Term 1 week 2 Flashcards
What is the Expenditure Minimisation problem and what does it yield?
EMP is minimising expenditure S.T given level of utility
-solving for x yields hicksean demands./ called compensated demands.
How are we dealing graphically with the EMP?
You have an IC and need to reach it with lowest BC.
How do you set up the Lagrange for EMP?
First you outline min budget constraint S.T given level of utility
Budget Constraint + theta ( U - function)
Then solve for FOC and get
1
2
3
Merge 1 and 2
Then plug this into 3 and solve for x1 and x2
How do we get the expenditure function?
What is the expenditure function a function of?
You get the hicksean demands and you plug them into the budget constraint.
E(p1,p2,u)
What are the properties of the expenditure function?
-e(p,u) is continuous in prices and utility
-Strictly increasing in prices and utility taking derivative of Expenditure function proves this.
-Homogenous of degree 1 in just prices, if you multiply all prices by same factor then expenditure increases by same factor. (UTILITY DOES NOT CHANGE)
-Expenditure function is concave in prices.
-Using Sheperd’s Lemma you can retrieve Hicksean demand for that good
What is Shepherd’s lemma?
if expenditure function is differentiable then hicksean demand for that good can be retrieved by
de(pi,u)/dpi
What are quasi-linear preferences?
What is an example?
-Type of utility function that is non-linear in one argument and non-linear in the other.
- u(x1,x2) = f(x1) + x2
What are the indifference curves of a quasi-linear utility function?
-Draw a quasi-linear indifference curve.
-Indifference curves are vertical translates of one another.
What types of situations do quasi-linear goods represent?
What do they depend on?
When one goods takes up a small portion of income and then all other goods
The non-linear function, is the small portion of income
The linear function is the all other goods.
non-linear is independent of income
linear is dependent of income
What is the MRS of quasi-linear goods and what implication does this have?
-MRS of quasilinear goods is only made up of non-linear good
-This means indifference curves are downward sloping and touching the y axis.
-Furthermore, for each value of x1 irrespective of x2 the slope of ICs is always the same.
-You have diminishing MRS which gives downwards sloping MRS.
Why do quasi-linear indifference curves touch the vertical axis but only tend towards the vertical axis?
They touch vertical because:
as x1 tends towards 0 —- MRS tends towards infinity which is vertical
And as x1 tends to infinity —— MRS tends towards 0.
What is the income implication of quasi-linear preferences?
- You will only demand goods if income is above certain threshold
-There is no income effect under a certain threshold.
