EC202 http://darp.lse.ac.uk/ec202 24th March 2011 Frank Cowell Revision Lecture EC202 http://darp.lse.ac.uk/ec202 24th March 2011 Frank Cowell Aim of this lecture A look back at Term 1 Some solutions Tips on technique http://darp.lse.ac.uk/presentations/ec202/RevisionLecture_11.ppt Leila: 6674 6300 (or 7437 or 6460). A31 Audio Visual Unit DESMOND Mr George 6271 g.desmond@lse.ac.uk FLOOD Mr Ray 7694 r.flood@lse.ac.uk GALE Mr Adam 6520 a.gale@lse.ac.uk HEAD Mr Chris 6417 c.head@lse.ac.uk 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.

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

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

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

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

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

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*

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!

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

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

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…

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)

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

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!!!

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

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]

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

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

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

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 :

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

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

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

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

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

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

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

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 

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

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)

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 

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

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

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

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

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)

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?

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

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

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

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

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

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

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

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