1. Frank Cowell: EC202 Revision Lecture REVISION LECTURE EC202 http://darp.lse.ac.uk/ec202 26 th April 2012 Frank Cowell April 2012 1

2. 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 2012 2

3. 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) 2008 1(b) 2009 1(c) 2010 1(a), 5 2011 1(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 2012 3

4. 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 2012 4

5. 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 2012 5

6. 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 2012 6

7. Frank Cowell: EC202 Revision Lecture 2009 1(c)  Straightforward “principles” question  Just say what you need to say April 2012 7

8. Frank Cowell: EC202 Revision Lecture 2010 1(a)  Straight “principles”  Be sure to read the question carefully  Be sure to give your reasons April 2012 8

9. Frank Cowell: EC202 Revision Lecture 2010 1(a) April 2012 9

10. Frank Cowell: EC202 Revision Lecture 2011 1(a)  A simple model  Be sure to draw a diagram…  …and think April 2012 10

11. Frank Cowell: EC202 Revision Lecture 2011 1(a) April 2012 11

12. Frank Cowell: EC202 Revision Lecture 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… April 2012 12

13. Frank Cowell: EC202 Revision Lecture 2011 3  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 2012 13

14. Frank Cowell: EC202 Revision Lecture Overview... Styles of question Doing short questions Doing long questions Revision lecture How to do well in exams April 2012 14

15. 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 2012 15

16. 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 2012 16

17. 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 2012 17

18. Frank Cowell: EC202 Revision Lecture Overview... Styles of question Doing short questions Doing long questions Revision lecture A problem about price control April 2012 18 Preparing and planning CfD 3.4 2010 Q5 and CfD 8.12

19. Frank Cowell: EC202 Revision Lecture Ex 3.4(1) Question  purpose: to derive competitive supply function  method: derive AC, MC

20. 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

21. 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

22. Frank Cowell: EC202 Revision Lecture Ex 3.4(2) Question  purpose: to derive monopolist’s solution  method: derive AR, MR

23. 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

24. 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**

25. Frank Cowell: EC202 Revision Lecture Ex 3.4(3) Question  purpose: to derive modified monopoly solution  method: derive modified AR, MR – watch for discontinuity!

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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.

32. Frank Cowell: EC202 Revision Lecture Overview... Styles of question Doing short questions Doing long questions Revision lecture Modelling choice under uncertainty April 2012 32 Preparing and planning CfD 3.4 2010 Q5 and CfD 8.12

33. Frank Cowell: EC202 Revision Lecture 2010 Q5 (a) April 2012 33

34. Frank Cowell: EC202 Revision Lecture 2010 Q5 (b) April 2012 34

35. Frank Cowell: EC202 Revision Lecture 2010 Q5 (c) April 2012 35

36. Frank Cowell: EC202 Revision Lecture 2010 Q5 (d) [partial] April 2012 36

37. 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 2012 37

38. 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 2012 38

39. 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 2012 39

40. 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 2012 40

41. Frank Cowell: EC202 Revision Lecture Ex 8.12(2): Question Method Standard optimisation Differentiate expected utility with respect to t April 2012 41

42. 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 2012 42

43. 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 2012 43

44. 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 2012 44

45. 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 2012 45

46. 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 2012 46