5SSPP217 Microeconomics
Mock exam 20/21






Answer all questions
Please show ALL your work.
If you answer a question by showing just the solution or provide inconsistent or
too sketchy workings, your answer will receive a mark of 0.
Obtaining the right answer does not guarantee full marks.
Wrong numerical answers which nonetheless follow the right procedure will
receive partial credit.
Important note: This mock exam is for you to have an idea of the exam format.
You should not use it to guess which questions will or will not appear in the final
exam. Note that solutions provided at the end are sketchy and just for you to be
able to use these questions as additional practice. Attempt this exam without
looking at the solutions.
Problem 1
Suppose there are two firms in a market and the demand curve is given by P = 145 – 7Q, where
Q = Q1 + Q2 is the combined output of both firms and P is the price. The firms’ cost functions
are C1(Q1) = 5Q1 and C2(Q2) = 12Q2.
a) Use the Cournot model to find each firm’s equilibrium output and profit if they behave
non-cooperatively?
b) How much should Firm 1 be willing to pay to purchase Firm 2?
c) How much would Firm 1 pay to become the Stackelberg leader in this market?
Problem 2
Louise is a monopoly producer of patchwork quilts. She is deciding how to allocate output
between Scotland and England in order to maximise her profits. Demand in the two markets
is:
PS = 210 – QS
PE = 120 – 0.25QE
where PS and PE are the prices in Scotland and England respectively (in pounds), and QS and
QE the number of quilts demanded annually. Louise’s total cost is C = 5000 + 40(Q1 + Q2).
a) What are Louise’s prices, total output and profits if she can price discriminate between
the two markets.
b) What are Louise’s price, total output and profits if the law prohibits her from charging
different prices in Scotland and England.
c) In which case will have the firm larger market power? Which situation (a or b) will
consumers in each market prefer?
Problem 3
a) Jack is risk neutral and must choose whether to become an accountant or a musician. If he
becomes an accountant, then he will earn £60,000 for sure. If he becomes a musician, then
he will earn £200,000 if he is good at it and £10,000 if he is not. Jack does not know whether
he is good or not but believes the probability he is good is 0.25. Suppose that Katie is a
music critic and can tell Jack whether he is good or not. What is the maximum Jack would
be willing to pay for this information?
b) Sarah has the following expected utility, which she wishes to maximize,
where W is her wealth, p is the probability she loses her wealth, r is the insurance premium
rate, and K is the amount of insurance she chooses to purchase. Show analytically that if
insurance is fair Sarah will fully insure. Explain in words why that is.
Problem 4
Margaret has 60 hours of personal time she can use to either work or pursue leisurely activities.
The number of hours she works is denoted by h, and the number of leisure hours is denoted by
l. She uses all her income for consumption, denoted by c.
a) Margaret’s current wage is £15 per hour and her non-labor income is £100. Sketch her
budget constraint on a graph, where the number of leisure hours l is on the x-axis, and
her money consumption of all other goods c, on the y-axis. If she works for h=30 hours,
how much c can she consume? Show this bundle of consumption and leisure on the
graph and label it ‘D’.
b) What is the slope of the budget constraint? What happens to the budget constraint if her
non-labour income increases? What happens if the wage decreases?
c) Assume that Margaret is a utility maximiser and let her preferences be represented by
the utility function u(l, c) = ln l + 2 ln c. Use the Lagrange methods to find the optimal
bundle (l*,c*) for Margaret when w = £15. Is it the same as the point D you found in
(a)? Why or why not? Justify your answer.
Problem 5
There are two agents, A and B, in a two-commodity X and Y pure exchange economy. Agents
are allowed to trade. Endowments are eA = (3,1) and eB = (0,1). Their utility functions are
UA(xA,yA)=(xA)1/2(yA)1/2 and UB(xB,yB)=(xB)1/2(yB)1/2.
a) Use the Lagrange method to find the agents’ demands.
b) Find the competitive equilibrium, i.e. the price ratio, of this exchange economy and the
resulting equilibrium allocation.
c) Find the expression of the contract curve for this economy as a function of xA and yA.
d) Find the transfer T of good X from agent A to agent B which supports as an equilibrium
of this economy the Pareto efficient allocation where both individuals enjoy the same
level of utility.
Solutions
Sketch of solutions for Problem 1:
a) Firm 1 chooses Q1 to maximize π1 with Q2 being treated as a constant.
π1 = (145 – 7Q1 – 7Q2)Q1 – 5Q1
So,
𝝏𝝅𝟏
= 𝟏𝟒𝟓 − 𝟏𝟒𝑸𝟏 − 𝟕𝑸𝟐 − 𝟓 = 𝟎
𝜹𝑸𝟏
Therefore, Q1 = 10 – 0.5Q2.
By similar logic:
π2 = (145 – 7Q1 – 7Q2)Q2 – 12Q2
So,
𝝏𝝅𝟐
= 𝟏𝟒𝟓 − 𝟕𝑸𝟏 − 𝟏𝟒𝑸𝟐 − 𝟏𝟐 = 𝟎
𝜹𝑸𝟐
Therefore, Q2 = 9.5 – 0.5Q1.
Solving the reaction functions simultaneously gives:
Q1 = 10 – 0.5(9.5 – 0.5Q1) = 5.25 + 0.25Q1
Q1 = 7
Q2 = 6
π1 = 7(54 – 5) = £343
π2 = 6(54 – 12) = £252
b) If firm 1 were a monopolist, they would set MR = 145 – 14Q = 5 so Q1 = 10 and P = 75
(they would produce everything in their original plant with MC=5). Profit would be equal
to π1 = 10(75-5) = £700. So firm 1 would be willing to pay up to 700 – 343 = £357 to
purchase firm 2.
c) If Firm 2 were the follower, its best response function would not change compared to
a). The difference is that now Firm 1 will factor that output choice when deciding its own
output. Firm 1 will then maximise
π1 = (145 – 7Q1 – 7(9.5 – 0.5Q1))Q1 – 5Q1 = (78.5 – 3.5Q1)Q1 – 5Q1
So,
𝝏𝝅𝟏
= 𝟕𝟖. 𝟓 − 𝟕𝑸𝟏 − 𝟓 = 𝟎
𝜹𝑸𝟏
Therefore, Q1* = 10.5 and firm 1 will collect profits π1* = £385.87. Firm 1 will thus be
willing to pay up to £42.87.
Sketch of solutions for Problem 2:
a) If she can price discriminate, Louise sets MR = MC in each market separately.
MRS = 210 – 2QS = 40
MRE = 120 – 0.5QE = 40
This gives QS = 85 and QE = 160, and QT = 245. Substituting back into the demand
curves gives, PS = 125 and PE = 80. Louise’s profits are π = (85*125) + (160*80) – 5000
– 40(245) = £8,625.
b) If she cannot price discriminate, she must charge a single price. Demand is given by
the Scottish demand at prices greater than 120, and by the horizontal sum of demands
for prices below that.
If the firm dices to serve only to Scotland, its problem will be identical to hat in part
a) for Scotland. The firm will set a price P = 125, will only sell in Scotland and collect
profits
π = (85*125) – 5000 – 40(125) = £625.
If the firm decides to serve to the two markets, it will face aggregate demand
QT = 690 – 5P
Inverting this we can find demand and MR, and set MR equal to MC.
MR = 138 – 0.4QT = 40
Therefore QT = 245, P = 89 (which is indeed smaller than 120) and will collect profits
π = (245*89) – 5000 – 40(245) = £7,005.
This is hence the monopolist’s optimum choice.
c) The Lerner index of market power in Scotland in section (a) is (125-40)/125 = 0.68
whereas in England is (80 – 40)/80 = 0.5. On the other hand, the Lerner index of
market power in the uniform price case is (89-40)/89 = 0.61. The monopolist enjoyed
the highest market power in Scotland when it could discriminate, surely because
demand was more inelastic there as we know from the inverse elasticity rule. Because
of that, Scottish consumers prefer the uniform price setting as they will be paying
lower prices then, whereas the opposite would be true for English consumers (you
could support your answer by providing calculations of the consumer surplus in each
case and market).
Sketch of solutions for Problem 3:
a) If Jack does not have the information, then he will become an accountant and earn
£60,000. This is higher than his expected earnings as a musician, which are (0.25)
£200,000 + (0.75) £10,000 = £57,500. If Jack does have the information, then he will
become a musician if he is good at it and an accountant if he is not. His expected
earnings are then (0.25) £200,000 + (0.75) £60,000 = £95,000. His willingness to pay
for the information is the difference between these two values (£95,000 – £60,000), so
£35,000.
b) Differentiating w.r.t. K and setting this equal to zero gives:
So
If r = p, then this gives:
which in turn implies K = W. This shows that Sarah, a risk‐averse individual,
who will choose to fully insure when offered insurance at the actuarially fair
premium rate.
Sketch of solutions for Problem 4:
a) Margaret cannot consume more than what she earns, so:
c ≤ wh + V = 15(60 - l) + 100 = 900 - 15l + 100 = 1000 - 15l
When h = 30, l = 60 - 30 = 30 and c = 1000 – 15*30 = 550.
b) In this case, the slope is equal to w = 15. If V increases, the budget line shifts upwards
(left figure below, where V increases to V’ > V). If w decreases, the budget line rotates
inward around the endowment point (right figure, where w decreases to w’ < w).
c) The Lagrangian function is L(l,c,λ) = ln l + 2 ln c – λ(c – 1000 + 15l). The FOCs are
1/l - 15λ = 0 and 2/c – λ = 0
From here you can obtain than at any optimal choice Margaret will choose c = 30l.
Plugging that back in the budget constraint yields l* = 22.22 and c*=666.66. Hence, D
was not an optimal choice. At D, Margaret was working to little. In the further
discussion on why D is not optimal you should discuss the relationship between
Margaret’s MRS’s and the relative price of leisure and how different that is at the
optimal bundle.
Sketch of solutions for Problem 5:
a) The two agents have standard Cobb-Douglas utilities. For agent A the Lagrangian
function is L(xA,yA,λ) = (xA)1/2(yA)1/2 – λ(pxxA + pyyA - 3px - py). The FOCs are
(1/2)(xA)-1/2(yA)1/2 - λpx = 0 and (1/2)(xA)1/2(yA)-1/2 – λpy = 0
Plugging this back into the budget constraint gets you the demands xA* = (3/2) +
(py/2px) and yA* = (1/2) + (3/2)(px/py). You must use the same procedure to obtain the
demands for agent B which are xB* = (py/2px) and yB* = 1/2.
b) The excess demands for the two goods are:
xA* + xB* = (3/2) + (py/2px) + (py/2px) = 3
yA* + yB* = (1/2) + (3/2)(px/py)+ (1/2) = 2,
which that the equilibrium price ratio is px/py = 2/3. The equilibrium allocation is thus
xA* = 9/4, yA* = 3/2, xB* = 3/4 and yB* = ½.
c) The utilities are Cobb-Douglas, so the contract curve is just the set of allocations
where the MRS of the two consumers coincide. On the one hence MRSA = yA/xA
whereas MRSB = yB/xB. Hence, the contract curve are the allocations such that
yA/xA = yB/xB  yA/xA = (2-yA)/(3-xA)  yA = (2/3)xA
d) First we need to find the allocation that we actually want to support as an equilibrium
of the economy. The two consumers enjoy the same level of utility when
(xA)1/2(yA)1/2 = (xB)1/2(yB)1/2  (xA)(yA) = (3 – xA)(2 – yA)
By the 2nd Fundamental Theorem we will be able to support among the allocations
where the two consumers enjoy the same utility that one which in addition is Pareto
efficient, that is, where yA = (2/3)xA. Hence, the allocation we are looking to support is
(xA)((2/3)xA) = (3 – xA)(2 – (2/3)xA)  xA = 3/2 and yA = 1
After the transfer, the budget of agent B is Tpx + py whereas the budget of agent A is
now (3-T)px + py. We want to find the transfer T and the new equilibrium price ratio
px/py for which our consumers demand exactly the allocation we want to support, i.e.
xA = xB = 3/2, yA = yB =1.
Using the same method you used in section (a) you can obtain that the new demands
for these consumers are:
xA* = ((3-T)/2) + (py/2px) and yA* = (1/2)+ ((3-T)/2)(px/py)
xB* = (T/2) + (py/2px) and yB* = ½ + (T/2)(px/py)
From using yA* = 1 and yA* = 1 we can get that T* = 3/2.