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REVISION LECTURE
EC202
http://darp.lse.ac.uk/ec202
9th May 2013
Frank Cowell
May 2013
Frank Cowell: EC202 Revision Lecture
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Overview...
Revision lecture
How to see what you
need to do
Styles of
question
Doing short
questions
Doing long
questions
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Objectives of the lecture
A look back at Term 1
Exam preparation
Reference materials used (1)
• Exam papers (and outline answers)
• 2008 1(b)
• 2009 1(c)
• 2010 1(a)
• 2011 1(a), 3
• 2012 4
Reference materials used (2)
• CfD presentations 3.4, 5.7
• Related to past exam questions
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The exam paper
Scope of exam material
• what’s covered in the lectures…
• … is definitive for the exam
Structure and format of paper
• same as that of last two years
• (there was a change from 2010 to 2011)
• only 3 long questions in each of parts B and C
Mark scheme
• 40 marks for question 1 (8 marks for each of the five parts)
• 20 marks for each of the other three questions
• multipart questions: marks per part shown on the exam paper
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Question style – three types
1 Principles
• reason on standard results and arguments
• can use verbal and/or mathematical reasoning
2 Model solving
• a standard framework
• you just turn the wheels
3 Model building
• usually get guidance in the question
• longer question sometimes easier?
Examples from
past question 1
One type not necessarily “easier” or “harder” than another
• part A (question 1) usually gets you to do both types 1 and 2
• type 3 is usually only in parts B and C of paper
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Overview...
Revision lecture
How to tackle the main
types of question
Styles of
question
Doing short
questions
Doing long
questions
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2009 1(c)
Straightforward
“principles” question
Just say what you
need to say
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2010 1(a)
Straight “principles”
Be sure to read the question carefully
Be sure to give your reasons
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2010 1(a)
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2011 1(a)
A simple model
Be sure to draw a
diagram…
…and think
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2011 1(a)
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2008 1(b)
Principles and model-solving
Write down the principle
Write down the basics of the model
WARP can be stated simply in terms of “affordability”
To check whether week 2’s bundle can be afforded at week 1’s prices
(etc. etc.) we need to write down the costs
Check the on-line answers for the (short) detailed reasoning…
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2011 3
Stating principles can come up in long questions
Don’t ignore them in a rush to get to the model!
There are sometimes easy marks just writing down the definition…
…and then you can apply it to the problem
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Overview...
Revision lecture
How to do well in
exams
Styles of
question
Doing short
questions
Doing long
questions
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Planning Answers
What’s the point?
• take a moment or two...
• …make notes to yourself
• what is the main point of the question?
• and the subpoints?
See the big picture
• balance out the answer
• imagine that you’re drawing a picture
• if pressed for time, don’t rush to put in extra detail…
• …you can go back
Be an economist with your own time
• don’t solve things twice!
• reuse results
• answer the right number of questions!!!
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Tips
Follow the leads
• examiners may be on your side!
• so if you’re pointed in the right direction, follow it…
Pix
• help you to see the solution
• help you to explain your solution to examiner
What should the answer be?
• take a moment before each part of the question
• check the “shape” of the problem
• use your intuition
Does it make sense?
• again take a moment to check after each part
• we all make silly slips
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Long questions
Let’s look at examples
• taken from exercises in the book
• but of “exam type” difficulty
• covered in CfD
Illustrates two types of question
• Ex 3.4, 5.7 is straight model solving
• 2012 Q4 incorporates some model building
Look out for tips
• use pictures to clarify solution
• following hints inEx 3.4
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Overview...
Revision lecture
A problem about price
control
Styles of
question
Doing short
questions
Doing long
questions
May 2013
•Preparing and planning
•CfD 5.7
•2012 Q4
•CfD 3.4
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Ex 5.7: Question
purpose: Illustration of labour supply model with very simple
preferences
method: Consumer optimisation with endogenous budget constraint
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Ex 5.7: Worker’s problem
Basic constraints on worker are
• x is consumption
• `y is non-labour income
• w is wage rate
• ℓ is labour supply
Worker’s problem can therefore be written as
• found by substituting from above into utility function
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Ex 5.7: Worker’s optimum
Take log of maximand to get
• a log(wℓ +`y) + [1 a] log(1 ℓ)
Differentiate with respect to ℓ
This is zero if
• wℓ + aw + [a 1]`y = 0
• which implies ℓ = a + [a 1]`y / w
But this only makes sense if ℓ is non-negative
• requires w ≥ [1 a]`y / a
• so optimal labour supply is
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Ex 5.7: Interior maximum
(leisure, consumption)-space
x
Max value of leisure
Indifference curves
Non-labour income
Budget constraint
Optimum
w ≥ [1 a]`y / a
0 < ℓ* < 1
slope = w
`y
0
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1
ℓ*
1ℓ
1
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Ex 5.7: Corner solution
Indifference curves as before
x
Non-labour income
Budget constraint
Optimum
w < [1 a]`y / a
ℓ* = 0
•`y
0
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1ℓ
1
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Ex 5.7: Points to note
Treat leisure as a conventional good
Has a natural upper bound
• where labour is zero
Have to allow for corner solution
• where person chooses not to work
Type of equilibrium depends on
• wage rate
• non-labour income
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Overview...
Revision lecture
Modelling choice
under uncertainty
Styles of
question
Doing short
questions
Doing long
questions
May 2013
•Preparing and planning
•CfD 5.7
•2012 Q4
•CfD 3.4
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2012 Q4 (a)
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2012 Q4 (b)
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2012 Q4 (c)…
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…2012 Q4 (c)
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2012 Q4 (d)
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2012 Q4 (e)
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2012 Q4 (f)
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2012 Q4 assessment
It seems like a long question
• broken into digestible pieces
• makes model-building easier
• shows you exactly what to do, stage by stage
• important message….
“long” “difficult”
Core of problem involves elementary things
• carefully specify budget constraint in each part of the Q
• plug into simple utility function
• use FOC to get result
• applies to parts (b)—(e)
Finishing off
• final part just involves simple differentiation of the solution
• don’t forget the “explain why” in part (e)
• see also Ex 8.12
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Overview...
Revision lecture
Modelling choice
under uncertainty
Styles of
question
Doing short
questions
Doing long
questions
May 2013
•Preparing and planning
•CfD 5.7
•2012 Q4
•CfD 3.4
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Ex 3.4(1) Question
purpose: to derive competitive supply function
method: derive AC, MC
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Ex 3.4(1) Costs
Integrate MC to get total cost
Divide by q to get average costs
Differentiate to find minimum AC at
Average costs at this point are
If price is above this level find
equilibrium where price = MC:
Solving this we get
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Ex 3.4(1): Firm’s supply curve
Average cost
Marginal cost
Supply of output
a+bq
Relation between price & output
p
F0/q+a+0.5bq
q
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pa
q*= ——
b
q
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Ex 3.4(2) Question
purpose: to derive monopolist’s solution
method: derive AR, MR
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Ex 3.4(2) Monopolist’s equilibrium
Given the demand curve total revenue is Aq ½Bq2
So, MR is
Monopolist’s FOC (MR=MC)
Solving for q we get
And from this we have
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P
Ex 3.4(2): Monopoly output and price
AC and MC curves
Demand (average revenue)
Marginal revenue
a+bq
Profit-maximising output
MC and price at q**
p**
F0/q+a+0.5bq
c**
A 0.5bq
A bq
q**
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q
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Ex 3.4(3) Question
purpose: to derive modified monopoly solution
method: derive modified AR, MR – watch for discontinuity!
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Ex 3.4(3) Regulated monopolist
Price ceiling alters the effective demand curve
So AR is now:
Multiply by q and then differentiate to get MR:
MR is discontinuous, exactly where AR is kinked
Effect of price ceiling depends on position of MC relative to
this discontinuity
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Ex 3.4(3): High price ceiling
AC and MC curves
Demand (average revenue)
Marginal revenue
Profit-maximising output
MC and price at q**
p**
high ceiling: no effect
on equilibrium
c**
q**
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q
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Ex 3.4(3): Low price ceiling
AC and MC curves
Demand (average revenue)
Marginal revenue
Profit-maximising output
p**
Low ceiling : equilibrium
at reduced output q0
price = MC = price ceiling
c**
q0
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q**
q
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Ex 3.4(3): Medium price ceiling (i)
AC and MC curves
Demand (average revenue)
Marginal revenue
Profit-maximising output
p**
Medium ceiling : eqm
at increased output q0
c**
q**
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q0
q
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Ex 3.4(3): Medium price ceiling (ii)
AC and MC curves
Demand (average revenue)
Marginal revenue
Profit-maximising output
p**
Medium ceiling: eqm at
increased output again
c**
q**
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q0
q
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Ex 3.4: Points to remember
Make good use of a diagram to “see” the problem
Re-use the solutions
• one part of the problem…
• …helps to build the next.
Don’t be fazed by the presence of a discontinuity
• everything is nice and regular either side of it.
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