1. EC202 http://darp.lse.ac.uk/ec202 24th March 2011 Frank Cowell
Revision Lecture
EC202
24th March 2011
Frank Cowell
Aim of this lecture
A look back at Term 1
Some solutions
Tips on technique
Leila: 6674
6300 (or 7437 or 6460). A31 Audio Visual Unit
DESMOND Mr George 6271
FLOOD Mr Ray 7694
GALE Mr Adam 6520
HEAD Mr Chris 6417
Microphone safe: 0000# Put mic back once finished. Ensure that you have pressed the 'on' button for the radio mic and that the 'Mute' button isn't on.

2. Overview... How to see what you need to do Revision lecture
Styles of question
How to see what you need to do
Doing short questions
Doing long questions

3. Objectives of the lecture
A look back at Term 1
Exam preparation
Reference materials used (1)
Exam papers (and outline answers)
2006 1(a), 4
2008 1(b)
2009 1(c)
2010 1(a), 3, 5
Reference materials used (2)
CfD presentations 3.3, 8.12
Related to past exam questions
CfD now available on the web site
Check out and use the resources on the web

4. The exam paper Scope of exam material Structure and format of paper
what’s covered in the lectures…
… is definitive for the exam
Structure and format of paper
similar to that of last five years
rubric changed from last year’s paper
now 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
Change in format as announced

5. 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

6. Overview... How to tackle the main types of question Revision lecture
Styles of question
How to tackle the main types of question
Doing short questions
Doing these right can get you quite a lot of marks in a short time
Remember: 8 marks per question!
Doing long questions

7. 2009 1(c) Straightforward “principles” question
Just say what you need to say
Use recent papers constructively.
Don’t just find out the solutions
Study the *method*

8. 2010 1(a) Straight “principles” Be sure to read the question carefully
Be sure to give your reasons
There’s no special merit in last year’s paper!

9. 2010 1(a) Notice how very short the core of the answer is
Notice how short a complete answer is

10. 2006 1(a) Principles again But format of question gives you a hint…
…write out decomposition formula
Then read off results

11. 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…

12. 2006 4 Straight principles can come up in long questions
Don’t ignore them in a rush to get to the model!
Compare this with CfD 8.12
CfD (from book) doesn’t have this bit, but take it seriously
There are some easy marks just writing down the definition…
…and the diagram helps you to answer part (b)

13. Overview... How to do well in exams Revision lecture
Styles of question
How to do well in exams
Doing short questions
First look at overall strategy, before and during exam
Then look at a couple of case studies
Doing long questions
Preparing and planning
CfD 3.3
CfD 8.12 13

14. Planning Answers What’s the point? See the big picture
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!!!

15. Tips Follow the leads Pix What should the answer be?
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
Shape – is the problem like another one that you know?
Very often you can get the form of the solution as the spinoff from another problem

16. Long questions Let’s look at two examples
taken from exercises in the book
but of “exam type” difficulty
covered in CfD
Illustrates two types of question
Ex 3.3 is straight model solving
Ex 8.12 incorporates some model building
Look out for tips
In all both questions, use pictures to clarify solution
following hints in 3.3 [The “Explain carefully…” bits]

17. Overview... A problem with discontinuous supply… Revision lecture
Styles of question
A problem with discontinuous supply…
Doing short questions
Doing long questions
Preparing and planning
CfD 3.3
CfD 8.12 17

18. Ex 3.3(1) Question purpose: to derive competitive supply function
method: derive AC, MC

19. Ex 3.3(1) Costs Total cost is: F0 + ½ aqi2 Marginal cost: aqi
Average cost: F0/qi + ½ aqi
Therefore MC intersects AC where:
This is at output level q where:
At this point AC is at a minimum p where:
For q below q there is IRTS and vice versa

20. Ex 3.3(1) Supply
If p > p the firm supplies an amount of output such that
p = MC
If p < p the firm supplies zero output
otherwise the firm would make a loss
If p = p the firm is indifferent between supplying 0 or q
in either case firm makes zero profits
To summarise the supply curve consists of :

21. Ex 3.3(1): Supply by a single firm
Average cost p
Marginal cost
Supply of output q qi

22. Ex 3.3(2) Question
purpose: to demonstrate possible absence of equilibrium
method: examine discontinuity in supply relationship

23. Ex 3.3(2): Equilibrium?  AC MC
AC,MC and supply of firm p
Demand, low value of b
Demand, med value of b
Demand, high value of b AC
Solution for high value of b is where Supply = Demand
Supply (one firm)  MC qi

24. Ex 3.3(2) Equilibrium Outcome for supply by a single price-taking firm
High demand: unique equilibrium on upper part of supply curve
Low demand: equilibrium with zero output
In between: no equilibrium
Given case 1 “Supply = Demand” implies
This implies:
But for case 1 we need p ≥ p
from the above this implies

25. Ex 3.3(3) Question purpose: to demonstrate effect of averaging
method: appeal to a continuity argument

26. Ex 3.3(3) Average supply, N firms
Define average output
Set of possible values for average output:
Therefore the average supply function is

27. Ex 3.3(3) Average supply, limit case
As N the set J(q) becomes dense in [0, q]
So, in the limit, if p = p average output can take any value in [0, q]
Therefore the average supply function is

28. Ex 3.3(3): Average supply by N firms
Average cost (for each firm) p
Marginal cost (for each firm)
Supply of output for averaged firms q q 

29. Ex 3.3(4) Question purpose: to find equilibrium in large-numbers case
method: re-examine small-numbers case

30. Ex 3.3(4) Equilibrium
Equilibrium depends on where demand curve is located
characterise in terms of (price, average output)
High demand
equilibrium is at (p, p/a) where p = aA / [a+b]
Medium demand
equilibrium is at (p, [A – p]/b)
equivalent to (p, bq) where b := a[A – p] / [bp]
Achieve this with a proportion b at q and 1–b at 0
Low demand
equilibrium is at (p, 0)

31. Ex 3.3(4): Eqm (medium demand)
AC and MC (for each firm) p
Supply of output (averaged)
Demand
Equilibrium
Equilibrium achieved by mixing firms at 0 and at q
1b here
b here q* q q 

32. Ex 3.4: Points to remember Model discontinuity carefully
Averaging may eliminate discontinuity problem in a large economy
depends whether individual agents are small.
Equilibrium in averaged model may involve identical firms doing different things
equilibrium depends on the right mixture

33. Ex 3.4: spinoff – 2010 Q3
Replace discontinuous supply function of firm…
… with discontinuous demand function of household
Equilibrium issue is the same with small numbers
The large number “averaging” solution follows in the same way

34. Overview... Modelling choice under uncertainy Revision lecture
Styles of question
Modelling choice under uncertainy
Doing short questions
Doing long questions
Preparing and planning
CfD 3.3
CfD 8.12 34

35. Ex 8.12(1): Question
purpose: to develop an analysis of insurance where terms are less than actuarially fair
method: model payoffs in each state-of-the-world under different degrees of coverage. Find optimal insurance coverage. Show how this responds to changes in wealth

36. Ex 8.12(1): model Use the two-state model (no-loss, loss)
Consider the person’s wealth in extremes
if uninsured: (y0, y0  L)
if fully insured: (y0  κ, y0  κ)
Suppose partial insurance is possible
if person insures a proportion t of loss L…
…pro-rata premium is tκ
So if a proportion t is insured wealth is
([1  t]y0 + t [y0  κ], [1  t][y0  L] + t [y0 κ])
which becomes (y0  tκ, y0  tκ + [1  t]L)

37. Ex 8.12(1): utility
Put payoffs (y0  tκ, y0  tκ + [1  t]L) into the utility function
Expected utility is
Therefore effect on utility of changing coverage is
Could there be an optimum at t =1?

38. Ex 8.12(1): full insurance?
What happens in the neighbourhood of t = 1?
We get
Simplifying, this becomes [Lπ  κ] uy(y0  κ)
positive MU of wealth implies uy(y0  κ) > 0
by assumption Lπ <κ
so [Lπ  κ] uy(y0  κ) < 0
In the neighbourhood of t =1 the individual could increase expected utility by decreasing t
Therefore will not buy full insurance

39. Ex 8.12(2): Question Method Standard optimisation
Differentiate expected utility with respect to t

40. Ex 8.12(2): optimum For an interior maximum we have
Evaluating this we get
So the optimal t∗ is the solution to this equation

41. Ex 8.12(3): Question Method Take t* as a function of the parameter y0
This function satisfies the FOC
So to get impact of y0:
Differentiate the FOC w.r.t. y0
Rearrange to get t* / y0

42. Ex 8.12(3): response of t* to y0
Differentiate the following with respect to y0:
This yields:
On rearranging we get:

43. Ex 8.12(3): implications for coverage
Response of t* to y0 is given by
The denominator of this must be negative:
uyy(⋅) is negative
all the other terms are positive
The numerator is positive if DARA holds
Therefore ∂t*/∂y0 < 0
So, given DARA, an increase in wealth reduces the demand for insurance

44. Ex 8.12: Points to remember
Identify the payoffs in each state of the world
ex-post wealth under…
…alternative assumptions about insurance coverage
Set up the maximand
expected utility
Derive FOC
Check for interior solution
Get comparative static effects from FOCs

45. Ex 8.12 spinoff : 2010 Q5 More model-building than model solving
But question shows you how to do it, step by step
Key thing is that budget constraint is different
-- status quo is where you have a safe endowment