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Revision Lecture

EC202EC202http://darp.lse.ac.uk/ec202

2424thth March 2011 March 2011Frank Cowell Frank Cowell

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Overview...

Styles of question

Doing short questions

Revision lecture

How to see what you need to do

Doing long questions

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Objectives of the lecture

A look back at Term 1A look back at Term 1 Exam preparationExam preparation Reference materials used (1)Reference materials used (1)

Exam papers (and outline answers)Exam papers (and outline answers) 2006 1(a), 4 2006 1(a), 4 2008 1(b) 2008 1(b) 2009 1(c) 2009 1(c) 2010 1(a), 3, 5 2010 1(a), 3, 5

Reference materials used (2) Reference materials used (2) CfD presentations CfD presentations 3.3, 8.123.3, 8.12 Related to past exam questionsRelated to past exam questions CfD now available on the web siteCfD now available on the web site

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The exam paper

Scope of exam materialScope of exam material what’s covered in the lectures…what’s covered in the lectures… … … is definitive for the examis definitive for the exam

Structure and format of paperStructure and format of paper similar to that of last five yearssimilar to that of last five years rubric changed from last year’s paperrubric changed from last year’s paper now only 3 long questions in each of parts B and Cnow only 3 long questions in each of parts B and C

Mark schemeMark scheme 40 marks for question 1 (8 marks for each of the five parts)40 marks for question 1 (8 marks for each of the five parts) 20 marks for each of the other three questions20 marks for each of the other three questions multipart questions: marks per part shown on the exam paper multipart questions: marks per part shown on the exam paper

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Question style – three types

1 Principles1 Principles reason on standard results and argumentsreason on standard results and arguments can use verbal and/or mathematical reasoningcan use verbal and/or mathematical reasoning

2 Model solving2 Model solving a standard frameworka standard framework you just turn the wheelsyou just turn the wheels

3 Model building3 Model building usually get guidance in the questionusually get guidance in the question longer question sometimes easier?longer question sometimes easier?

One type not necessarily “easier” or “harder” than another One type not necessarily “easier” or “harder” than another part A (question 1) usually gets you to do both types 1 and 2part A (question 1) usually gets you to do both types 1 and 2 type 3 is usually only in parts B and C of papertype 3 is usually only in parts B and C of paper

Examples from past question 1

Examples from past question 1

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Overview...

Styles of question

Doing short questions

Revision lecture

How to tackle the main types of question

Doing long questions

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2009 1(c) Straightforward Straightforward

“principles” question“principles” question Just say what you Just say what you

need to sayneed to say

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2010 1(a)

Straight “principles”Straight “principles” Be sure to read the question carefullyBe sure to read the question carefully Be sure to Be sure to give your reasonsgive your reasons

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2010 1(a)

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2006 1(a) Principles againPrinciples again But format of question But format of question

gives you a hint…gives you a hint… ……write out write out

decomposition formuladecomposition formula Then read off resultsThen read off results

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2008 1(b) Principles and model-solving Principles and model-solving Write down the principle Write down the principle Write down the basics of the modelWrite down the basics of the model

WARP can be stated simply in terms of “affordability” WARP can be stated simply in terms of “affordability” To check whether week 2’s bundle can be afforded at week 1’s To check whether week 2’s bundle can be afforded at week 1’s

prices (etc. etc.) we need to write down the costsprices (etc. etc.) we need to write down the costs Check the on-line answers for the (short) detailed reasoning…Check the on-line answers for the (short) detailed reasoning…

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2006 4 Straight principles can come up in long questionsStraight principles can come up in long questions Don’t ignore them in a rush to get to the model!Don’t ignore them in a rush to get to the model!

Compare this with CfD 8.12Compare this with CfD 8.12 CfD (from book) doesn’t have this bit, but take it seriouslyCfD (from book) doesn’t have this bit, but take it seriously There are some easy marks just writing down the definition…There are some easy marks just writing down the definition… ……and the diagram helps you to answer part (b)and the diagram helps you to answer part (b)

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Overview...

Styles of question

Doing short questions

Doing long questions

Revision lecture

How to do well in exams

•Preparing and planning•CfD 3.3•CfD 8.12

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Planning Answers What’s the point?What’s the point?

take a moment or two..take a moment or two.. ……make notes to yourself make notes to yourself what is the what is the main pointmain point of the question? of the question? and the subpoints?and the subpoints?

See the big pictureSee the big picture balance out the answerbalance out the answer imagine that you’re drawing a pictureimagine that you’re drawing a picture if pressed for time, don’t rush to put in extra detail…if pressed for time, don’t rush to put in extra detail… ……you can go backyou can go back

Be an economist with your own timeBe an economist with your own time don’t solve things twice!don’t solve things twice! reuse resultsreuse results answer the right number of questions!!!answer the right number of questions!!!

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Tips Follow the leadsFollow the leads

examiners may be on your side!examiners may be on your side! so if you’re pointed in the right direction, follow it…so if you’re pointed in the right direction, follow it…

PixPix help you to see the solutionhelp you to see the solution help you to explain your solution to examinerhelp you to explain your solution to examiner

What What shouldshould the answer be? the answer be? take a moment before each part of the questiontake a moment before each part of the question check the “shape” of the problemcheck the “shape” of the problem use your intuitionuse your intuition

Does it make sense?Does it make sense? again take a moment to check after each partagain take a moment to check after each part we we allall make silly slips make silly slips

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Long questions Let’s look at two examples Let’s look at two examples

taken from exercises in the booktaken from exercises in the book but of “exam type” difficultybut of “exam type” difficulty covered in CfDcovered in CfD

Illustrates two types of questionIllustrates two types of question Ex 3.3 is straight model solvingEx 3.3 is straight model solving Ex 8.12 incorporates some model buildingEx 8.12 incorporates some model building

Look out for tipsLook out for tips In all both questions, use pictures to clarify solutionIn all both questions, use pictures to clarify solution following hints in 3.3 [The “Explain carefully…” bits]following hints in 3.3 [The “Explain carefully…” bits]

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Overview...

Styles of question

Doing short questions

Doing long questions

Revision lecture

A problem with discontinuous supply…

•Preparing and planning•CfD 3.3•CfD 8.12

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Ex 3.3(1) Question

purpose: to derive competitive supply function method: derive AC, MC

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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

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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 :

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Ex 3.3(1): Supply by a single firm

qi

p

Average cost

Marginal costSupply of output

q

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Ex 3.3(2) Question

purpose: to demonstrate possible absence of equilibrium method: examine discontinuity in supply relationship

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Ex 3.3(2): Equilibrium?

AC

MC

qi

p

AC,MC and supply of firm

Demand, low value of b

Demand, high value of b

Supply

(one firm)

Solution for high value of b is where Supply = Demand

Demand, med value of b

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Ex 3.3(2) Equilibrium

Outcome for supply by a single price-taking firm1. High demand: unique equilibrium on upper part of supply curve

2. Low demand: equilibrium with zero output

3. 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

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Ex 3.3(3) Question

purpose: to demonstrate effect of averaging method: appeal to a continuity argument

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Ex 3.3(3) Average supply, N firms

Define average output

Set of possible values for average output:

Therefore the average supply function is

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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

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Ex 3.3(3): Average supply by N firms

p

Average cost (for each firm)

Marginal cost (for each firm)

Supply of output for averaged firms

q q

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Ex 3.3(4) Question

purpose: to find equilibrium in large-numbers case method: re-examine small-numbers case

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Ex 3.3(4) Equilibrium

Equilibrium depends on where demand curve is locatedcharacterise in terms of (price, average output)

High demandequilibrium is at (p, p/a) where p = aA / [a+b]

Medium demandequilibrium is at (p, [A – p]/b)equivalent to (p, q) where := a[A – p] / [bp]Achieve this with a proportion at q and 1– at 0

Low demand equilibrium is at (p, 0)

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Ex 3.3(4): Eqm (medium demand)

p

AC and MC (for each firm)Supply of output (averaged)

q

DemandEquilibrium

q*

Equilibrium achieved by mixing firms at 0 and at q

here here1 here1 here

q

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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

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Ex 3.4: spinoff – 2010 Q3

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Overview...

Styles of question

Doing short questions

Doing long questions

Revision lecture

Modelling choice under uncertainy

•Preparing and planning•CfD 3.3•CfD 8.12

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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

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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)

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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?

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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

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Ex 8.12(2): Question

Method Standard optimisation Differentiate expected utility with respect to t

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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

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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

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Ex 8.12(3): response of t* to y0

Differentiate the following with respect to y0:

This yields:

On rearranging we get:

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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

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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

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Ex 8.12 spinoff : 2010 Q5