Frank Cowell: Microeconomics Revision Lecture EC th April 2010 Frank Cowell

Frank Cowell: Microeconomics Overview... Styles of question Doing short questions Planning answers Doing long questions Revision lecture How to see what you need to do

Frank Cowell: Microeconomics Objectives of the lecture A look back at Term 1 A look back at Term 1 Exam preparation Exam preparation Reference materials used (1) Reference materials used (1)  Exam papers (and outline answers)  (a)  (a)   (b)  (c) Reference materials used (2) Reference materials used (2)  CfD presentations 2.9, 3.3, 8.12  All related to past exam questions

Frank Cowell: Microeconomics The exam paper Scope of exam material Scope of exam material  what’s covered in the lectures…  … is definitive for the exam Structure and format of paper Structure and format of paper  follows that of last four years  check out the rubric from, last year’s paper Mark scheme 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: except where it’s obvious, roughly equal marks across parts

Frank Cowell: Microeconomics Question style – three types 1 Principles 1 Principles  reason on standard results and arguments  can use verbal and/or mathematical reasoning 2 Model solving 2 Model solving  a standard framework  you just turn the wheels 3 Model building 3 Model building  usually get guidance in the question  longer question sometimes easier? One type not necessarily “easier” or “harder” than another 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

Frank Cowell: Microeconomics Overview... Styles of question Doing short questions Planning answers Doing long questions Revision lecture How to tackle the main types of question

Frank Cowell: Microeconomics (c) Straightforward “principles” question Straightforward “principles” question Just say what you need to say Just say what you need to say

Frank Cowell: Microeconomics (a) Straight “principles” Straight “principles” Note the contrast between firm and consumer Note the contrast between firm and consumer Be sure to give your reasons Be sure to give your reasons

Frank Cowell: Microeconomics (a) Principles again Principles again But format of question gives you a hint… But format of question gives you a hint… …write out decomposition formula …write out decomposition formula Then read off results Then read off results

Frank Cowell: Microeconomics (b) Principles and model-solving Principles and model-solving Write down the principle Write down the principle Write down the basics of the model Write down the basics of the model WARP can be stated simply in terms of “affordability” 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 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… Check the on-line answers for the (short) detailed reasoning…

Frank Cowell: Microeconomics Straight principles can come up in long questions Straight principles can come up in long questions Don’t ignore them in a rush to get to the model! Don’t ignore them in a rush to get to the model! Compare this with CfD 8.12 Compare this with CfD 8.12 CfD (from book) doesn’t have this bit, but take it seriously CfD (from book) doesn’t have this bit, but take it seriously There are some easy marks just writing down the definition… There are some easy marks just writing down the definition… …and the diagram helps you to answer part (b) …and the diagram helps you to answer part (b)

Frank Cowell: Microeconomics Overview... Styles of question Doing short questions Planning answers Doing long questions Revision lecture How to do well in exams

Frank Cowell: Microeconomics Planning Answers What’s the point? 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 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 Be an economist with your own time  don’t solve things twice!  reuse results  answer the right number of questions!!!

Frank Cowell: Microeconomics Tips Follow the leads Follow the leads  examiners may be on your side!  so if you’re pointed in the right direction, follow it… Pix Pix  help you to see the solution  help you to explain your solution to examiner What should the answer be? 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? Does it make sense?  again take a moment to check after each part  we all make silly slips

Frank Cowell: Microeconomics Long questions Let’s look at three examples Let’s look at three examples  taken from exercises in the book  but of “exam type” difficulty  covered in CfD Illustrates two types of question Illustrates two types of question  Ex 2.9 and 3.3 are straight model solving  Ex 8.12 incorporates some model building Look out for tips Look out for tips  In all three questions, use pictures to clarify solution  following hints in 3.3 [The “Explain carefully…” bits]

Frank Cowell: Microeconomics Overview... Styles of question Doing short questions Planning answers Doing long questions Revision lecture How to combine principles and model-solving… CfD 2.9 CfD 3.3 CfD 9.12

Frank Cowell: Microeconomics Ex 2.9(1): Question purpose: demonstrate relationship between short and long run method: Lagrangean approach to cost minimisation. First part can be solved by a “trick”

Frank Cowell: Microeconomics Ex 2.9(1): Long-run costs Production function is homogeneous of degree 1   increase all inputs by a factor t > 0 (i.e. z → tz)…   …and output increases by the same factor (i.e. q → tq)   constant returns to scale in the long run CRTS implies constant average cost   C(w, q) / q = A (a constant)   so C(w, q) = Aq   differentiating: C q (w, q) = A So LRMC = LRAC = constant   Their graphs will be an identical straight line

Frank Cowell: Microeconomics Ex 2.9(2): Question method: Standard Lagrangean approach

Frank Cowell: Microeconomics Ex 2.9(2): short-run Lagrangean In the short run amount of good 3 is fixed   z 3 =  z 3 Could write the Lagrangean as But it is more convenient to transform the problem thus where

Frank Cowell: Microeconomics z2z2 z1z1 Ex 2.9(2): Isoquants Sketch the isoquant map Isoquants do not touch the axes So maximum problem must have an interior solution

Frank Cowell: Microeconomics Ex 2.9(2): short-run FOCs Differentiating Lagrangean, the FOCS are This implies To find conditional demand function must solve for   use the above equations…   …and the production function

Frank Cowell: Microeconomics Ex 2.9(2): short-run FOCs (more) Using FOCs and the production function: This implies   where This will give us the short-run cost function

Frank Cowell: Microeconomics Ex 2.9(2): short-run costs By definition, short- run costs are: This becomes Substituting for k: From this we get   SRAC:   SRMC:

Frank Cowell: Microeconomics q Ex 2.9(2): short-run MC and AC marginal cost average cost

Frank Cowell: Microeconomics Ex 2.9(3): Question method: Draw the standard supply-curve diagram Manipulate the relationship p = MC

Frank Cowell: Microeconomics Ex 2.9(3): short-run supply curve   average cost curve   marginal cost curve   supply curve q p q p   minimum average cost

Frank Cowell: Microeconomics Use the expression for marginal cost: Set p = MC for p ≥ p Rearrange to get supply curve Differentiate last line to get supply elasticity Ex 2.9(3): short-run supply elasticity

Frank Cowell: Microeconomics Ex 2.9: Points to remember Exploit CRTS to give you easy results Try transforming the Lagrangean to make it easier to manipulate Use MC curve to derive supply curve

Frank Cowell: Microeconomics Overview... Styles of question Doing short questions Planning answers Doing long questions Revision lecture A problem with discontinuous supply… CfD 2.9 CfD 3.3 CfD 8.12

Frank Cowell: Microeconomics Ex 3.3(1) Question purpose: to derive competitive supply function method: derive AC, MC

Frank Cowell: Microeconomics Ex 3.3(1) Costs Total cost is: F 0 + ½ aq i 2 Marginal cost: aq i Average cost: F 0 /q i + ½ aq i Therefore MC intersects AC where: This is at output level q where: At this point AC is at a minimum p where: For q below q there is IRTS and vice versa

Frank Cowell: Microeconomics Ex 3.3(1) Supply If p > p the firm supplies an amount of output such that   p = MC If p < p the firm supplies zero output   otherwise the firm would make a loss If p = p the firm is indifferent between supplying 0 or q   in either case firm makes zero profits To summarise the supply curve consists of :

Frank Cowell: Microeconomics Ex 3.3(1): Supply by a single firm qiqi p   Average cost   Marginal cost   Supply of output q

Frank Cowell: Microeconomics Ex 3.3(2) Question purpose: to demonstrate possible absence of equilibrium method: examine discontinuity in supply relationship

Frank Cowell: Microeconomics Ex 3.3(2): Equilibrium? AC MC  qiqi p   AC,MC and supply of firm   Demand, low value of b   Demand, high value of b Supply (one firm)   Solution for high value of b is where Supply = Demand   Demand, med value of b

Frank Cowell: Microeconomics Ex 3.3(2) Equilibrium Outcome for supply by a single price-taking firm High demand: unique equilibrium on upper part of supply curve Low demand: equilibrium with zero output In between: no equilibrium Given case 1 “Supply = Demand” implies This implies: But for case 1 we need p ≥ p   from the above this implies

Frank Cowell: Microeconomics Ex 3.3(3) Question purpose: to demonstrate effect of averaging method: appeal to a continuity argument

Frank Cowell: Microeconomics Ex 3.3(3) Average supply, N firms Define average output Set of possible values for average output: Therefore the average supply function is

Frank Cowell: Microeconomics Ex 3.3(3) Average supply, limit case As N  the set J(q) becomes dense in [0, q] So, in the limit, if p = p average output can take any value in [0, q] Therefore the average supply function is

Frank Cowell: Microeconomics Ex 3.3(3): Average supply by N firms p   Average cost (for each firm)   Marginal cost (for each firm)   Supply of output for averaged firms q q 

Frank Cowell: Microeconomics Ex 3.3(4) Question purpose: to find equilibrium in large-numbers case method: re-examine small-numbers case

Frank Cowell: Microeconomics Ex 3.3(4) Equilibrium Equilibrium depends on where demand curve is located   characterise in terms of (price, average output) High demand   equilibrium is at (p, p/a) where p = aA / [a+b] Medium demand   equilibrium is at (p, [A – p]/b)   equivalent to (p,  q) where  := a[A – p] / [bp]   Achieve this with a proportion  at q and 1–  at 0 Low demand   equilibrium is at (p, 0)

Frank Cowell: Microeconomics Ex 3.3(4): Eqm (medium demand) p   AC and MC (for each firm)   Supply of output (averaged) q   Demand   Equilibrium q*   Equilibrium achieved by mixing firms at 0 and at q  here 1  here q 

Frank Cowell: Microeconomics Ex 3.4: Points to remember Model discontinuity carefully Averaging may eliminate discontinuity problem in a large economy   depends whether individual agents are small. Equilibrium in averaged model may involve identical firms doing different things   equilibrium depends on the right mixture

Frank Cowell: Microeconomics Overview... Styles of question Doing short questions Planning answers Doing long questions Revision lecture Modelling choice under uncertainy CfD 2.9 CfD 3.3 CfD 8.12

Frank Cowell: Microeconomics 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

Frank Cowell: Microeconomics 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)

Frank Cowell: Microeconomics 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?

Frank Cowell: Microeconomics 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

Frank Cowell: Microeconomics Ex 8.12(2): Question Method Standard optimisation Differentiate expected utility with respect to t

Frank Cowell: Microeconomics 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

Frank Cowell: Microeconomics 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

Frank Cowell: Microeconomics Ex 8.12(3): response of t * to y 0 Differentiate the following with respect to y 0 : This yields: On rearranging we get:

Frank Cowell: Microeconomics 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 So, given DARA, an increase in wealth reduces the demand for insurance

Frank Cowell: Microeconomics 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