REVISION LECTURE
EC202
http://darp.lse.ac.uk/ec202
1st May 2014
Frank Cowell
May 2014
Frank Cowell: EC202 Revision Lecture
1
Overview...
Revision lecture
How to see what you
need to do
Styles of
question
Doing short
questions
Doing long
questions
May 2014
Frank Cowell: EC202 Revision Lecture
2
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
May 2014
Frank Cowell: EC202 Revision Lecture
3
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
May 2014
Frank Cowell: EC202 Revision Lecture
4
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
May 2014
Frank Cowell: EC202 Revision Lecture
5
Overview...
Revision lecture
How to tackle the main
types of question
Styles of
question
Doing short
questions
Doing long
questions
May 2014
Frank Cowell: EC202 Revision Lecture
6
2009 1(c)
 Straightforward
“principles” question
 Just say what you
need to say
May 2014
Frank Cowell: EC202 Revision Lecture
7
2010 1(a)
 Straight “principles”
 Be sure to read the question carefully
 Be sure to give your reasons
May 2014
Frank Cowell: EC202 Revision Lecture
8
2010 1(a)
May 2014
Frank Cowell: EC202 Revision Lecture
9
2011 1(a)
 A simple model
 Be sure to draw a
diagram…
 …and think
May 2014
Frank Cowell: EC202 Revision Lecture
10
2011 1(a)
May 2014
Frank Cowell: EC202 Revision Lecture
11
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
May 2014
Frank Cowell: EC202 Revision Lecture
12
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
May 2014
Frank Cowell: EC202 Revision Lecture
13
Overview...
Revision lecture
How to do well in
exams
Styles of
question
Doing short
questions
Doing long
questions
May 2014
Frank Cowell: EC202 Revision Lecture
14
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!!!
May 2014
Frank Cowell: EC202 Revision Lecture
15
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
May 2014
Frank Cowell: EC202 Revision Lecture
16
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
Frank Cowell: EC202 Revision Lecture
17
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
Frank Cowell: EC202 Revision Lecture
18
Ex 5.7: Question
 purpose: Illustration of labour supply model with very simple
preferences
 method: Consumer optimisation with endogenous budget constraint
May 2014
Frank Cowell: EC202 Revision Lecture
19
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
May 2014
Frank Cowell: EC202 Revision Lecture
20
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
May 2014
Frank Cowell: EC202 Revision Lecture
21
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
May 2014
1
ℓ*
1ℓ
1
Frank Cowell: EC202 Revision Lecture
22
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
May 2014
1ℓ
1
Frank Cowell: EC202 Revision Lecture
23
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
May 2014
Frank Cowell: EC202 Revision Lecture
24
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
Frank Cowell: EC202 Revision Lecture
25
2012 Q4 (a)
May 2014
Frank Cowell: EC202 Revision Lecture
26
2012 Q4 (b)
May 2014
Frank Cowell: EC202 Revision Lecture
27
2012 Q4 (c)…
May 2014
Frank Cowell: EC202 Revision Lecture
28
…2012 Q4 (c)
May 2014
Frank Cowell: EC202 Revision Lecture
29
2012 Q4 (d)
May 2014
Frank Cowell: EC202 Revision Lecture
30
2012 Q4 (e)
May 2014
Frank Cowell: EC202 Revision Lecture
31
2012 Q4 (f)
May 2014
Frank Cowell: EC202 Revision Lecture
32
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
Frank Cowell: EC202 Revision Lecture
33
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
Frank Cowell: EC202 Revision Lecture
34
Ex 3.4(1) Question
 purpose: to derive competitive supply function
 method: derive AC, MC
May 2014
Frank Cowell: EC202 Revision Lecture
35
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
May 2014
Frank Cowell: EC202 Revision Lecture
36
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
May 2014
pa
q*= ——
b
q
Frank Cowell: EC202 Revision Lecture
37
Ex 3.4(2) Question
 purpose: to derive monopolist’s solution
 method: derive AR, MR
May 2014
Frank Cowell: EC202 Revision Lecture
38
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
May 2014
Frank Cowell: EC202 Revision Lecture
39
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**
May 2014
q
Frank Cowell: EC202 Revision Lecture
40
Ex 3.4(3) Question
 purpose: to derive modified monopoly solution
 method: derive modified AR, MR – watch for discontinuity!
May 2014
Frank Cowell: EC202 Revision Lecture
41
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
May 2014
Frank Cowell: EC202 Revision Lecture
42
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**
May 2014
q
Frank Cowell: EC202 Revision Lecture
43
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
May 2014
q**
q0
q
Frank Cowell: EC202 Revision Lecture
44
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**
May 2014
q2
q0
q
Frank Cowell: EC202 Revision Lecture
45
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**
May 2014
q0
q
Frank Cowell: EC202 Revision Lecture
46
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.
May 2014
Frank Cowell: EC202 Revision Lecture
47