7-slutsky equation

Question 1

what is the interpretation of the substitution effect offered by slutsky?

Answer 1

It shows how the consumption changes due to change in the rate of exchange between the two goods when purchasing power remains the same (the original bundle remains just affordable).

Question 2

what are the steps for the derivation of slutsky decomposition?

Answer 2

1)We calculate how much we need to adjust income in order to keep the old bundle just affordable
2)We compute the substitution effect that is the change in demand for good 1 when the price changes to 𝑝_1^′ and at the same time income changes to 𝑀^′
3) We compute the income effect that shows the change in the demand for good 1 when we change income from 𝑀′ to 𝑀 under new prices
4)Now we can decompose the total change in demand
5)Let’s divide both sides of the equation by Δ𝑝_1, and remember that the income change ΔM=x_1 Δ𝑝_1

Question 3

how can the slutsky equation be written?

Answer 3

(𝜕𝑥_1^∗)/(𝜕𝑝_1 )=(𝜕𝑥_1^ℎ)/(𝜕𝑝_1 )−(𝜕𝑥_1^∗)/𝜕𝑀 𝑥_1^∗ where 𝑥_1^∗ is the consumer’s Marshallian demand function, and 𝑥_1^ℎ is the consumer’s Hicksian demand function for good 1.

Question 4

what is the law of demand?

Answer 4

If the demand for a good increases when income increases, then the demand for that good must decrease when its price increases.

Question 5

how can you represent the slutsky decomposition graphically?

Answer 5

you start with an original budget constaint and indifference curve. when there is a price decrease for good 1 for example the budget line will pivot around good 2 and stretch along the good 1 axis. this will result in a flatter budget line. the new budget line will be tangential to a new indifference curve. if you then shift this new budget line so its tangential to the original indifference curve and the change in good 1 from original to the new tangent on indifference curve shows the substitution effect and the rest of the change is due to the income effect.

Question 6

what is the slutsky effect for normal goods/

Answer 6

most goods are normal so demand increases with income therefore the substitution and income effects reinforce each other when a normal goods own price changes. since both the substitution and income effects increase demand when own price falls, a normal goods ordinary demand curve slopes down

Question 7

what is the slutsky effects for perfect complements?

Answer 7

in case of perfect complements, the substitution effect is zero because the consumer always wants to consume goods in the fixed proportion, therefore the total effect is the income effect

Question 8

what is the slutsky effects for perect substitutes?

Answer 8

when we tilt the budget line due to a decrease in price of good 1 the demand bundle jumps from the vertical axis to the horizontal axis and so the entire change in demand is due to the substitution effect

Question 9

how does the slutsky equation explain giffen goods?

Answer 9

In rare cases of extreme income-inferiority, the income effect can overturn the substitution effect, causing quantity demanded to fall as own price decreases:
(𝜕𝑥_1^∗)/(𝜕𝑝_1 )=(𝜕𝑥_1^ℎ)/(𝜕𝑝_1 )−(𝜕𝑥_1^∗)/𝜕𝑀 𝑥_1^∗
if th income effect is greater then the substitution effect then there will be a fall in demand