6) hicksian (compensated)

Question 1

what does the compensated demand show?

Answer 1

the compensated demand function shows how the optimal consumption bundle changes when consumers are compensated to preserve the same utility level after a price change

Question 2

what are the two effects that we can decompose a price change into?

Answer 2

the income effect and the substitution effects

Question 3

what are the properties of a hicksian demand function?

Answer 3

the functions are homogenous of degree zero in p1 and p2
the law of demand must hold for the hicksian demand function so if price rises demand must fall
if demand for good 1 increases then it must be that x2 doesn’t increase because the utility level doesn’t change

Question 4

what is the slope of the iso expenditure function and what does this mean?

Answer 4

p1/p2, therefore if both price are increased by the same proportion the slope doesn’t change ie the same tangent price

Question 5

what does the slope of the hicksian demand function give?

Answer 5

it gives the substitution effect,

Question 6

what does the hicksian demand function not depend on and therefore what are not applicable?

Answer 6

it does not depend on income and therefore the definitions on inferior, normal, luxury or necessity are not applicable here

Question 7

what is shepards lemma?

Answer 7

Shepard’s Lemma: the derivate of the expenditure function w.r.t. the price of the relevant good gives the Hicksian demand function:
𝜕𝐸/(𝜕𝑝_1 )=𝑥_1^ℎ
𝜕𝐸/(𝜕𝑝_2 )=𝑥_2^ℎ

Question 8

what is the relationship between the expenditure function and prices?

Answer 8

Expenditure function is always increasing in prices:
𝜕𝐸/(𝜕𝑝_1 )>0
𝜕𝐸/(𝜕𝑝_2 )>0

Question 9

what are examples of situations when we want to decompose income and substitution effects?

Answer 9

Government needs to adjust its benefit payments in line with inflation
Economists want to estimate the effects of a proportional tax on household consumption.
Studying the effect of income tax on labour supply.

Question 10

how are pensioners compensated for the price increases?

Answer 10

the two general ideas: 1) the pensioners old utility level is protected at the new prices (hicks compensation or compensating variation)
2) the pensioners old consumption bundle is protected under the new prices (slutskys compensation)