econ 101 tutorial: week 25 shane murphy [email protected] office hours: monday 3:00-4:00 –...

ECON 101 Tutorial: Week 25

Shane [email protected]

Office Hours: Monday 3:00-4:00 – LUMS C85

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.

• 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.

Questions?

2012 Past Exam Essay Questions

Microeconomics essay 2012 Q41

2012 Q1) Governments are often concerned that by providing financial support for individuals with low incomes they undermine the incentive to work hard. Following the steps below explain the basis for this concern and explain how an “in-work” welfare policy might be used to overcome this problem.

A) Using an appropriate diagram, explain the economic theory of labour supply where individuals have preferences defined over c (consumption) and l (leisure) and face a budget constraint defined by c = w.h + m where w is the hourly wage, hours of work are given by h=24-l, and m is unearned income. Show how you can characterise the equilibrium optimal level of hours of work, h*, in this theory.

Microeconomics Essay 2012 Q41(A)• U = U(c, l) where U increasing in c and in l• l = T-h where h is work hours and T is total hours

available. • Hence U=U(c, T-h) where U is increasing in c and

decreasing in h. • So there is a trade-off between c and l. • So the indifference map is given by:

Microeconomics Essay 2012 Q41(A)• Next, we draw the budget constraint: c = wh + m• If h = 0, then c = m (ie the vertical part of the blue

line below).• If h>0 then earnings can finance c as well• ie c rises with h along the sloping part of the blue

constraint below.

• So, in general the budget constraint is defined by c = m + wh.

• Hence the budget constraint is given by:

Microeconomics Essay 2012 Q41(A)In this step, we put the indifference curves and the budget constraint together to find the equilibrium.• If the individual does the best she can (ie max

utility) subject to the constraint she faces (ie c=m+w.h), then equilibrium will defined by:• a tangency where slope IC = slope BC. • That is, MRShc = w .• This equation defines the optimal labour supply h*

which depends on w and m, ie h*=h(w,m).• And if h* is chosen then the max utility is U*.

Microeconomics Essay 2012 Q41(B)

Show how a change in w might affect the equilibrium labour supply, h*.

Microeconomics Essay 2012 Q41(B)

• A rise in w, from w0 to w1, holding m constant at m0, implies that h increases.

• Having two values for w and two h*’s, we can begin to plot a labour supply curve, h*=h(w,m0) as in the bottom panel.

Microeconomics Essay 2012 Q41(C)

It is often the case that governments provide welfare payments to individuals who have incomes below a certain level such that if m+wh is less than this level, S, then the government pays the individual an amount that raises their income to S. Show, in a diagram, what this does to the budget constraint and use this diagram to explain how this adversely affects work incentives.

Microeconomics Essay 2012 Q41(C)• Suppose for simplicity that m=0, and w is such that the

budget contraint then looks like the blue sloped line.• If the government decides to top up the income of those

people whose income is below S then the BC would have the red lines for low hours worked and the blue line for higher h.• With the red line, someone is better off not working and

receiving the higher green utility curve than working and receiving the lower green curve.• A small loss in income gives a large increase in the

amount of leisure enjoyed.• Thus, there is an adverse effect on the incentive to work

for a wide rang of h. Many countries have welfare programmes that have such a feature.

Microeconomics Essay 2012 Q41(D)To overcome the adverse effects of such a welfare scheme governments sometimes use in-work welfare payments. The UK has such a scheme which provides additional income for individuals whose incomes are less than some level, F, but who are working at least some given level of hours, hF. Such welfare payments are means-tested so that the amount paid is reduced until it falls to zero when m+wh=F.

Explain in a diagram how this affects the budget constraint. Using this diagram and the previous one show how this in-work welfare scheme might overcome the adverse incentive effects of the low income welfare scheme.

Microeconomics Essay 2012 Q41(D)

• This graph shows our old welfare program.

• The new UK working tax credit requires 24 hours of work a week.• So for h>24 hours a week the in-work

welfare payment will move the agent to a higher utility curve.

Microeconomics Essay 2012 Q41(D)

• So for h>24 hours a week the in-work welfare payment will move the agent to a higher utility curve. The new payment scheme is shown in purple.

• Note for someone at h=0 and receiving S, there is now an incentive to work 24 hours because you get 24w in earnings and this gets topped up by the in-work welfare programme – to such an extent that working now becomes attractive.

Microeconomics Essay 2012 Q41(E)

Explain the weaknesses of such an in-work welfare policy• There a number of problems with a policy like this in work welfare

programme. • One is “stigma” - the government has found that people are reluctant to

take up their entitlement to such programmes - the forms are difficult, you need to get your employer to sign that you work 24+ hours, and you might feel that people on welfare are looked down on by others. • A second problem is that while it incentivises non workers to work, it

disincentivizes those that already work, or they would tend to work less so as to generate an entitlement (or bigger entitlement) to this welfare payment.

Microeconomics Essay 2012 Q42

An 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.

Microeconomics Essay 2012 Q42• 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(.) =C2(.) =C(.).• If total output is q1+q2 then market price is P(q1+q2) – ie 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• Firm 1: for any value of q2, there is a “best response”

level of q, 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:

• 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:


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 are mutually consistent:


C) Using an appropriate diagram examine whether, if we started away from equilibrium, the model would tend towards the equilibrium.• Suppose, in the figure below, Firm 1 chooses

q1a. 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 if we start away from it.


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 A in figure below. Note that each firm

could get higher π than at A - if they agreed to reduce their outputs (along the red arrow). For example, each could agree to produce ½q*M (ie at B).


E) Explain, using this diagram, why each firm has an incentive to cheat on such a collusive agreement. • But, at B, each have incentive to cheat - to get higher

profits. For example firm 2 would look at its reaction function and , if firm 1’s output is ½q*M , and decide that producing more would yield higher profit (providing firm 1 staying producing ½q*M). 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.


• There is only one road from the village to the city. The capacity of the road is such that driving from the village to the city will take min if x cars are taking the road. 7000 drivers want to go to the city every morning during rush hour. No driver wants to go before rush hour. Instead of driving during rush-hour a driver can decide to get up earlier and drive before rush-hour. But each driver suffers a disutility from getting up early, which is just as bad as spending an additional 30min in traffic.• Example, for you to understand the assumptions better:

Suppose x=6000 drivers travel during rush-hour, and the rest, i.e. 1000 cars, travel before rush hour. Then it takes the rush hour drivers 70min each, while the drivers who get up early have a travel time of 20min. While these early birds have a travel time of only 20min, they consider that just as bad as if they had a travel time of 50min during rush hour. Clearly this example of x=6000 is not a Nash-equilibrium.

Microeconomics Essay 2012 Q43A) Explain in one sentence why the situation given, x=6000, is not a Nash-equilibrium. • None of the rush hour drivers are choosing their best response strategy, one of them could

deviate and get a payoff of 50min instead of 70min, where less is better.

B) Find a Nash-equilibrium. Please show your work and derivation and briefly explain each step. • Two time periods are available (rush hour and early).• To find a Nash-equilibrium set the effective travel times for the two periods equal, such that

drivers are indifferent between leaving during rush hour and leaving early):


C) Consider the negative non-pecuniary externalities drivers are exerting on each other in the Nash-equilibrium you found in (b): i) What is the negative externality a rush-hour driver exerts on all other drivers (in minutes)? ii) How much is that driver herself delayed by all other drivers? (If you know of a shortcut to answer these last two questions, don’t hesitate to use it).• A driver delays all others just by the same amount as she is delayed by all the

others, therefore the answer for the two questions is the same. If there is no other driver, then the driver needs 10.01min. During rush hour with x=5000 her travel time is 60min. Thus she delays all others, and is delayed by all others about 50min.


iii) What is the negative externality an early-bird driver exerts on all other drivers (in minutes)? iv) How much is that early-bird driver herself delayed by all other drivers?• By the same logic as above: Since there are 7k-5k=2k drivers on the road, he

needs 30 min, almost 20min more than an all empty road would take. Therefore the answer is 20min to both questions.

Microeconomics Essay 2012 Q43D) Assume that the opportunity cost of time for each driver is GBP12 per hour. What is the optimal Pigouvian road toll during rush hour, and during off-peak?• An rush-hour driver exerts a negative externality of x/100, thus that should be the Pigouvian toll

(in minutes), while for an off peak driver that is (7000-x)/100. Thus adding them to the absolute value of the payoffs gives:

• Off-peak:

•

• Setting them equal:• • • • Thus the Pigouvian toll during rush hour is: 8.50GBP.

And the Pigouvian toll during off-peak is:


• Consider streetlights as an example of a non-rival good. The reservation price or benefit of a certain number of streetlights is as given in the table. Streetlights have a price of £100 each: that is, the marginal cost of a streetlight is £100.

Number of street lights

Lisa Josh Andrey

Reservation Price Reservation Price Reservation Price

1 £150 £150 £1502 £180 £180 £5003 £200 £200 £5904 £210 £210 £610


A) Suppose each person lives by themselves on a street. How many lights does Lisa buy? How many lights does Josh buy? How many lights does Andrey buy?• In the table, reservation price really means total benefit. So you just buy while

marginal benefit > marginal cost.• Lisa buys 1 light, Josh buys 1 light, Andrey buys 2 lights.

Microeconomics Essay 2012 Q44In (b) to (d), suppose all three live on the same street, and streetlights are a perfectly non-rival good.B) Suppose by majority vote they decide how many streetlights to install. Suppose the cost is shared equally. What is the Condorcet-winner (recall that a Condorcet winner is an option that wins a pairwise vote against any other alternative)? Can you explain why the median-voter theorem predicts that in a situation such as the one given there will be a Condorcet-winner?• The Condorcet winner is 1 streetlight. This is predicted by the median-voter theorem since

the preferences are single-peaked in the ordering as given. The peak is 1 for Lisa, 1 for Josh, and 3 for Andrey. Thus a Condorcet winner exists, and moreover the Condorcet winner is 1, the median voter’s (Josh/Lisa) peak (most preferred alternative).


C) Suppose the three individuals install the streetlights by non-cooperative, simultaneous provision. That is, in a simultaneous-move game, what is the number of streetlights Lisa, Josh and Andrey each buy? • Lisa only installs one streetlight if zero are installed by the others. The same is

true for Josh. Andrey installs 2 streetlights if zero are installed by the others, and installs one if one is installed by the others, and zero if two or more are installed by the others. Therefore the Nash-equilibrium is Lisa installs zero, Josh installs zero, Andrey installs 2.


D) What is the Pareto-efficient number of streetlights? What rule or condition tells you that amount? Compare your solutions in the cost-sharing scenario and in the non-cooperative provision scenario with the Pareto-efficient amount.• A necessary condition for an allocation to be Pareto-efficient is the Samuelson

which states for the special case of reservation prices (i.e. quasi-linear preferences or no income effects) that for a non-rival good the sum of individual marginal benefits equals (if continuous, else integer problem) the marginal cost.In this example thus the Pareto-efficient amount of streetlights is 3.Here democracy/cost-sharing is furthest from the Pareto-efficient amount, the non-cooperative solution is closer but still underprovides the non-rival good.


E) Briefly comment on whether excludability of streetlights (such as by automatic sensors that turn the lights on and off) could help achieve the Pareto-efficient amount of lighting. You can assume that government or one of the three persons operate the system, whichever you find easier/better.• Suppose Andrey (for example, government or any other person same logic)

could install as many streetlights as he wants and exclude others from use. He could and would then install the Pareto-efficient amount of 3 streetlights and charge Josh and Lisa, say 190 each. Thus excludability would get us the Pareto-efficient solutions. (extra information/bonus credit: this works only since we have perfect information and know everyone’s reservation prices).

Macroeconomics Essay 2012 Q 45

The motives for holding money are often classified as: transactions; precautionary; speculative. How do these motives relate to the liquidity preference function? How does the liquidity preference function help us understand the determination of equilibrium in the market for money?

Macroeconomics Essay 2012 Q 45• The transactions motive implies that the demand for real balances is positively related to

income, since a higher value of transactions is undertaken as income rises.• Extra: transactions demand only exists because of the lack of synchronisation between incomes and

expenditures.

• The speculative motive implies that the demand for real balances is negatively related to the interest rate, since the interest rate is the opportunity cost of holding assets in the form of money.• Extra: consider a bond market interpretation where demand for bonds increases when price of bonds is

low, so interest high, and this increase in demand for bonds implies a decrease in the demand for money.

• A demand curve for money can be drawn in (r,M) space, and the demand curve shifts out as income rises.• Superimposing onto this a supply curve (typically vertical) shows that money market

equilibrium can be obtained either at low r-low Y or high r-high Y combinations.• Extra: derive the LM curve. • Extra: note how the interest rate moves in response to excess supply or demand in the money market.

Macroeconomics Essay 2012 Q 46

In simple models, the Keynesian income multiplier is calculated as the inverse of the marginal propensity to withdraw. Why then in real world applications, does the true value of the multiplier often turn out to be less than one?

Macroeconomics Essay 2012 Q 46• The simple answer is because of crowding out. A full answer is to look at how the

multiplier is obtained in both a simple model (where there is no crowding out) and in a full ISLM model (where there is).• The former can be achieved either by way of a Keynesian cross (45 degree) model

or by way of an ISLM model with a flat LM curve.• The latter requires the ISLM analysis.• For a good answer, describe the mechanism of the multiplier process particularly

clearly, or have a particularly good explanation of crowding out (eg increase in G raises income which raises transactions demand for money; given money supply this means that speculative demand must fall, and that requires an increase in the interest rate. This increase in the interest rate chokes off private sector investment.) • Extra: comment on real world estimates of the multiplier.

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 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.

econ 101 tutorial: week 25 shane murphy [email protected] office hours: monday 3:00-4:00 –...

Documents