Frank Cowell: EC202 Revision Lecture REVISION LECTURE EC202 26 th April 2012 Frank Cowell April 2012 1.

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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