Welfare: The Social-Welfare Functiondarp.lse.ac.uk/pdf/EC202/RevisionLecture_15.pdf · Take log of maximand to get • α log(w. ℓ + y) + [1 − α] log(1 − ℓ) Differentiate

Frank Cowell: EC202 Revision Lecture

REVISION LECTURE EC202 http://darp.lse.ac.uk/ec202 7th May 2015 Frank Cowell

May 2015 1

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


Overview...

Styles of question

Doing short questions

Doing long questions

Revision lecture

How to see what you need to do

May 2015 2


Objectives of the lecture A look back at Term 1 Exam preparation Reference materials used (1)

• Exam papers (and outline answers) • 2010 1(a) • 2011 1(a), 3 • 2012 3, 4 • 2013 1(c) • 2014 1(d)

Reference materials used (2) • CfD presentation 5.7 • Related to past exam questions

May 2015 3


The exam paper Scope of exam material

• what’s covered in the lectures… • … is definitive for the exam

Structure and format of paper • similar to previous years • 6 short questions (answer 5) • 3 long questions in each of parts B and C • answer 3 long (at least one from each of B and C)

Mark scheme • 8 marks for each short question • 20 marks for each long question • multipart questions: marks per part shown on the exam paper

May 2015 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?

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

May 2015 5


Overview...

Styles of question



Revision lecture

How to tackle the main types of question

May 2015 6


2014 1(d)

Straightforward “principles” question Just say what you need to say

• define “fairness” • describe key property of competitive equilibrium

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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

May 2015 13


Overview...

Styles of question



Revision lecture

How to do well in exams

May 2015

•Preparing and planning •2012 Q3 •CfD 5.7 •2012 Q4

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

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

May 2015 15


Tips Follow the leads

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

Pictures • 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 2015 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 • 2012 Q3 and Ex 5.7 are straight model solving • 2012 Q4 incorporates some model building

Look out for tips • use pictures to clarify solution • following hints in 2012 Q3

May 2015 17


Overview...

Styles of question



Revision lecture

Modelling choice under uncertainty

May 2015


18


2012 Q3 (a)

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2012 Q3 (a)

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For prices above min AC the FOC for max profit is:

From which optimal output is:


2012 Q3 (a)

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2012 Q3 (b)

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2012 Q3 (b)

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2012 Q3 (b)

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2012 Q3 (c)

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2012 Q3 (d, e)

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2012 Q3 − assessment

27 May 2015

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.


Overview...

Styles of question



Revision lecture

A problem about price control

May 2015 28



Ex 5.7: Question

purpose: Illustration of labour supply model with very simple preferences method: Consumer optimisation with endogenous budget constraint

May 2015 29


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 2015 30


Ex 5.7: Worker’s optimum Take log of maximand to get

• α log(wℓ +y) + [1 − α] log(1 − ℓ)

Differentiate with respect to ℓ

This is zero if • − wℓ + αw + [α − 1]y = 0 • which implies ℓ = α + [α − 1]y / w

But this only makes sense if ℓ is non-negative • requires w ≥ [1 − α]y / α • so optimal labour supply is

May 2015 31


Ex 5.7: Interior maximum (leisure, consumption)-space Max value of leisure

Non-labour income Budget constraint

x

1 − ℓ 0

Indifference curves

1

y

Optimum

1 − ℓ*

slope = w

w ≥ [1 −α]y / α 0 < ℓ* < 1

May 2015 32


Ex 5.7: Corner solution

Non-labour income

Budget constraint

x

1 − ℓ 0

Indifference curves as before

1

y

Optimum

•

w < [1 − α]y / α ℓ* = 0

May 2015 33


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 2015 34


Overview...

Styles of question



Revision lecture

Modelling choice under uncertainty

May 2015 35



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

May 2015 43

Documents

Welfare: The Social-Welfare Functiondarp.lse.ac.uk/pdf/EC202/RevisionLecture_15.pdf · Take log of maximand to get • α log(w. ℓ + y) + [1 − α] log(1 − ℓ) Differentiate