
Figure 14: Income and Substitution Effects
(Fall in px)
A
A
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y
0 x
I1
E0
E1
I0
Figure 14: Income and Substitution Effects
(Fall in px)
A
A B
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7. Income & Substitution Effects
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.
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y
0 x
I1
E0
E1
I0
Figure 14: Income and Substitution Effects
(Fall in px)
A
A B
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y
0 x
I1
E0
E2
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I0
Figure 14: Income and Substitution Effects
(Fall in px)
A
A C B
C
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y
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I1
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Figure 14: Income and Substitution Effects
(Fall in px)
A
A C B
C
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y
0 x
I1
E0
E2
E1
I0
Figure 14: Income and Substitution Effects
(Fall in px)
A
A B
E0-E1: Total Effect (x0-x1)
E0-E2: Substitution Effect (x0-x2)
E2-E1: Income Effect (x2-x1)
x0 x2 x1
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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.’
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8. Inferior and Giffen Goods
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
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8. Inferior and Giffen Goods
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
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y
x0
E0E1
E2
A
A C B
Figure 15: Income and Substitution Effects
Good x: Normal / Non-Giffen
I1
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C
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y
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E0
E1
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A
A C B
Figure 15: Income and Substitution Effects
Good x: Inferior / Non-Giffen
I1
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C
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y
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E0
E1
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A
A C B
Figure 15: Income and Substitution Effects
Good x: Inferior / Giffen
I1
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C
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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
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9. Measuring Real Income
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.
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y
0 x
I1
A
B C
I0
Figure 16.1: Hicks Compensating Variation(Price Fall)
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y
0 x
I1
CB
A
I0
Figure 16.2: Hicks Compensating Variation(Price Rise)
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9. Measuring Real Income
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.
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y
0 x
I2
A
B
CI0
I1
Figure 16.3: Slutsky Compensating Variation(Price Fall)
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y
0 x
I2
C
B
A
I0
I1
Figure 16.4: Slutsky Compensating Variation(Price Rise)
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9. Measuring Real Income
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
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9. Measuring Real Income
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
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y
0 x
I1
A
B
C
I0
Figure 16.5: Hicks Equivalent Variation(Price Fall)
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y
0 x
I1
C
B
A
I0
Figure 16.6: Hicks Equivalent Variation(Price Rise)
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y
0 x
I2
A
B
C
I0
I1
Figure 16.7: Slutsky Equivalent Variation(Price Fall)
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y
0 x
I2
C
B
AI0
I1
Figure 16.8: Slutsky Equivalent Variation(Price Rise)
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9. Measuring Real Income
To summarise, we have eight cases
Hicks / Slutsky
Compensating Variation / Equivalent Variation
Price Rise / Price Fall
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y
0 x
I1
A
B C
I0
Figure 16.1: Hicks Compensating Variation(Price Fall)
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y
0 x
I1
CB
A
I0
Figure 16.2: Hicks Compensating Variation(Price Rise)
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y
0 x
I2
A
B
CI0
I1
Figure 16.3: Slutsky Compensating Variation(Price Fall)
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y
0 x
I2
C
B
A
I0
I1
Figure 16.4: Slutsky Compensating Variation(Price Rise)
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y
0 x
I1
A
B
C
I0
Figure 16.5: Hicks Equivalent Variation(Price Fall)
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y
0 x
I1
C
B
A
I0
Figure 16.6: Hicks Equivalent Variation(Price Rise)
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y
0 x
I2
A
B
C
I0
I1
Figure 16.7: Slutsky Equivalent Variation(Price Fall)
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y
0 x
I2
C
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AI0
I1
Figure 16.8: Slutsky Equivalent Variation(Price Rise)
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10. Applications
Two key areas:
(i) Labour Supply;
(ii) Intertemporal Choice.
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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
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Y
L0
Ymax
T
Y0w
Figure 17: Budget Constraint
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Y
L0
I0
I1
I2
Figure 18: Preferences
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Y
L0
E0
Ymax
A Y0
w
L1 T
Y1
I1
Figure 21: Labour Market Equilibrium
Y1 = Y0 + w(T – L1)
Ymax = Y0 + wT
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Y
L0
E1
A Y0
L1 L2 T
Y1 B
Y2E2
I2
I1
Figure 22: Increase in Unearned Income
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Y
L0
E1
T
L2 L1
E2
I1
I2
Figure 23: Increase in Wage Rate
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Y
L0
E1
T
L3 L2 L1
E2
I1
I2
Figure 23: Increase in Wage Rate
E3
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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
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Y
L0
E1
T
L3 L2 L1
E2
I1
I2
Figure 23: Increase in Wage Rate
E3
E1-E2: Total Effect (L1-L2)E1-E3: Substitution Effect (L1-L3)E3-E2: Income Effect (L3-L2)
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w
(T-L) 0
w2
(T-L1) (T-L2) T
w1
Ls
E1
E2
Figure 24: Labour Supply Curve
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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!
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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
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Y
L0
E1
L3 L1 L2 T
E2
E3
I1
I2
Figure 25: Increase in Wage Rate
E1-E2: Total Effect (L1-L2)E1-E3: Substitution Effect (L1-L3)E3-E2: Income Effect (L3-L2)
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w
(T-L) 0
w2
(T-L2) (T-L1) T
w1
Ls
Figure 26: Labour Supply Curve
E2
E1
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10.1 Labour Supply
Empirically, we tend to see labour supply curves bending backwards at high wage rates
i.e.
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w
H = (T-L) 0
Ls
Figure 27: Labour Supply Curve
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10.1 Labour Supply
Rather than at low wage rates
i.e.
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w
H = (T-L) 0
Ls
Figure 28: Labour Supply Curve
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10.1 Labour Supply
Moreover, backward bending labour supply curves are usually observed for males but nor females
i.e.
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w
H = (T-L) 0
Figure 29: Labour Supply Curve
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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*
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w
H = (T-L) 0
Ls
Figure 29: Labour Supply Curve
Ld
Unstable Equilibrium
Stable Equilibrium
E1
E2
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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
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10.2 Intertemporal Choice
Conversely, the present value of £x received tomorrow (i.e. period 2) is:
Intuitively, if we receive £x tomorrow, can borrow £z today, where:
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10.2 Intertemporal Choice
Thus, given an income endowment of:
Then the maximum period 1 income is:
And the maximum period 2 income is:
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y2
0 y1
Figure 30: Intertemporal Budget Constraint
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10.2 Intertemporal Choice
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, :
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10.2 Intertemporal Choice
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c2, y2
0 c1, y1
Figure 30: Intertemporal Budget Constraint
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c2, y2
0 c1, y1
Figure 30: Intertemporal Budget Constraint
slope = -(1+r)
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c2, y2
0 c1, y1
Figure 30: Intertemporal Budget Constraint
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c2, y2
0 c1, y1
Figure 30: Intertemporal Budget Constraint
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10.2 Intertemporal Choice
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
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c2, y2
0 y1
Figure 30: Intertemporal Budget Constraint
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c2, y2
0 y1
Figure 30: Intertemporal Budget Constraint
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c2, y2
0 c1, y1
Figure 30: Intertemporal Budget Constraint
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c2, y2
0 c1, y1
Figure 30: Intertemporal Budget Constraint
Increase in Rate of Interest
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10.2 Intertemporal Choice
Consider a (period 1) borrower
That is:
(c1 - y1) > 0
How does he react to changes in interest rate?
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c2, y2
0 c1, y1
Figure 30: Intertemporal Budget Constraint
Period 1 Borrowing
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c2, y2
0 c1, y1
Figure 30: Intertemporal Budget Constraint
Borrower (Fall in Interest Rate)
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10.2 Intertemporal Choice
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
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c2, y2
0 c1, y1
Figure 30: Intertemporal Budget Constraint
Borrower (Fall in Interest Rate):
(i) Substitution Effect E0-E2;
(ii) Income Effect E2-E1
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10.2 Intertemporal Choice
If interest rate rises:
(i) Borrower is definitely worse off;
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c2, y2
0 c1, y1
Figure 30: Intertemporal Budget Constraint
Borrower: Increase in Interest Rate:
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10.2 Intertemporal Choice
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
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c2, y2
0 c1, y1
Figure 30: Intertemporal Budget Constraint
Saver (Rise in Interest Rate)
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c2, y2
0 c1, y1
Figure 30: Intertemporal Budget Constraint
Saver (Rise in Interest Rate)
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