decomposition of the total effect into substitution and ... · decomposition of the total effect...

Decomposition of the Total Effect

into Substitution and Income

Effects and

Application of Consumer Theory

Lecture 4

Lecturer: Priscilla T. Baffour (PhD)

Priscilla T. Baffour (PhD) 1

mailto:[email protected]

In a demand relationship the quantity consumed

changes with price but what does the quantity change

actually consist of?

Substitution Effect - substitute other goods for A as

Price of A rises

Income Effect - as price of A falls, real income rises and so

spend more on all goods

Income and Substitution Effects


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


Other Goods

QA

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


Other Goods

QA

U1

U2

BC2

BC1 BC3 2 3

A

B

C

Inferior Good


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


1


Other Goods

QA

U2

U1 BC2

BC1 BC3 1 3 2

A

B

C

Giffen Good


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




• Slutsky equation

• Total effect of price change = SE + IE

• Slutsky’s theorem states that the substitution effect of a price change (relative to quantity) is negative.

• We isolate the substitution effect by taking away from (giving) the consumer enough money to put her at the same level of satisfaction as before the price change.

7 Priscilla T. Baffour (PhD)


• Total effect of a price change for:

– normal good is negative. Because the negative IE

reinforces the already negative SE. For price fall,

quantity DD increases.

– Inferior good is still negative, but –SE > +IE.

Quantity DD increases but less than the case for

normal goods

– Giffen good is positive because –SE < +IE. Quantity

DD falls.


Labor-Leisure Choice

• Leisure - all time spent not working.

• The number of hours worked per day, H, equals 24

minus the hours of leisure or nonwork, 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.

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

U = U(Y, N)

• Jackie’s earned income equal:

wH

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

Y = wH + Y*


Figure 5.8 Demand for Leisure

Budget Line, L1

Y = w1H

Y = w1(24 − N).

Each extra hour of leisure

she consumes costs her w1

goods.

Y ,

Goods p

er

day

Time constraint

H 1 = 8 24 0 N1 = 16 0 24

H, Work hours per day

N , Leisure hours per day

H 1 = 8

N1 = 16 0


N, Leisure hours per day

I 1

L 1

w , W

age p

er

hour (b) Demand Curve

– w 1 1

Y 1

w 1

e 1

E1

(a) Indifference Curves and Constraints


Figure 5.8 Demand for Leisure

Budget Line, L1

Y = w1H

Y = w1(24 − N).

Budget Line, L2

Y = w2H

Y = w2(24 − N).

w2 > w1

Y , G

oods p

er

day

Time const r aint

H 2 = 12 H 1 = 8 24 0

N 2 = 12 N1 = 16 0 24


N , Leisure hours per day

H 2 = 12

N 2 = 12 0


N, Leisure hours per day

Demand for leisure

I 2

I 1 1

– w 2

L 1

L 2

w , W

age p

er

hour

– w 1 1

e 2 Y 2

Y 1

w 1

w 2

e 1

E 2

(b) Demand Curve

E1

H 1 = 8

N1 = 16

(a) Indifference Curves and Constraints


Figure 5.9 Supply Curve of Labor


Income and Substitution Effects of

a Wage Change

Since income effect is

positive, leisure is a normal

good. Y ,

Go

od

s p

er

d a

y

Time const r aint

H 2

H * H 1

24 0

N 2

N * N 1

0 24

Substitution effect

Income effect

Total effect

H , W o r k hours per d a y

N , Leisure hours per d a y

I 2

I 1

L 2

L *

L 1

e 2

e 1

e *


Backward Bending Labor Supply Curve Y

, G

oods p

er

d a

y

(a) Labor-Leisure Choice

Time const r aint

H 2 H

3 H 1

24 0

H , W o r k hours per d a y

E 1

E 3

E 2

L 2

I 2

I 3

I 1

L 3

L 1

e 2

e 1

e 3

w ,

W age p

er

hour

(b) Supply Cu r v e of Labor

Supply curve of labor

H 2 H 3

H 1 24 0

, W o r k hours per d a y

At low wages, an increase in the

wage causes the worker to work

more….

H

but at high wages, an increase in the

wage causes the worker to work

less….


Ordinary curve vrs compensated demand curve

• Compensating variation ensures that the consumer remains on the same IC. DDc is steeper than ordinary DDo curve. The slope of the DDc curve is higher in value for a normal good. The Hicksian demand function.

• Ordinary DDo curve considers both the Substitution and Income effects. The DDo is flatter. The slope of the DDo curve is smaller. The Marshallian demand function.

• The Marshallian demand function is the ordinary market demand function we have been discussing all along.


Other Goods

QA

U1

U2

BC2

BC1 1 3 2

Normal Good

Derive the Ordinary and Compensated Demand curves from this diagram

A

B

C

BC3


Ordinary curve vrs compensated demand curves

• Compensating variation ensures that the consumer remains on the same IC. DDc is steeper than ordinary DDo curve. The slope of the DDc curve is larger for a normal good. This is the Hicksian demand function.

• Ordinary DDo curve considers the effect of IE. The DDo is flatter. The slope of the DDo curve is smaller. This is the Marshallian demand function.

• The Marshallian demand function is the ordinary market demand function we have been discussing all along.


Marshallian and Hicksian demand functions

• Marshal: maximize utility subject to income constraint.

D=f(P, I)

• Hicks: minimize budget constraint subject to utility.

D=f(P, U)

• Given U=f(XaYb), and I = PxX + PyY,

• Try and derive both demand functions


Gross substitutes and gross complements

• If goods X and Y are both normal goods and if Px falls, the

IE and SE would both encourage the consumer to buy

more of X, but the gross (combined) effect on Y is

ambiguous.

• IE encourages the consumer to buy more of Y

• SE encourages the consumer to buy less of Y

• If SE > IE, he will buy less of Y = X & Y are gross

substitutes

• If SE < IE, he will buy more of Y = X & Y are gross

complements


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.

• 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.

Priscilla T. Baffour (PhD) Slide 21

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.

• 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.




Graphical representation of CV (Increase in Price)

X

U1 U0

Y

P1 P0

CV

E2

E0

E1

B2

B1

B0

P1 > P0


• Where; 𝑈0, 𝑃0 , 𝐸0, and 𝐵0 are the initial utility, price, equilibrium, and budget line respectively.

• With the increase in price, the new price (𝑃0) shifts the budget line inwards ( 𝐵1 ). The new equilibrium and utility are represented by 𝐸1and 𝑈1respectively.

• For the consumer to enjoy the same utility (𝑈0), another budget line (𝐵2), tangential to the initial indifference curve (𝑈0) and parallel to the new budget line (𝐵1) is drawn.

Priscilla T. Baffour/ F.K. Agyire-Tettey Slide 24

Equivalent Variation

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

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

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




Graphical representation of EV (Increase in Price)

U1 U0

X

Y

P1 P0

EV P1 > P0


• Where; 𝑈0, 𝑃0 , 𝐸0, and 𝐵0 are the initial utility, price, equilibrium, and budget line respectively.

• With the increase in price, the new price (𝑃0) shifts the budget line inwards ( 𝐵1 ). The new equilibrium and utility are represented by 𝐸1and 𝑈1respectively.

• Get know how much to take from the consumer to make him/her equally worse off as the price increase does, , another budget line (𝐵2), tangential to the new indifference curve (𝑈1) and parallel to the initial budget line (𝐵0) is drawn.

• The difference between the old budget line 𝐵0 and the new budget line 𝐵2 is Equivalent variation.


Comparison Between EV and CV


U1

U0

X

Y

P1 P0

P1 > P0 CV

EV

Comparison Between EV and CV

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

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

• 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.


Application of EV and CV

• Let’s suppose;

– The government in an attempt to encourage agriculture, subsidizes an agricultural input (x) by s per each unit of x. This implies an outward shifting of budget line since the subsidy reduces the price of input x.

– In addition to consuming commodity x, individuals consume other commodities (y).

– Input x is plotted on the horizontal axis and other commodities consumed on the vertical axis.

• This is shown by the figure in the next slide.


Application of EV and CV


X

U0 U1

Y

P0 P1

EV

E2

E1

E0

B2

B0

B1

P1 < P0

X1 Xa

Yb

Ya

Food subsidy or supplementary income?

• Food subsidy enables the consumer to buy at half the market price. The budget line rotates outward. The consumer ends up buying more than at the initial equilibrium.

• Supplementary income shifts the budget line to the right to touch a higher IC. The consumer buys more quantities than at the initial equilibrium

• The cost of food subsidy is greater than the cost of supplementary income. The quantity of goods bought under food subsidy is greater than supplementary income.

• Choosing one of these policies depends on the other goals of government and the indirect effects of each policy.


The End


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