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