Hicksian and Slutsky condition

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.

Hence total Price effect is sum of Substitution effect and income effectPE = SE + IEHence 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.

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 constantIncome effect: Change in demand due to having more purchasing powerGiffen goods must be inferior but not all inferior goods are Giffern goods. They are extreme inferior goods.Here we will perform 6 different cases Decrease in price of X when it is normal goodIncrease in price of X when it is normal goodDecrease in price of X when it is inferior goodIncrease in price of X when it is inferior goodDecrease in price of X when it is giffen goodIncrease in price of X when it is giffen good

I/PyI/Px

E1E2E3I/PxX1X2X3PESEIEIC1IC2Decrease in PxCase 1: Normal good, decrease priceSubstitution from E1 to E2Here Y will fall as X is relative cheapPrice effect from X1 to X3Substitution effect from X1 to X2 (+ve as X is normal)Income effect from X2 to X3 (+ve as X is normal)

I/PyI/Px

E3E2E1I/PxX3X2X1PESEIEIC2IC1Increase in PxCase 2: Normal good, increase priceSubstitution from E1 to E2Here Y will fall as X is relative expensive

Price effect from X1 to X3Substitution effect from X1 to X2 (-ve as X is normal)Income effect from X2 to X3 (-ve as X is normal)

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.

I/PyI/Px

E1E2E3I/PxX1X2X3PESEIEIC1IC2Decrease in PxCase 3: Inferior good, decrease priceSubstitution from E1 to E2Here Y will fall as X is relative cheapPrice effect from X1 to X3Substitution effect from X1 to X2 (+ve as X is normal)Income effect from X2 to X3 (-ve as X is inferior)

I/PyI/Px

E3E2E1I/PxX3X2X1PESEIEIC2IC1Increase in PxCase 4: Inferior good, increase priceSubstitution from E1 to E2Here Y will fall as X is relative expensive

Price effect from X1 to X3Substitution effect from X1 to X2 (-ve as X is normal)Income effect from X2 to X3 (+ve as X is inferior)

8

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.

I/PyI/Px

E1E2E3I/PxX1X2X3PESEIEIC1IC2Decrease in PxCase 5: Giffen good, decrease priceSubstitution from E1 to E2Here Y will fall as X is relative cheapPrice effect from X1 to X3Substitution 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)

10

I/PyI/Px

E3E2E1I/PxX3X2X1PESEIEIC2IC1Increase in PxCase 4: Inferior good, increase priceSubstitution from E1 to E2Here Y will fall as X is relative expensive

Price effect from X1 to X3Substitution effect from X1 to X2 (-ve as X is normal)Income effect from X2 to X3 (+ve as X is inferior)

11

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 effectPE = SE + IEHence 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 constantIncome effect: Change in demand due to having more purchasing powerHere we will perform 6 different cases Decrease in price of X when it is normal goodIncrease in price of X when it is normal goodDecrease in price of X when it is inferior goodIncrease in price of X when it is inferior goodDecrease in price of X when it is giffen goodIncrease in price of X when it is giffen good

I/PyI/Px

E1E2E3I/PxX1X2X3PESEIEIC1IC2Decrease in PxCase 1: Normal good, decrease priceSubstitution from E1 to E2Here Y will fall as X is relative cheapPrice effect from X1 to X3Substitution effect from X1 to X2 (+ve as X is normal)Income effect from X2 to X3 (+ve as X is normal)

IC1

I/PyI/Px

E3E2E1I/PxX3X2X1PESEIEIC2IC1Increase in PxCase 2: Normal good, increase priceSubstitution from E1 to E2Here Y will fall as X is relative expensive

Price effect from X1 to X3Substitution effect from X1 to X2 (-ve as X is normal)Income effect from X2 to X3 (-ve as X is normal)

IC1

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.

I/PyI/Px

E1E2E3I/PxX1X2X3PESEIEIC1IC2Decrease in PxCase 3: Inferior good, decrease priceSubstitution from E1 to E2Here Y will fall as X is relative cheapPrice effect from X1 to X3Substitution effect from X1 to X2 (+ve as X is normal)Income effect from X2 to X3 (-ve as X is inferior)

IC1

I/PyI/Px

E3E2E1I/PxX3X2X1PESEIEIC2IC1Increase in PxCase 4: Inferior good, increase priceSubstitution from E1 to E2Here Y will fall as X is relative expensive

Price effect from X1 to X3Substitution effect from X1 to X2 (-ve as X is normal)Income effect from X2 to X3 (+ve as X is inferior)

IC1

19

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.

I/PyI/Px

E1E2E3I/PxX1X2X3PESEIEIC1IC2Decrease in PxCase 5: Giffen good, decrease priceSubstitution from E1 to E2Here Y will fall as X is relative cheapPrice effect from X1 to X3Substitution 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)

IC1

21

I/PyI/Px

E3E2E1I/PxX3X2X1PESEIEIC2IC1Increase in PxCase 4: Inferior good, increase priceSubstitution from E1 to E2Here Y will fall as X is relative expensive

Price effect from X1 to X3Substitution effect from X1 to X2 (-ve as X is normal)Income effect from X2 to X3 (+ve as X is inferior)

IC1

22

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