frank cowell: microeconomics revision lecture ec202 24 th march 2011 frank cowell
TRANSCRIPT
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
Revision Lecture
EC202EC202http://darp.lse.ac.uk/ec202
2424thth March 2011 March 2011Frank Cowell Frank Cowell
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
Overview...
Styles of question
Doing short questions
Revision lecture
How to see what you need to do
Doing long questions
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
Overview...
Styles of question
Doing short questions
Revision lecture
How to tackle the main types of question
Doing long questions
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
2009 1(c) Straightforward Straightforward
“principles” question“principles” question Just say what you Just say what you
need to sayneed to say
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
2010 1(a)
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
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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…
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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)
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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
Frank C
owell:
Frank C
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icroeconomics
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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!!!
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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]
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
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Ex 3.3(1) Question
purpose: to derive competitive supply function method: derive AC, MC
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owell:
Frank C
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icroeconomics
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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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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 :
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
Ex 3.3(1): Supply by a single firm
qi
p
Average cost
Marginal costSupply of output
q
Frank C
owell:
Frank C
owell: M
icroeconomics
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Ex 3.3(2) Question
purpose: to demonstrate possible absence of equilibrium method: examine discontinuity in supply relationship
Frank C
owell:
Frank C
owell: M
icroeconomics
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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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owell:
Frank C
owell: M
icroeconomics
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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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
Ex 3.3(3) Question
purpose: to demonstrate effect of averaging method: appeal to a continuity argument
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owell:
Frank C
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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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
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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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
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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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owell:
Frank C
owell: M
icroeconomics
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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)
Frank C
owell:
Frank C
owell: M
icroeconomics
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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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
Ex 3.4: spinoff – 2010 Q3
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
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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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owell:
Frank C
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icroeconomics
Microeconom
ics
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?
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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
Frank C
owell:
Frank C
owell: M
icroeconomics
Microeconom
ics
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
Frank C
owell:
Frank C
owell: M
icroeconomics
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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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owell:
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owell: M
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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
Frank C
owell:
Frank C
owell: M
icroeconomics
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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