ECON 100 Tutorial: Week 25

Shane Murphys.murphy5@lancaster.ac.uk

Last Office Hour: Monday 3:00 PM – 4:00 PM LUMS C85

Outline for the Last Tutorial

• Go over any questions from Exam 4• Students not taking the exam are free to go – have a nice summer!• Prep for Final Exam: Review of Past Micro Essay Question• Best way to prepare for Essay Exam

2012 Past Exam Essay Questions

Note: Some of these solutions/suggested answers were provided for revision last year by last year’s Professors, so I’ve included them in this

year’s slides.

Microeconomics Essay 2012 Q42An oligopolistic market structure is often thought to lead to collusion between firms. But collusion is often said to be unstable. Following the steps below, explain these propositions, using a Cournot duopoly model of two identical profit maximising firms selling identical products facing a linear market demand curve.

A) In the Cournot model each firm is assumed to maximise their own profits by taking the output of the rival firm as given. Explain, using the idea of an iso-profit function, how this leads to the “reaction curve” for one of the firms.

B) If both firms have linear reaction curves use an appropriate diagram to explain where the Nash equilibrium occurs.

C) Using an appropriate diagram examine whether, if we started away from equilibrium, the model would tend towards the equilibrium.

D) Explain, using an appropriate diagram, why there is an incentive to depart from the Nash equilibrium through agreeing to collude. Show what the collusive equilibrium looks like.

Microeconomics Essay 2012 Q42(A)A) In the Cournot model each firm is assumed to maximise their own profits by taking the output of the rival firm as given. Explain, using the idea of an iso-profit function, how this leads to the “reaction curve” for one of the firms.

• Cournot model: Same good produced by 2 firms (could be 3, 4..). Cost to firm i depends on qi, ie Ci(qi), where i=1,2.• If cost functions are the same across i, C1(q1) =C2(q2) =Ci (qi).• If total output is q1+q2 then market price is P(q1+q2); ie price depends on INDUSTRY output.• Note that profit of firm 1 depends on the firm 2’s output (as well as its own), and vice versa

ie π1(q1,q2) = q1.P(q1+q2) – C(q1) and π2(q1,q2) = q2.P(q1+q2) – C(q2).

• Strategic game between firm 1 and firm 2: each firm’s action is its output; each firm’s preferences (payoffs) is represented by its profits.

Microeconomics Essay 2012 Q42(A) ctd.• Firm 1: for any value of q2, there is a “best response”

level of q1 that maximises π1.• The lower is q2, the higher will be q1, and thus π1. This

defines “reaction function” R1, which is the dashed line.• The closer the isoprofit curve to the q1 axis, the higher π1

• Firm 2: for each q1, there is a best response q2 that max π2 The lower is q1, the higher is π2. This defines “reaction function” R2:

Microeconomics Essay 2012 Q42(B)If both firms have linear reaction curves, use an appropriate diagram to explain where the Nash equilibrium occurs.• The NE is a pair (q*1, q*2) such that each firm’s

action is a best response to the other firm’s action. • This is q*1 = R1(q*2) and q*2 = R2(q*1). In other

words this pair of outputs is a mutual best response.

(the curved red and blue lines are iso-profit functions)

Microeconomics Essay 2012 Q42(C)Using an appropriate diagram examine whether, if we started away from equilibrium, the model would tend towards the equilibrium.• Suppose, Firm 1 chooses q1a. • Then Firm 2’s best response is q2a=R2(q1a). • Then Firm 1’s best response to that is q1b=R1(q2a). • Then Firm 2’s best response to that is q2b=R2(q1b).

Etc. • This NE is STABLE – ie we converge towards the NE, even if we start away from it.

Microeconomics Essay 2012 Q42(D)Explain, using an appropriate diagram, why there is an incentive to depart from the Nash equilibrium through agreeing to collude. Show what the collusive equilibrium looks like.• Suppose the Nash Equilibrium is at point A. • Note that each firm could get higher π than at

A if they agreed to reduce their outputs. For example, each could agree to produce ½q*M (ie at B).

(The green line represents production at monopoly quantity.)

How do we know profit is higher at point B than at point A?

It is on an iso-profit curve that is closer to the axis (see part A of this question)

Microeconomics Essay 2012 Q42(E)Explain, using a diagram, why each firm has an incentive to cheat on such a collusive agreement. • From Point B, each firm has incentive to cheat - to

get higher profits. • For example firm 2 would look at its reaction

function and, if firm 1’s output stays at ½q*M , then firm 2 would decide that producing more would yield higher profit (better iso-profit curve). • Similarly for firm 1. • So cheating is the dominant strategy. So both cheat.

Both end up worse off. • This is a Prisoner’s dilemma problem. So a collusive

agreement is likely to be unstable.

Final Exam Info

• May 31st – Check your timetable for time & location• Bring a pencil, eraser, calculator and Student ID #• 40 Multiple Choice Questions• 20 Micro• 20 Macro

• Choose 1 Micro Essay Question & 1 Macro Essay Question (from 3 micro questions and 3 macro)

Best ways to revise for the Final Exam• Review anything your Professors tell you to review.• Review Tutorial Questions • A lot of exam questions from these.• There will be a mix of Theory, Definitions, and Application Problems.• At least 5 David Peel-type math problems

• Review Tests 1-4 from this year.• Review Past exams 2013 and 2012, etc. • Note: The course materials change slightly from year to year, that is why I

think revising this year’s tutorials and tests is better preparation than revising past year’s exams.

Some MICRO topics you should definitely revise:• Supply & Demand (finding equilibrium, what causes shifts in S & D)• Consumer Surplus & Producer Surplus• Normal, inferior, complementary, substitute goods• Competitive markets, monopoly • Elasticities (i.e. price elasticity of demand, elastic vs. inelastic)• Average product of Labor, marginal product of Labor • Effects of taxes and subsidies• Be able to find equilibrium (and CS, PS, DWL, etc.) both graphically AND

algebraically • Game theory concepts and applications: Nash equilibrium, Cournot duopoly,

Prisoner’s dilemma, how to solve normal form & extensive form games• David Peel’s math questions: exponents, logarithms, Cobb Douglass production

function, derivatives (as in marginal means take the derivative)

Some MACRO topics you should definitely revise:• David Peele’s math questions:

• derivatives, partial derivatives, exponents, logarithms

• Coskeran:• National Income Accounts, GDP, GNP, etc. – How to calculate these• Life cycle hypothesis/Permanent Income hypothesis• IS-LM model• Aggregate Demand/Aggregate Supply model

• Steele:• Phillips curve & Expectations augmented Phillips curve• Goodhart’s law• Taylor Rule• Lucas Critique• Quantitative easing and bonds

Good luck and have a nice summer!