#### Transcript Extensive Form - London School of Economics

Frank Cowell: Microeconomics Revision Lecture EC202 http://darp.lse.ac.uk/ec202 24th March 2011 Frank Cowell Overview... Revision lecture Frank Cowell: Microeconomics Styles of question How to see what you need to do Doing short questions Doing long questions Objectives of the lecture Frank Cowell: Microeconomics 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 The exam paper Frank Cowell: Microeconomics Scope of exam material Structure and format of paper what’s covered in the lectures… … is definitive for the exam 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 Question style – three types Frank Cowell: Microeconomics 1 Principles 2 Model solving a standard framework you just turn the wheels 3 Model building reason on standard results and arguments can use verbal and/or mathematical reasoning usually get guidance in the question longer question sometimes easier? Examples from past question 1 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 Overview... Revision lecture Frank Cowell: Microeconomics Styles of question How to tackle the main types of question Doing short questions Doing long questions 2009 1(c) Frank Cowell: Microeconomics Straightforward “principles” question Just say what you need to say 2010 1(a) Frank Cowell: Microeconomics Straight “principles” Be sure to read the question carefully Be sure to give your reasons 2010 1(a) Frank Cowell: Microeconomics 2006 1(a) Frank Cowell: Microeconomics Principles again But format of question gives you a hint… …write out decomposition formula Then read off results 2008 1(b) Frank Cowell: Microeconomics 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 Frank Cowell: Microeconomics 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... Revision lecture Frank Cowell: Microeconomics Styles of question How to do well in exams Doing short questions Doing long questions •Preparing and planning •CfD 3.3 •CfD 8.12 Planning Answers Frank Cowell: Microeconomics 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? 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!!! Frank Cowell: Microeconomics Tips Follow the leads Pix help you to see the solution help you to explain your solution to examiner What should the answer be? examiners may be on your side! so if you’re pointed in the right direction, follow it… 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 Frank Cowell: Microeconomics Long questions Let’s look at two examples Illustrates two types of question taken from exercises in the book but of “exam type” difficulty covered in CfD 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... Revision lecture Frank Cowell: Microeconomics Styles of question A problem with discontinuous supply… Doing short questions Doing long questions •Preparing and planning •CfD 3.3 •CfD 8.12 Ex 3.3(1) Question Frank Cowell: Microeconomics purpose: to derive competitive supply function method: derive AC, MC Ex 3.3(1) Costs Frank Cowell: Microeconomics 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 Frank Cowell: Microeconomics If p > p the firm supplies an amount of output such that 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 p = MC in either case firm makes zero profits To summarise the supply curve consists of : Ex 3.3(1): Supply by a single firm Frank Cowell: Microeconomics Average cost p Marginal cost Supply of output q qi Ex 3.3(2) Question Frank Cowell: Microeconomics purpose: to demonstrate possible absence of equilibrium method: examine discontinuity in supply relationship Ex 3.3(2): Equilibrium? Frank Cowell: Microeconomics AC,MC and supply of firm p Demand, low value of b Demand, med value of b Demand, high value of b Solution for high value of b is where Supply = Demand AC MC qi Ex 3.3(2) Equilibrium Frank Cowell: Microeconomics Outcome for supply by a single price-taking firm High demand: unique equilibrium on upper part of supply curve 2. Low demand: equilibrium with zero output 3. In between: no equilibrium 1. 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 Frank Cowell: Microeconomics purpose: to demonstrate effect of averaging method: appeal to a continuity argument Ex 3.3(3) Average supply, N firms Frank Cowell: Microeconomics Define average output Set of possible values for average output: Therefore the average supply function is Ex 3.3(3) Average supply, limit case Frank Cowell: Microeconomics 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 Frank Cowell: Microeconomics Average cost (for each firm) Marginal cost (for each firm) p Supply of output for averaged firms q q Ex 3.3(4) Question Frank Cowell: Microeconomics purpose: to find equilibrium in large-numbers case method: re-examine small-numbers case Ex 3.3(4) Equilibrium Frank Cowell: Microeconomics Equilibrium depends on where demand curve is located High demand characterise in terms of (price, average output) 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) Frank Cowell: Microeconomics AC and MC (for each firm) Supply of output (averaged) Demand p Equilibrium Equilibrium achieved by mixing firms at 0 and at q b here 1b here q* q q Ex 3.4: Points to remember Frank Cowell: Microeconomics 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 Frank Cowell: Microeconomics Overview... Revision lecture Frank Cowell: Microeconomics Styles of question Modelling choice under uncertainy Doing short questions Doing long questions •Preparing and planning •CfD 3.3 •CfD 8.12 Ex 8.12(1): Question Frank Cowell: Microeconomics 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 Frank Cowell: Microeconomics Use the two-state model (no-loss, loss) Consider the person’s wealth in extremes Suppose partial insurance is possible if uninsured: (y0, y0 L) if fully insured: (y0 κ, y0 κ) 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 Frank Cowell: Microeconomics 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? Frank Cowell: Microeconomics 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 Frank Cowell: Microeconomics Method Standard optimisation Differentiate expected utility with respect to t Ex 8.12(2): optimum Frank Cowell: Microeconomics 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 Frank Cowell: Microeconomics 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 Frank Cowell: Microeconomics Differentiate the following with respect to y0: This yields: On rearranging we get: Ex 8.12(3): implications for coverage Frank Cowell: Microeconomics 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 Frank Cowell: Microeconomics Identify the payoffs in each state of the world Set up the maximand ex-post wealth under… …alternative assumptions about insurance coverage expected utility Derive FOC Check for interior solution Get comparative static effects from FOCs Ex 8.12 spinoff : 2010 Q5 Frank Cowell: Microeconomics