Revision Lecture

Report
REVISION LECTURE
EC202
http://darp.lse.ac.uk/ec202
1st May 2014
Frank Cowell
May 2014
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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)
• 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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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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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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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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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 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
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Overview...
Revision lecture
A problem about price
control
Styles of
question
Doing short
questions
Doing long
questions
May 2014
•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*
1ℓ
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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1ℓ
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 2014
•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 2014
•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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pa
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 q1
price = MC = price ceiling
c**
q1
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q**
q0
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 q2
c**
q**
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q2
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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