ES20011 Whole group problems - 2
1. Compute the MRS for the following utility functions
1
1
(i) U(x, y) = x 2 y 2
3
1
(ii) U (x, y) = x 4 y 4
1
1
(iii) U (x, y) = (x 2 + y 2 )2
(iv)U(x, y) = ln x + ln
The SLUTSKY EQUATION
Duality tells us that (see slide 10 of the duality slides)
x(U , Px , Py ) = x( M , Px , Py )
Differentiating this with respect to Px gives us:
x(U , Px , Py )
Px
=
x( M , Px ,
The Marshallian, Hicksian
and Slutsky Demand
Curves
Graphical Derivation
1
An aside: before we look at how price changes affect demand
we should look at how income changes affect the demand for
a good
ES20011 Problem Set 5 (for completion by end of week 9)
1.
(a) Explain attitude towards risk using a utility function U (c) = c.
(b) How can revealed preference analysis help us learn about an individ
ES20011 Problem Set 4 (for completion by end of week 7)
1. Suppose a consumers preferences are represented by the following utility function
U (x, y ) =
x + b y,
where b > 0, and faces a budget constr
ES20011 Problem Set 3 (for completion by end of week 5)
1. An individual has a utility function dened over two goods
1
1
U (C1 , C2 ) = C12 + C22
and faces a budget constraint
Pc1 C1 + Pc2 C2 = M,
whe
ES20011 Problem Set 2 (for completion by end of week 3)
1.
An individual has income M. Clearly marking the intercepts, draw the individuals budget
constraint in (x, y ) space when
(i)Px = Py = 1.
(ii)
ES20011: Coursework 1 to be completed by end of week 1
1. An individual has income . Draw their budget curves in ( ) space when
(i) = = 1
(ii) = 1 = 05
(iii) = 1 = 05 and the individual is prevented f
A couple of examples of production type questions.
1. A competitive industry consists of 1000 identical rms, each with a production technology
given by
1
1
q (K, L) = 6K 2 L 2
where K and L represent
d)
Questions for decision-making under uncertainty wholegroup session
1. Suppose a houseowner has a house worth £250,000 faces a 5% chance in any given
year that there will be a ood, in which case,
Production
Technology: y = f (x)
1
y=f(x)
y
Production set
x
2
Technology: y = f (x1, x2, x3, . xn)
For simplicity consider the case of 2 inputs
e.g. labour and capital, L and K
y = f (K, L)
3
y
y
The Effect of Taxation:
an application of
Expected Utility Approach
in the context of investment
Suppose Consumer has some wealth
She can invest an amount
in a risky asset with
returns rg (>0) in good
Mean-Variance Analysis
an alternative approach to the
Expected Utility Approach
Suppose W = 100 and bet 50
on flip of a coin
Probability
0.5
Outcomes
50
150
EU=0.5U(50) + 0.5 U(150)
More outcomes =>
Choice
under
Uncertainty
1
Note that were maximising utility before we
know what the circumstances will be
were maximising ex-ante welfare
which does not necessarily mean that ex-post
welfare is actua
Intertemporal Choice
What if we allow consumers consume at different
points in time?
We can still deal with this problem by thinking of
each good at each point in time as a separate
commodity.
This
Consumer Surplus
- attaches a monetary measure to changes in welfare
resulting from some policy change (e.g. change in tax
rate)
- 2 questions we could ask:
- How much are you willing to pay for a pri
Revealed Preference Approach
Rather than go from preferences to demand, can
we get from demand to the underlying
preferences?
This approach is based on the simple idea that if
we choose bundle q1 wh
ES20011 Whole group problems
1
1. If Q 200P 2 what is the price elasticity of demand, QP ?
2. If Q 400 10P
(i) what is the price elasticity of demand, QP at P 30 and P 10?
(ii) at what price is the pr
Duality
Instead of maximising utility subject to a
budget constraint (UMP), we could
minimise the cost of achieving a certain
level of utility (CMP)
1
So, instead of
1
Max U = x 2 y
1
2
s.t. Px x + Py
Choice: solving for x and y
Now we are ready to combine preferences
with the budget constraint to determine the
consumers optimal bundle
1
y
optimal bundle is where
the slopes are equal
x
2
So, we can
Preferences
Now we look at the other determinant of
consumer choice preferences.
Axioms of consumer choice utility
functions
Once we have a utility function we can
maximise this function subject to a
Relationship between the
indifference curve & utility
function
1
Note that restrictions on preferences will
impose restrictions on the utility function
Monotonicity of preferences implies that if
x1 >
ES20011 Intermediate
Microeconomics
- Introduction
This course sits best between ES10005 and ES20012
These slides are based on notes originally devised by Dr. Cillian Ryan
Key elements include:
Constr
ES20013
Intermediate Macroeconomics 1
Topic 5
Aggregate supply
Based on Gartner chapter 6
Plan of the lecture
1. Meaning of potential output.
2. Wages and unemployment determination in the
labour mark
ES20013
Intermediate Macroeconomics 1
Topic 5
Aggregate supply
Based on Gartner chapter 6
Plan of the lecture
1. Meaning of potenCal output.
2. Wages and unemployment