CCT3- Slutsky Equation, Hicksian Demand, Consumer Welfare + Revealed Preferences Flashcards
What does the Slutsky equation do?
It breaks down the price effect into two different parts, the income effect and the substitution effect.
Which two versions are there of the Slutsky decomposition?
- The Hicksian
* The Slutsky
Which is the theoretically correct method for breaking down the price effect?
The Hicksian
Is the Hicksian empirically useful, why?
Often it is not, it focuses on bringing a budget constraint back to an indifference curve, and indifference curves aren’t typically observable.
What is a Slutsky decomposition an approximation of?
The Slutsky decomposition is an approximation of the “correct” Hicksian decomposition.
So why is the Slutsky equation often more useful, but what is this dependant on?
- As it is based on observable effects
* The price effects being fairly small
What is the Hicksian decomposition equation for own effects?
∂x/∂px = ∂x/∂px| ̅u -(∂x/∂m)x
where | ̅u means keeping utility constant
Which part of the Hicksian gives the SE and which gives the IE?
- ∂x/∂px| ̅u represents the SE
* (∂x/∂m)x represents the IE.
Under a Hicksian decomposition, will be income and substitution effects the positive or negative?
- 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.
What is the difference between normal and inferior goods?
When people’s income rises
• Demand for inferior goods will fall
• Demand for normal goods will rise.
What is the difference between the Hicksian Demand and Marshallian demand?
Marshallian Demand focuses on the whole price effect, whereas Hicksian demand only focuses on the substitution effect, as it is a compensated demand curve.
What is the Hicksian demand curve sometimes known as?
The compensated demand curve
The Hicksian decomposition keeps utility constant. What does the Slutsky decomposition keep constant?
The Slutsky decomposition keeps income constant.
What does the compensation do differently to the budget line in the Slutsky decomposition than the Hicksian decomposition?
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.
Does the Slutsky decomposition also exclude the income effect, as the Hicksian decomposition does?
Yes
What is the Hicksian decomposition equation for cross-price effects?
∂y/∂px = ∂y/∂px| ̅u -(∂x/∂m)y
where | ̅u means keeping utility constant
What is the Gross Effect?
• ∂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.
What does it mean if the Gross Effect is positive or negative?
- 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.
What is an independant good?
Where there is no gross effect, aka both tangencies are at the same height.
What kind of goods do Cobb-Douglas utility functions yield?
Independent goods
If ∂y/∂Px<0, does this mean ∂x/∂Py<0?
No
How do we get net substitutes and net complements?
- 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.
Is the net effect symmetric?
Yes, if y is a net substitute for x, x is a net substitute for y.
List the steps to solving the Hicksian decomposition to find the value of the income and substitution effects.
• 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
List the steps to identifying the change in income between budget lines in a Slutsky decomposition?
- 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
What does net surplus equal?
Gross surplus- what they actually paid
aka the triangle part of the trapezium
Why is Marshallian Consumer surplus as a measure of welfare incorrect?
- 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.
When will Consumer Surplus be a theoretically correct measure of the change in welfare of the consumer?
- 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.
Under a Hicksian decomposition, what are theoretically correct measures of the change in consumer welfare following a price change?
- The Compensating Variation
* The Equivalent Variation
Do we write the Compensating Variation in positive or negative terms?
No, we use the absolute value. ie +3 or -3 = |3|
What is the Compensating Variation?
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.
What is the Equivalent Variation?
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.
How do is the Slutsky Compensating Variation?
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.
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?
We can say that A is Directly Revealed Preferred to B.
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?
If a bundle A is chosen when B is affordable and B is selected when C is affordable then A is IRP to C.
What is the Weak Axiom of revealed preference?
If A is DRP to B and B is not the same as A then B cannot be DRP to A.
What is the Strong Axiom of revealed preference?
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.
What is one implication of SARP?
The Strong Axiom of revealed preference can be used as a test of transitivity
What is one implication of WARP?
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
