Frank Cowell: EC202 Revision Lecture REVISION LECTURE EC th April 2012 Frank Cowell April
Frank Cowell: EC202 Revision Lecture Overview... Styles of question Doing short questions Doing long questions Revision lecture How to see what you need to do April
Frank Cowell: EC202 Revision Lecture Objectives of the lecture A look back at Term 1 Exam preparation Reference materials used (1) Exam papers (and outline answers) (b) (c) (a), (a), 3 Reference materials used (2) CfD presentations 3.4, 8.12 Related to past exam questions CfD now available on the web site April
Frank Cowell: EC202 Revision Lecture The exam paper Scope of exam material what’s covered in the lectures… … is definitive for the exam Structure and format of paper same as that of last year (there was a change from 2010 to 2011) 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 April
Frank Cowell: EC202 Revision Lecture 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 April
Frank Cowell: EC202 Revision Lecture Overview... Styles of question Doing short questions Doing long questions Revision lecture How to tackle the main types of question April
Frank Cowell: EC202 Revision Lecture (c) Straightforward “principles” question Just say what you need to say April
Frank Cowell: EC202 Revision Lecture (a) Straight “principles” Be sure to read the question carefully Be sure to give your reasons April
Frank Cowell: EC202 Revision Lecture (a) April
Frank Cowell: EC202 Revision Lecture (a) A simple model Be sure to draw a diagram… …and think April
Frank Cowell: EC202 Revision Lecture (a) April
Frank Cowell: EC202 Revision Lecture (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… April
Frank Cowell: EC202 Revision Lecture 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 April
Frank Cowell: EC202 Revision Lecture Overview... Styles of question Doing short questions Doing long questions Revision lecture How to do well in exams April
Frank Cowell: EC202 Revision Lecture 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… …you can go back Be an economist with your own time don’t solve things twice! reuse results answer the right number of questions!!! April
Frank Cowell: EC202 Revision Lecture Tips Follow the leads 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 April
Frank Cowell: EC202 Revision Lecture Long questions Let’s look at examples taken from exercises in the book but of “exam type” difficulty covered in CfD Illustrates two types of question Ex 3.4 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 3.4 April
Frank Cowell: EC202 Revision Lecture Overview... Styles of question Doing short questions Doing long questions Revision lecture A problem about price control April Preparing and planning CfD Q5 and CfD 8.12
Frank Cowell: EC202 Revision Lecture Ex 3.4(1) Question purpose: to derive competitive supply function method: derive AC, MC
Frank Cowell: EC202 Revision Lecture Ex 3.4(1) Costs Integrate MC to get total cost Divide by q to get average costs Differentiate to find minimum AC at Average costs at this point are If price is above this level find equilibrium where price = MC: Solving this we get
Frank Cowell: EC202 Revision Lecture Ex 3.4(1): Firm’s supply curve q q a+bq F 0 /q+a+0.5bq p a —— b q*= p Average cost Marginal cost Supply of output Relation between price & output
Frank Cowell: EC202 Revision Lecture Ex 3.4(2) Question purpose: to derive monopolist’s solution method: derive AR, MR
Frank Cowell: EC202 Revision Lecture Ex 3.4(2) Monopolist’s equilibrium Given the demand curve total revenue is Aq ½Bq 2 So, MR is Monopolist’s FOC (MR=MC) Solving for q we get And from this we have
Frank Cowell: EC202 Revision Lecture q Ex 3.4(2): Monopoly output and price A 0.5bq P q** p** c** A bq a+bq F 0 /q+a+0.5bq AC and MC curves Demand (average revenue) Marginal revenue Profit-maximising output MC and price at q**
Frank Cowell: EC202 Revision Lecture Ex 3.4(3) Question purpose: to derive modified monopoly solution method: derive modified AR, MR – watch for discontinuity!
Frank Cowell: EC202 Revision Lecture Ex 3.4(3) Regulated monopolist Price ceiling alters the effective demand curve So AR is now: Multiply by q and then differentiate to get MR: MR is discontinuous, exactly where AR is kinked Effect of price ceiling depends on position of MC relative to this discontinuity
Frank Cowell: EC202 Revision Lecture q Ex 3.4(3): High price ceiling q** p** c** AC and MC curves Demand (average revenue) Marginal revenue Profit-maximising output MC and price at q** high ceiling: no effect on equilibrium
Frank Cowell: EC202 Revision Lecture q Ex 3.4(3): Low price ceiling q** p** c** AC and MC curves Demand (average revenue) Marginal revenue Profit-maximising output Low ceiling : equilibrium at reduced output q 0 price = MC = price ceiling q0q0
Frank Cowell: EC202 Revision Lecture q Ex 3.4(3): Medium price ceiling (i) q** p** c** AC and MC curves Demand (average revenue) Marginal revenue Profit-maximising output Medium ceiling : eqm at increased output q 0 q0q0
Frank Cowell: EC202 Revision Lecture q Ex 3.4(3): Medium price ceiling (ii) q** p** c** AC and MC curves Demand (average revenue) Marginal revenue Profit-maximising output Medium ceiling: eqm at increased output again q0q0
Frank Cowell: EC202 Revision Lecture Ex 3.4: Points to remember 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.
Frank Cowell: EC202 Revision Lecture Overview... Styles of question Doing short questions Doing long questions Revision lecture Modelling choice under uncertainty April Preparing and planning CfD Q5 and CfD 8.12
Frank Cowell: EC202 Revision Lecture 2010 Q5 (a) April
Frank Cowell: EC202 Revision Lecture 2010 Q5 (b) April
Frank Cowell: EC202 Revision Lecture 2010 Q5 (c) April
Frank Cowell: EC202 Revision Lecture 2010 Q5 (d) [partial] April
Frank Cowell: EC202 Revision Lecture 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 April
Frank Cowell: EC202 Revision Lecture Ex 8.12(1): model Use the two-state model (no-loss, loss) Consider the person’s wealth in extremes if uninsured: (y 0, y 0 L) if fully insured: (y 0 κ, y 0 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]y 0 + t [y 0 κ], [1 t][y 0 L] + t [y 0 κ]) which becomes(y 0 tκ, y 0 tκ + [1 t]L) April
Frank Cowell: EC202 Revision Lecture Ex 8.12(1): utility Put payoffs (y 0 tκ, y 0 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? April
Frank Cowell: EC202 Revision Lecture Ex 8.12(1): full insurance? What happens in the neighbourhood of t = 1? We get Simplifying, this becomes [Lπ κ] u y (y 0 κ) positive MU of wealth implies u y (y 0 κ) > 0 by assumption Lπ <κ so [Lπ κ] u y (y 0 κ) < 0 In the neighbourhood of t =1 the individual could increase expected utility by decreasing t Therefore will not buy full insurance April
Frank Cowell: EC202 Revision Lecture Ex 8.12(2): Question Method Standard optimisation Differentiate expected utility with respect to t April
Frank Cowell: EC202 Revision Lecture 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 April
Frank Cowell: EC202 Revision Lecture Ex 8.12(3): Question Method Take t* as a function of the parameter y 0 This function satisfies the FOC So to get impact of y 0 : Differentiate the FOC w.r.t. y 0 Rearrange to get t* / y 0 April
Frank Cowell: EC202 Revision Lecture Ex 8.12(3): response of t * to y 0 Differentiate the following with respect to y 0 : This yields: On rearranging we get: April
Frank Cowell: EC202 Revision Lecture Ex 8.12(3): implications for coverage Response of t * to y 0 is given by The denominator of this must be negative: u yy ( ⋅ ) is negative all the other terms are positive The numerator is positive if DARA holds Therefore ∂t * /∂y 0 < 0 Given DARA increase in wealth reduces demand for insurance April
Frank Cowell: EC202 Revision Lecture 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 April