ECON 101 Tutorial: Week 25
Shane Murphy
s.murphy5@lancaster.ac.uk
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 isoprofit 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:
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
are mutually consistent:
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, 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.
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 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).
Microeconomics Essay 2012 Q42
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.
Microeconomics Essay 2012 Q43
• There is only one road from the village to the city. The capacity of the road is such that
𝑥
driving from the village to the city will take 10 +
min if x cars are taking the road.
100
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 Q43
A) Explain in one sentence why the situation given, x=6000, is not a Nashequilibrium.
• 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):
x
7000 − x
10 +
= 10 +
+ 30
100
100
x = 5000
Microeconomics Essay 2012 Q43
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.
Microeconomics Essay 2012 Q43
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 Q43
D) 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:
7000 − x
7000 − x
+ 30 +
100
100
x
x
• 𝑅𝑢𝑠ℎ − ℎ𝑜𝑢𝑟:
+
100
100
• Setting them equal:
7000−x
x
•
2
+ 30 = 2
100
100
•
7000 − x + 1500 = x
•
x = 4250
4250
• Thus the Pigouvian toll during rush hour is:
min = 42.5min =8.50GBP.
And the Pigouvian toll during off-peak is:
100
7000−4250
𝑚𝑖𝑛
100
= 27.5𝑚𝑖𝑛 = 5.50𝐺𝐵𝑃.
Microeconomics Essay 2012 Q44
• 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
Lisa
Josh
Andrey
lights
1
2
3
4
Reservation Price
Reservation Price
Reservation Price
£150
£180
£200
£210
£150
£180
£200
£210
£150
£500
£590
£610
Microeconomics Essay 2012 Q44
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 Q44
In (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).
Microeconomics Essay 2012 Q44
C) Suppose the three individuals install the streetlights by noncooperative, 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.
Microeconomics Essay 2012 Q44
D) What is the Pareto-efficient number of streetlights? What rule or
condition tells you that amount? Compare your solutions in the costsharing 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.
Microeconomics Essay 2012 Q44
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.