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**Hicksian and Slutsky Analysis**

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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 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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**Income effect: Change in demand due to having more purchasing power **

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 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

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**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 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) E1 E3 E2 IC2 IC1 X1 X2 I/Px X3 I/P’x SE IE PE

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**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 I/P’x X1 I/Px IE SE PE

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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.

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**Case 3: Inferior good, decrease price**

Decrease in Px I/Py 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 I/Px I/P’x PE IE SE

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**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 X1 X3 I/P’x I/Px IE PE SE

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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.

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**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 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) IC2 E1 E2 IC1 I/Px X3 X1 X2 PE I/P’x SE IE

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**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 X1 X3 I/P’x I/Px PE IC2 SE IE

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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.

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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.

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**Income effect: Change in demand due to having more purchasing power **

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 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

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**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 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) E1 E3 E2 IC2 IC’1 IC1 X1 X2 I/Px X3 I/P’x SE IE PE

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**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 I/P’x X1 I/Px IE SE PE

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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.

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**Case 3: Inferior good, decrease price**

Decrease in Px I/Py 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 IC’1 IC1 X1 X3 X2 I/Px I/P’x PE IE SE

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**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 X1 X3 I/P’x I/Px IE PE SE

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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.

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**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 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) IC2 E1 E2 IC’1 IC1 X3 X1 X2 I/Px PE I/P’x SE IE

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**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 X1 X2 X3 I/P’x I/Px PE IC2 SE IE

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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

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