CCT3- Slutsky Equation, Hicksian Demand, Consumer Welfare + Revealed Preferences

Question 1

What does the Slutsky equation do?

Answer 1

It breaks down the price effect into two different parts, the income effect and the substitution effect.

Question 2

Which two versions are there of the Slutsky decomposition?

Answer 2

• The Hicksian

* The Slutsky

Question 3

Which is the theoretically correct method for breaking down the price effect?

Answer 3

The Hicksian

Question 4

Is the Hicksian empirically useful, why?

Answer 4

Often it is not, it focuses on bringing a budget constraint back to an indifference curve, and indifference curves aren’t typically observable.

Question 5

What is a Slutsky decomposition an approximation of?

Answer 5

The Slutsky decomposition is an approximation of the “correct” Hicksian decomposition.

Question 6

So why is the Slutsky equation often more useful, but what is this dependant on?

Answer 6

• As it is based on observable effects

* The price effects being fairly small

Question 7

What is the Hicksian decomposition equation for own effects?

Answer 7

∂x/∂px = ∂x/∂px| ̅u -(∂x/∂m)x

where | ̅u means keeping utility constant

Question 8

Which part of the Hicksian gives the SE and which gives the IE?

Answer 8

• ∂x/∂px| ̅u represents the SE

* (∂x/∂m)x represents the IE.

Question 9

Under a Hicksian decomposition, will be income and substitution effects the positive or negative?

Answer 9

• The substitution effect will always be negative

* The income effect will be negative if we have a normal good, but positive if we have an inferior good.

Question 10

What is the difference between normal and inferior goods?

Answer 10

When people’s income rises
• Demand for inferior goods will fall
• Demand for normal goods will rise.

Question 11

What is the difference between the Hicksian Demand and Marshallian demand?

Answer 11

Marshallian Demand focuses on the whole price effect, whereas Hicksian demand only focuses on the substitution effect, as it is a compensated demand curve.

Question 12

What is the Hicksian demand curve sometimes known as?

Answer 12

The compensated demand curve

Question 13

The Hicksian decomposition keeps utility constant. What does the Slutsky decomposition keep constant?

Answer 13

The Slutsky decomposition keeps income constant.

Question 14

What does the compensation do differently to the budget line in the Slutsky decomposition than the Hicksian decomposition?

Answer 14

The compensation for the price change brings the budget line at new prices back through the original consumption point rather than tangential to the original indifference curve.

Question 15

Does the Slutsky decomposition also exclude the income effect, as the Hicksian decomposition does?

Answer 15

Yes

Question 16

What is the Hicksian decomposition equation for cross-price effects?

Answer 16

∂y/∂px = ∂y/∂px| ̅u -(∂x/∂m)y

where | ̅u means keeping utility constant

Question 17

What is the Gross Effect?

Answer 17

• ∂y/∂px stands for the Gross Effect- the overall impact of the price of x changing the demand for y, taking into account the income and substitution effects.

Question 18

What does it mean if the Gross Effect is positive or negative?

Answer 18

• If the Gross Effect is positive, then we are said to have gross substitutes- y is a gross substitute for x.
• If the Gross Effect is negative, then we are said to have gross complements- y is a gross complements for x.

Question 19

What is an independant good?

Answer 19

Where there is no gross effect, aka both tangencies are at the same height.

Question 20

What kind of goods do Cobb-Douglas utility functions yield?

Answer 20

Independent goods

Question 21

If ∂y/∂Px<0, does this mean ∂x/∂Py<0?

Answer 21

No

Question 22

How do we get net substitutes and net complements?

Answer 22

• If the Net Effect (∂y/∂px| ̅u ) is positive we have net substitues
• We cannot get net complements with 2 goods as the indifference curve cannot be drawn in such a way where there is an increase in demand for good y after a fall in Px.

Question 23

Is the net effect symmetric?

Answer 23

Yes, if y is a net substitute for x, x is a net substitute for y.

Question 24

List the steps to solving the Hicksian decomposition to find the value of the income and substitution effects.

Answer 24

• Set up the Lagrangean
• Solve for First order conditions
• Solve simultaneously to find x* and y* (the Marshallian demands)
• Set out as tangency 1→ (Px,Py,m) = (n1,n2,n3)
• Work out the co-ordinates then plug into utility curve to find utility for indifference curve 1
• If price changes, work out x co-ordinates for tangency on new indifference curve (point 2)
• Work out the x co ordinates for point 3 by solving for m’
• Point 3- Point 1 = Sub Effect
• Point 2 - Point 3 = Income Effect
NB: For cross price sub or income effects use the y co-ordinate

Question 25

List the steps to identifying the change in income between budget lines in a Slutsky decomposition?

Answer 25

• Draw the relevant diagram to portray the initial price shift
• Set up equations for points 2,3 and 3. Remember the point 3 is m’ not m, as it is a new income.
• Solve simultaneously to find Py
• Substitute this to find m and m’
• The difference between the two is the change in income

Question 26

What does net surplus equal?

Answer 26

Gross surplus- what they actually paid

aka the triangle part of the trapezium

Question 27

Why is Marshallian Consumer surplus as a measure of welfare incorrect?

Answer 27

• If you maximise utility subject to a budget constraint using the Lagrangian and solve for optimising levels of the variables including the Lagrange multiplier, λ, note that as you change a price the optimising λ generally also changes.
• But λ is an approximation of the marginal utility of income – think of this as the exchange rate that converts utility to money. To be theoretically correct you need this exchange rate to consistently translate utility to money at the same rate.
• But if this exchange rate is continuously changing then the resulting measure of consumer surplus will not be correct.

Question 28

When will Consumer Surplus be a theoretically correct measure of the change in welfare of the consumer?

Answer 28

• If there is no income effect then the marginal utility of income will not change as price changes and so CS will be a theoretically correct measure of the change in welfare of the consumer.
• Note, this happens when utility is quasi-linear.

Question 29

Under a Hicksian decomposition, what are theoretically correct measures of the change in consumer welfare following a price change?

Answer 29

• The Compensating Variation

* The Equivalent Variation

Question 30

Do we write the Compensating Variation in positive or negative terms?

Answer 30

No, we use the absolute value. ie +3 or -3 = |3|

Question 31

What is the Compensating Variation?

Answer 31

CV is the change in income, following a price change, required to return the consumer to the original level of utility but at the new prices.

Question 32

What is the Equivalent Variation?

Answer 32

EV is the change in income, following a price change, required for the consumer to achieve the new utility but at old prices. It is exactly the same as the CV but for the reverse change in price.

Question 33

How do is the Slutsky Compensating Variation?

Answer 33

This is the exact same as the Hicksian, but remember we are bringing the budget line back through the original consumption bundle, rather than tangential to the utility curve.

Question 34

If 2 bundles, A and B are both affordable, but A is chosen and B is not chosen, what can we say about A in relation to B?

Answer 34

We can say that A is Directly Revealed Preferred to B.

Question 35

If a bundle A is chosen when B is affordable and B is selected when C is affordable then what can we say about A in relation to C?

Answer 35

If a bundle A is chosen when B is affordable and B is selected when C is affordable then A is IRP to C.

Question 36

What is the Weak Axiom of revealed preference?

Answer 36

If A is DRP to B and B is not the same as A then B cannot be DRP to A.

Question 37

What is the Strong Axiom of revealed preference?

Answer 37

If A is IRP or DRP to B and B is not the same as A then B cannot be DRP or IRP to A.

Question 38

What is one implication of SARP?

Answer 38

The Strong Axiom of revealed preference can be used as a test of transitivity

Question 39

What is one implication of WARP?

Answer 39

The Weak Axiom of revealed preference can be used to rule out a lot of bundles a consumer could go in when their budget line shifts