Income and Substitution Effects

In a demand relationship the quantity consumed changes with price but what does the quantity change actually consist of?

Substitution Effect – this effect looks at how the individual substitutes other goods for good A as Price of A rises.

Income Effect – here, as price the of A falls, real income rises and so the individual gets to spend more on all goods including A.

Direction and size of effects varies with type of good

Normal Good - as price falls, consumption rises

- as income rises, consumption rises

Inferior Good - as price falls, consumption rises

- as income rises, consumption falls

Giffen Good - as price falls, consumption falls

- as income rises, consumption falls

Application to Different Types of Goods

Decrease in Price

Other Goods

Q_A

U₁

U₂

BC₂

BC₁

1

3

2

Normal Good

Subs: 1 to 3 or A to C (-ve)

Income: 3 to 2 or C to B (-ve)

Price effect: A to B or 1 to 2

A

B

C

BC₃

Decrease in Price

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Other Goods

Q_A

U₁

U₂

BC₂

BC₁

BC₃

2

3

A

B

C

Inferior Good

Subs: 1 to 3 or A to C (-ve)

Income: 3 to 2 or C to B (+ve)

Price effect: A to B or 1 to 2

1

Decrease in Price

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Other Goods

Q_A

U₂

U₁

BC₂

BC₁

BC₃

1

3

2

A

B

C

Giffen Good

Subs: 1 to 3 or A to C (-ve)

Income: 3 to 2 or C to B (+ve)

Price effect: A to B or 1 to 2

�Income and Substitution Effects�

• Total effect of a price change consist of both the substitution and income effects. The total effect for;
• normal good is negative. Because the negative IE reinforces the already negative SE. For price fall, quantity demanded increases.
• inferior good is still negative, but –SE > +IE. Quantity demanded increases but less than the case for normal goods as price falls.
• Giffen good is positive because –SE < +IE. Quantity demanded falls as price falls.

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6

Labor-Leisure Choice

• The labour leisure choice model relates utility maximization to labour supply where the individual derives direct utility from leisure and by the consumption of composite goods and services which are purchased by working.
• Leisure - all time spent not working.
• The number of hours worked per day, H, equals 24 minus the hours of leisure or non-work, N, in a day:

H = 24 − N.

• The price of leisure is forgone earnings.
• The higher your wage, the more an hour of leisure costs you.

Labor-Leisure Choice: Example

• Jackie spends her total income, Y, on various goods.
• The price of these goods is $1 per unit.

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• Her utility, U, depends on how many goods and how much leisure she consumes:

U = U(Y, N).

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• Jackie’s earned income equal:

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wH.

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• And her total income, Y, is her earned income plus her unearned income, Y*:

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Y = wH + Y*.

Demand for Leisure

Budget Line, L¹

Y = w₁H

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Y = w₁(24 − N).

Each extra hour of leisure she consumes costs her w₁ goods.

Y

, Goods per day

Time constraint

24

0

0

24

H,

Work hours per day

N

, Leisure hours per day

0

H, Work hours per day

N, Leisure hours per day

(b) Demand Curve

1

E₁

(a) Indifference Curves and Constraints

Demand for Leisure

Budget Line, L¹

Y = w₁H

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Y = w₁(24 − N).

Budget Line, L²

Y = w₂H

​

Y = w₂(24 − N).

​

w₂ > w₁

Y

, Goods per day

24

0

0

24

H,

Work hours per day

N

, Leisure hours per day

0

H, Work hours per day

N, Leisure hours per day

Demand for leisure

1

1

E

2

(b) Demand Curve

E₁

(a) Indifference Curves and Constraints

Labour Supply Curve

Application of Consumer Theory

• As already indicated, an increase in the price of a commodity will result in an inward rotation of the budget line which leads to a decrease in the utility of the individual.
• The compensating and equivalent variations enable the measurement of how worse off (better off) an individual gets due to an increase (decrease) in the price of a commodity since utility is ordinal.

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Application of Consumer Theory Cont.

• Compensating variation (CV) measures welfare loss to the consumer as a result of an increase in price by estimating the amount of money needed to compensate the consumer by restoring him/her to his/her initial utility before the price change. Simply, CV measures the amount of money a consumer will need to accept a price change.

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• Equivalent variation (EV) on the other hand measures the amount of money needed to be taken away from the consumer to reduce his/her welfare just as would have resulted from the increase in price. In other words, the EV measures the amount of money a consumer is willing to sacrifice to avoid a price change.

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Compensating Variation

• CV is positive when there is a price increase, it tells the amount of money to be given to restore consumers to their initial utility level. Thus, the CV measures how much a consumer is made worse off as a result of the increase in price.

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• CV is negative when there a price decrease, it tells the amount of money to be taken from the consumer to restore him or her to his or her original utility. Here, CV measures how much the individual is made better off due to the decrease in price. This is equivalent to EV of an increase in price.

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Compensating Variation

Graphical representation of CV (Increase in Price)

X

U¹

U⁰

Y

P¹

P⁰

CV

E²

E⁰

E¹

B²

B¹

B⁰

P¹ > P⁰

Compensating Variation

Equivalent Variation

• EV is positive when there is a decrease in price. This is equivalent to CV of an increase in price.

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• Similarly, EV is negative when there is an increase in price. It is equivalent to CV of a decrease in price.

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• Although utilities are ordinal, it does not affect the value of the compensating variation.

Equivalent Variation

Graphical representation of EV (Increase in Price)

U¹

U⁰

X

Y

P¹

P⁰

EV

B²

B¹

B⁰

E⁰

E¹

E²

P¹ > P⁰

Equivalent Variation

Comparison Between EV and CV

U¹

U⁰

X

Y

P¹

P⁰

P¹ > P⁰

E⁰

E²

E¹

CV

EV

Comparison Between EV and CV

• Properly drawn, we expect that the EV and the CV will not be the same.

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• Hence, the EV and CV provide varying estimates of the cedi value between the two curves.

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• The difference between the EV and CV is due to the fact that the two measures use different sets of relative prices to estimate the welfare loss.

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