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Frank Cowell: EC202 Revision Lecture
REVISION LECTUREEC202http://darp.lse.ac.uk/ec202
1st May 2014Frank Cowell
May 2014 1
Frank Cowell: EC202 Revision Lecture
Overview...
Styles of question
Doing short questions
Doing long questions
Revision lecture
How to see what you need to do
May 2014 2
Frank Cowell: EC202 Revision Lecture
Objectives of the lecture A look back at Term 1 Exam preparation Reference materials used (1)
• Exam papers (and outline answers)• 2009 1(c) • 2010 1(a) • 2011 1(a), 3• 2012 4• 2013 1(c)
Reference materials used (2) • CfD presentations 3.4, 5.7• Related to past exam questions
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Frank Cowell: EC202 Revision Lecture
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 three 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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Frank Cowell: EC202 Revision Lecture
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?
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
Examples from past question 1
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Frank Cowell: EC202 Revision Lecture
Overview...
Styles of question
Doing short questions
Doing long questions
Revision lecture
How to tackle the main types of question
May 2014 6
Frank Cowell: EC202 Revision Lecture
2009 1(c)
Straightforward “principles” question
Just say what you need to say
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Frank Cowell: EC202 Revision Lecture
2010 1(a) Straight “principles” Be sure to read the question carefully Be sure to give your reasons
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Frank Cowell: EC202 Revision Lecture
2010 1(a)
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Frank Cowell: EC202 Revision Lecture
2011 1(a) A simple model Be sure to draw a
diagram… …and think
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Frank Cowell: EC202 Revision Lecture
2011 1(a)
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Frank Cowell: EC202 Revision Lecture
2013 1(c) Principles and model-solving Write down the principle Write down the basics of the model and solve
Use standard definition of expected utility and variance Define ARA Differentiate u Evaluate ARA Multiply by x to get RRA
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Frank Cowell: EC202 Revision Lecture
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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Frank Cowell: EC202 Revision Lecture
Overview...
Styles of question
Doing short questions
Doing long questions
Revision lecture
How to do well in exams
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Frank Cowell: EC202 Revision Lecture
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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Frank Cowell: EC202 Revision Lecture
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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Frank Cowell: EC202 Revision Lecture
Long questions Let’s look at examples
• taken from past papers • also from exercises in the book 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 in Ex 3.4
May 2014 17
Frank Cowell: EC202 Revision Lecture
Overview...
Styles of question
Doing short questions
Doing long questions
Revision lecture
A problem about price control
May 2014 18
•Preparing and planning•CfD 5.7•2012 Q4•CfD 3.4
Frank Cowell: EC202 Revision Lecture
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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Frank Cowell: EC202 Revision Lecture
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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Frank Cowell: EC202 Revision Lecture
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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Frank Cowell: EC202 Revision Lecture
Ex 5.7: Interior maximum(leisure, consumption)-spaceMax value of leisure
Non-labour incomeBudget constraint
x
1 ℓ0
Indifference curves
1
`y
Optimum
1 ℓ*
slope = w
w ≥ [1 a]`y / a 0 < ℓ* < 1
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Frank Cowell: EC202 Revision Lecture
Ex 5.7: Corner solution
Non-labour income
Budget constraint
x
1 ℓ0
Indifference curves as before
1
`y
Optimum
•
w < [1 a]`y / a ℓ* = 0
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Frank Cowell: EC202 Revision Lecture
Ex 5.7: Points to noteTreat leisure as a conventional goodHas a natural upper bound
• where labour is zeroHave to allow for corner solution
• where person chooses not to workType of equilibrium depends on
• wage rate• non-labour income
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Frank Cowell: EC202 Revision Lecture
Overview...
Styles of question
Doing short questions
Doing long questions
Revision lecture
Modelling choice under uncertainty
May 2014 25
•Preparing and planning•CfD 5.7•2012 Q4•CfD 3.4
Frank Cowell: EC202 Revision Lecture
2012 Q4 (a)
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Frank Cowell: EC202 Revision Lecture
2012 Q4 (b)
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Frank Cowell: EC202 Revision Lecture
2012 Q4 (c)…
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Frank Cowell: EC202 Revision Lecture
…2012 Q4 (c)
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Frank Cowell: EC202 Revision Lecture
2012 Q4 (d)
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Frank Cowell: EC202 Revision Lecture
2012 Q4 (e)
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Frank Cowell: EC202 Revision Lecture
2012 Q4 (f)
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Frank Cowell: EC202 Revision Lecture
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
May 2014 33
Frank Cowell: EC202 Revision Lecture
Overview...
Styles of question
Doing short questions
Doing long questions
Revision lecture
Modelling choice under uncertainty
May 2014 34
•Preparing and planning•CfD 5.7•2012 Q4•CfD 3.4
Frank Cowell: EC202 Revision Lecture
Ex 3.4(1) Question
purpose: to derive competitive supply function method: derive AC, MC
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Frank Cowell: EC202 Revision Lecture
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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Frank Cowell: EC202 Revision Lecture
Ex 3.4(1): Firm’s supply curve
q q
a+bq
F0/q+a+0.5bq
p a—— bq*=
p
Average costMarginal costSupply of outputRelation between price & output
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Frank Cowell: EC202 Revision Lecture
Ex 3.4(2) Question
purpose: to derive monopolist’s solution method: derive AR, MR
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Frank Cowell: EC202 Revision Lecture
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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Frank Cowell: EC202 Revision Lecture
q
Ex 3.4(2): Monopoly output and price
A 0.5bq
P
q**
p**
c**
A bq
a+bq
F0/q+a+0.5bq
AC and MC curvesDemand (average revenue)Marginal revenueProfit-maximising outputMC and price at q**
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Frank Cowell: EC202 Revision Lecture
Ex 3.4(3) Question
purpose: to derive modified monopoly solution method: derive modified AR, MR – watch for discontinuity!
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Frank Cowell: EC202 Revision Lecture
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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Frank Cowell: EC202 Revision Lecture
q
Ex 3.4(3): High price ceiling
q**
p**
c**
AC and MC curvesDemand (average revenue)Marginal revenueProfit-maximising outputMC and price at q**
high ceiling: no effect on equilibrium
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Frank Cowell: EC202 Revision Lecture
q
Ex 3.4(3): Low price ceiling
q**
p**
c**
AC and MC curvesDemand (average revenue)Marginal revenueProfit-maximising output
Low ceiling : equilibrium at reduced output q1
price = MC = price ceiling
q1
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q0
Frank Cowell: EC202 Revision Lecture
q
Ex 3.4(3): Medium price ceiling (i)
q**
p**
c**
AC and MC curvesDemand (average revenue)Marginal revenueProfit-maximising output
Medium ceiling : eqm at increased output q2
q2
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q0
Frank Cowell: EC202 Revision Lecture
q
Ex 3.4(3): Medium price ceiling (ii)
q**
p**
c**
AC and MC curvesDemand (average revenue)Marginal revenueProfit-maximising output
Medium ceiling: eqm at increased output again
q0
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Frank Cowell: EC202 Revision Lecture
Ex 3.4: Points to remember
Make good use of a diagram to “see” the problemRe-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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