Hicksian and
Slutsky
Analysis
Hicksian Analysis
According to Hicksian effect, for change in price consumer
first substitutes is consumption bundle (good x, good y)
within same utility curve and after that income effect
comes in where consumer shifts on higher indifference
curve.
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
Hence total Price effect is sum of Substitution effect and income
effect
PE = SE + IE
Hence this analysis describes how price effect is partitioned.
The benefit of this model is to see assuming utility constant, how does
demand of good Y is changed if price of good X is changed.
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
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The mechanism is when price decreases then budget line rotates
hence price ratio changes, so consumer first do substitution by
parallel shifting of new budget line downward on old indifference
curve. After this he jumps on new curve and line called as income
effect.
Substitution effect: Change in demand due to change in the rate
of exchange (price ratio) between two goods keeping utility
constant
Income effect: Change in demand due to having more
purchasing power
Giffen goods must be inferior but not all inferior goods are Giffern
goods. They are extreme inferior goods.
Here we will perform 6 different cases
1.
2.
3.
4.
5.
6.
Decrease in price of X when it is normal good
Increase in price of X when it is normal good
Decrease in price of X when it is inferior good
Increase in price of X when it is inferior good
Decrease in price of X when it is giffen good
Increase in price of X when it is giffen good
Case 1: Normal good, decrease
price
Decrease in Px
I/Py
Substitution from E1 to E2
Here Y will fall as X is
relative cheap
E1
E3
Price effect from X1 to X3
Substitution effect from X1
to X2 (+ve as X is normal)
Income effect from X2 to X3
(+ve as X is normal)
E2
IC2
IC1
X1
X2
SE
I/Px
IE
PE
X3
I/P’x
Case 2: Normal good, increase
price
Increase in Px
I/Py
Substitution from E1 to E2
Here Y will fall as X is
relative expensive
Price effect from X1 to X3
Substitution effect from X1
to X2 (-ve as X is normal)
Income effect from X2 to X3
(-ve as X is normal)
E2
E3
E1
IC1
IC2
X3
X2
IE
I/P’x
SE
PE
X1
I/Px

The assumption of X is normal means that for consumer good X
and good Y has same priority, which also means that the
indifference curve will shift parallel out or parallel inward.

Hence we can see that when product is normal then
substitution and income effect is in same direction

As indifference curve assumes that both products are weak
substitutes hence in substitution effect the demand of other
good is also changed.

So according to law of demand , decrease in price of X
increases its demand from X1 to X3 which is also price effect.
Case 3: Inferior good, decrease
price
I/Py
Decrease in Px
Substitution from E1 to E2
Here Y will fall as X is
relative cheap
Price effect from X1 to X3
Substitution effect from X1
to X2 (+ve as X is normal)
Income effect from X2 to X3
(-ve as X is inferior)
E3
E1
IC2
E2
IC1
X1
X3 X2
PE IE
SE
I/Px
I/P’x
Case 4: Inferior good, increase
price
Increase in Px
I/Py
Substitution from E1 to E2
Here Y will fall as X is
relative expensive
Price effect from X1 to X3
Substitution effect from X1
to X2 (-ve as X is normal)
Income effect from X2 to X3
(+ve as X is inferior)
E2
E3
E1
IC1
IC2
X2 X
3
IE PE
SE
X1
I/P’x
I/Px

The assumption of X is inferior means that for consumer good Y is
preferred over good X, which also means that the indifference
curve will shift away outward and shift near inward.

Hence we can see that when product is inferior then
substitution and income effect is in opposite direction

As indifference curve assumes that both products are weak
substitutes hence in substitution effect the demand of other
good is also changed.

So according to law of demand , decrease in price of X
increases its demand from X1 to X3 which is also price effect.
Case 5: Giffen good, decrease
price
Decrease in Px
I/Py
Substitution from E1 to E2
Here Y will fall as X is
relative cheap
E3
IC2
E1
Price effect from X1 to X3
Substitution effect from X1 to
X2 (+ve as X is normal)
Income effect from X2 to X3
(-ve and more than subs
effect in magnitude as X is
giffen)
E2
IC1
X3 X1
PE
X2
SE
IE
I/Px
I/P’x
Case 4: Inferior good, increase
price
Increase in Px
I/Py
Substitution from E1 to E2
Here Y will fall as X is
relative expensive
Price effect from X1 to X3
Substitution effect from X1
to X2 (-ve as X is normal)
Income effect from X2 to X3
(+ve as X is inferior)
E2
E1
IC1
E3
X2
SE
IE
X1 X3
PE I/P’x
IC2
I/Px

The assumption of X is giffen means that for consumer good Y is
very preferred over good X, which also means that the
indifference curve will shift far away outward and shift very near
inward.

Hence we can see that when product is giffen then substitution
and income effect is in opposite direction. But the income
effect is higher than substitution effect in magnitude.

As indifference curve assumes that both products are weak
substitutes hence in substitution effect the demand of other
good is also changed.

So according to exception in law of demand , decrease in
price of X decreases its demand from X1 to X3 which is also price
effect.
This approach is used to make Compensated Demand curve.

Slutsky Analysis
According to Slutsky effect, for change in price consumer first
substitutes is consumption bundle (good x, good y) within same
purchasing power and after that income effect comes in where
consumer shifts on higher indifference curve.


Hence total Price effect is sum of Substitution effect and income
effect
PE = SE + IE
Hence this analysis describes how price effect is partitioned.
The benefit of this model is to see assuming budget constant, how
does demand of good Y is changed if price of good X is changed
and how much extra utility is gained for the price decrease and
vice versa.




The mechanism is when price decreases then budget line
rotates hence price ratio changes, so consumer first do
substitution by parallel shifting of new budget line downward on
old equilibrium indifference curve. After this he jumps on new
curve and line called as income effect.
Substitution effect: Change in demand due to change in the
rate of exchange (price ratio) between two goods keeping
budget constant
Income effect: Change in demand due to having more
purchasing power
Here we will perform 6 different cases
1.
2.
3.
4.
5.
6.
Decrease in price of X when it is normal good
Increase in price of X when it is normal good
Decrease in price of X when it is inferior good
Increase in price of X when it is inferior good
Decrease in price of X when it is giffen good
Increase in price of X when it is giffen good
Case 1: Normal good, decrease
price
Decrease in Px
I/Py
Substitution from E1 to E2
Here Y will fall as X is
relative cheap
E1
E3
Price effect from X1 to X3
Substitution effect from X1
to X2 (+ve as X is normal)
Income effect from X2 to X3
(+ve as X is normal)
E2
IC2
IC1
X1
X2
SE
I/Px
IE
PE
X3
IC’1
I/P’x
Case 2: Normal good, increase
price
Increase in Px
I/Py
Substitution from E1 to E2
Here Y will fall as X is
relative expensive
Price effect from X1 to X3
Substitution effect from X1
to X2 (-ve as X is normal)
Income effect from X2 to X3
(-ve as X is normal)
E2
E3
E1
IC’1
IC1
IC2
X3
X2
IE
I/P’xX1
SE
PE
I/Px

The assumption of X is normal means that for consumer good X
and good Y has same priority, which also means that the
indifference curve will shift parallel out or parallel inward.

Hence we can see that when product is normal then
substitution and income effect is in same direction

As indifference curve assumes that both products are weak
substitutes hence in substitution effect the demand of other
good is also changed.

So according to law of demand , decrease in price of X
increases its demand from X1 to X3 which is also price effect.
Case 3: Inferior good, decrease
price
I/Py
Decrease in Px
Substitution from E1 to E2
Here Y will fall as X is
relative cheap
Price effect from X1 to X3
Substitution effect from X1
to X2 (+ve as X is normal)
Income effect from X2 to X3
(-ve as X is inferior)
E3
E1
IC2
E2
IC1
X1
X3
PE IE
SE
X2
I/Px
IC’1
I/P’x
Case 4: Inferior good, increase
price
Increase in Px
I/Py
Substitution from E1 to E2
Here Y will fall as X is
relative expensive
Price effect from X1 to X3
Substitution effect from X1
to X2 (-ve as X is normal)
Income effect from X2 to X3
(+ve as X is inferior)
E2
E3
E1
IC’1
IC1
IC2
X2 X
3
IE
X1
PE
SE
I/P’x
I/Px

The assumption of X is inferior means that for consumer good Y is
preferred over good X, which also means that the indifference
curve will shift away outward and shift near inward.

Hence we can see that when product is inferior then
substitution and income effect is in opposite direction

As indifference curve assumes that both products are weak
substitutes hence in substitution effect the demand of other
good is also changed.

So according to law of demand , decrease in price of X
increases its demand from X1 to X3 which is also price effect.
Case 5: Giffen good, decrease
price
Decrease in Px
I/Py
Substitution from E1 to E2
Here Y will fall as X is
relative cheap
E3
IC2
E1
Price effect from X1 to X3
Substitution effect from X1 to
X2 (+ve as X is normal)
Income effect from X2 to X3
(-ve and more than subs
effect in magnitude as X is
giffen)
E2
IC’1
IC1
X3 X1
PE
X2
SE
IE
I/Px
I/P’x
Case 4: Inferior good, increase
price
Increase in Px
I/Py
Substitution from E1 to E2
Here Y will fall as X is
relative expensive
Price effect from X1 to X3
Substitution effect from X1
to X2 (-ve as X is normal)
Income effect from X2 to X3
(+ve as X is inferior)
E2
E1
IC’1
IC1
E3
X2
SE
IE
X1 X3
PE I/P’x
IC2
I/Px

The assumption of X is giffen means that for consumer good Y is
very preferred over good X, which also means that the
indifference curve will shift far away outward and shift very near
inward.

Hence we can see that when product is giffen then substitution
and income effect is in opposite direction. But the income
effect is higher than substitution effect in magnitude.

As indifference curve assumes that both products are weak
substitutes hence in substitution effect the demand of other
good is also changed.

So according to exception in law of demand , decrease in
price of X decreases its demand from X1 to X3 which is also price
effect.

This approach is called Equivalent Income Variation