Revision Lecture

1. Revision Lecture EC202 http://darp.lse.ac.uk/ec202 1st May 2014 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) • 2009 1(c) • 2010 1(a) • 2011 1(a), 3 • 2012 4 • 2013 1(c) • Reference materials used (2) • CfD presentations 3.4, 5.7 • Related to past exam questions

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 three years • (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. 2013 1(c) • Principles and model-solving • Write down the principle • Write down the basics of the model and solve • Use standard definition of expected utility and variance • Define ARA • Differentiate u • Evaluate ARA • Multiply by x to get RRA

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 past papers • also from exercises in the book of “exam type” difficulty • covered in CfD • Illustrates two types of question • Ex 3.4, 5.7 is straight model solving • 2012 Q4 incorporates some model building • Look out for tips • use pictures to clarify solution • following hints in Ex 3.4

18. Overview... Revision lecture Styles of question A problem about price control Doing short questions Doing long questions • Preparing and planning • CfD5.7 • 2012 Q4 • CfD 3.4

19. Ex 5.7: Question • purpose: Illustration of labour supply model with very simple preferences • method: Consumer optimisation with endogenous budget constraint

20. Ex 5.7: Worker’s problem • Basic constraints on worker are • x is consumption • `y is non-labour income • w is wage rate • ℓ is labour supply • Worker’s problem can therefore be written as • found by substituting from above into utility function

21. Ex 5.7: Worker’s optimum • Take log of maximand to get • a log(wℓ +`y) + [1  a] log(1  ℓ) • Differentiate with respect to ℓ • This is zero if • wℓ + aw + [a 1]`y = 0 • which implies ℓ = a + [a 1]`y / w • But this only makes sense if ℓ is non-negative • requires w≥ [1 a]`y / a • so optimal labour supply is

22. slope = w Ex 5.7: Interior maximum • (leisure, consumption)-space x • Max value of leisure • Indifference curves • Non-labour income • Budget constraint • Optimum • w≥ [1 a]`y /a • 0 < ℓ*< 1 `y 1  ℓ 0 1  ℓ* 1

23. Ex 5.7: Corner solution • Indifference curves as before x • Non-labour income • Budget constraint • Optimum • w< [1 a]`y /a • ℓ* = 0 • `y 1  ℓ 0 1

24. Ex 5.7: Points to note • Treat leisure as a conventional good • Has a natural upper bound • where labour is zero • Have to allow for corner solution • where person chooses not to work • Type of equilibrium depends on • wage rate • non-labour income

25. Overview... Revision lecture Styles of question Modelling choice under uncertainty Doing short questions Doing long questions • Preparing and planning • CfD5.7 • 2012 Q4 • CfD 3.4

26. 2012 Q4 (a)

27. 2012 Q4 (b)

28. 2012 Q4 (c)…

29. …2012 Q4 (c)

30. 2012 Q4 (d)

31. 2012 Q4 (e)

32. 2012 Q4 (f)

33. 2012 Q4  assessment • It seems like a long question • broken into digestible pieces • makes model-building easier • shows you exactly what to do, stage by stage • important message…. • “long”  “difficult” • Core of problem involves elementary things • carefully specify budget constraint in each part of the Q • plug into simple utility function • use FOC to get result • applies to parts (b)—(e) • Finishing off • final part just involves simple differentiation of the solution • don’t forget the “explain why” in part (e) • see also Ex 8.12

34. Overview... Revision lecture Styles of question Modelling choice under uncertainty Doing short questions Doing long questions • Preparing and planning • CfD5.7 • 2012 Q4 • CfD3.4

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

36. 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

37. 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

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

39. 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

40. 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**

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

42. 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

43. 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**

44. 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 q1 • price = MC = price ceiling c** q q1 q0 q**

45. 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 q2 c** q q0 q2 q**

46. 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**

47. 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.