Revision Lecture

1. Revision Lecture EC202 http://darp.lse.ac.uk/ec202 26thApril 2012 Frank Cowell

2. Overview... Revision lecture Styles of question How to see what you need to do Doing short questions Doing long questions

3. 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

4. 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

5. 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

6. Overview... Revision lecture Styles of question How to tackle the main types of question Doing short questions Doing long questions

7. 2009 1(c) Straightforward “principles” question Just say what you need to say

8. 2010 1(a) • Straight “principles” • Be sure to read the question carefully • Be sure to give your reasons

9. 2010 1(a)

10. 2011 1(a) • A simple model • Be sure to draw a diagram… • …and think

11. 2011 1(a)

12. 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…

13. 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

14. Overview... Revision lecture Styles of question How to do well in exams Doing short questions Doing long questions

15. 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!!!

16. 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

17. 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

18. Overview... Revision lecture Styles of question A problem about price control Doing short questions Doing long questions • Preparing and planning • CfD3.4 • 2010 Q5 and CfD8.12

19. Ex 3.4(1) Question • purpose: to derive competitive supply function • method: derive AC, MC

20. 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. p  a —— b q*= Ex 3.4(1): Firm’s supply curve • Average cost • Marginal cost • Supply of output • Relation between price & output a+bq p F0/q+a+0.5bq q q

22. Ex 3.4(2) Question • purpose: to derive monopolist’s solution • method: derive AR, MR

23. Ex 3.4(2) Monopolist’s equilibrium • Given the demand curve total revenue is Aq½Bq2 • So, MR is • Monopolist’s FOC (MR=MC) • Solving for q we get • And from this we have

24. Ex 3.4(2): Monopoly output and price P • AC and MC curves • Demand (average revenue) • Marginal revenue • Profit-maximising output a+bq • MC and price at q** p** F0/q+a+0.5bq c** A 0.5bq A  bq q q**

25. Ex 3.4(3) Question • purpose: to derive modified monopoly solution • method: derive modified AR, MR – watch for discontinuity!

26. 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. Ex 3.4(3): High price ceiling • AC and MC curves • Demand (average revenue) • Marginal revenue • Profit-maximising output • MC and price at q** p** • high ceiling: no effect on equilibrium c** q q**

28. Ex 3.4(3): Low price ceiling • AC and MC curves • Demand (average revenue) • Marginal revenue • Profit-maximising output p** • Low ceiling : equilibrium at reduced output q0 • price = MC = price ceiling c** q q0 q**

29. Ex 3.4(3): Medium price ceiling (i) • AC and MC curves • Demand (average revenue) • Marginal revenue • Profit-maximising output p** • Medium ceiling : eqmat increased output q0 c** q q0 q**

30. Ex 3.4(3): Medium price ceiling (ii) • AC and MC curves • Demand (average revenue) • Marginal revenue • Profit-maximising output p** • Medium ceiling: eqmat increased output again c** q0 q q**

31. 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. Overview... Revision lecture Styles of question Modelling choice under uncertainty Doing short questions Doing long questions • Preparing and planning • CfD3.4 • 2010 Q5 and CfD8.12

33. 2010 Q5 (a)

34. 2010 Q5 (b)

35. 2010 Q5 (c)

36. 2010 Q5 (d) [partial]

37. 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

38. 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)

39. 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?

40. 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

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

42. 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

43. 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

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

45. 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 • Given DARA increase in wealth reduces demand for insurance

46. 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