WINTER TERM 2021
DEPARTMENTALLY ARRANGED 2-HOUR ONLINE
EXAMINATION ECON0029: ECONOMICS OF
INFORMATION
Instructions
This is an open book exam. Answer ALL questions from Part A and Answer ONE question
from Part B. Questions in Part A carry 50 per cent of the total mark and questions in Part
B carry 50 per cent of the total mark each. In cases where a student answers more questions
than requested by the examination rubric, the policy of the Economics Department is that the
student’s first set of answers up to the required number will be the ones that count (not the
best answers). All remaining answers will be ignored.
For all questions: You may use all results and observations that were discussed in the lecture.
You should not replicate the derivations unless the problems explicitly asks for it!
Part A
Answer all questions from this Part.
A.1 (35 Points) A risk-neutral hedge fund wants to hire a manager for one of the companies
she owns. Assume that the companie’s value either stays constant (x1 = 0) or increases
by £200 million (outcome x2 = 200) in the next year. The probability for these events
depend on the manager’s effort. He can choose to exert high or low effort: eH or eL.
The effect of his effort choice on the outcome probabilities is summarised in the following
table:
eL eH
x1 1− pL 1/4
x2 pL 3/4
with 0 ≤ pL ≤ 3/4.
The manager’s disutility from exerting effort is given by v(eL) = 6 and v(eH) = 8. His
Bernoulli utility function with respect to money (in millions) is given by u(w) =
√
w. His
utility from exerting effort ej with j ∈ {L,H} and receiving a wage of w million pounds
is then given by: √
w − v(ej).
When the manager does not work for the company, his utility is U = 0.
The hedge fund makes the manager a take-it-or-leave-it offer.
(a) Suppose (only for this part) that effort is verifiable.
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i. What does a contract specify in this setting (with verifiable effort)?
Answer: A contract specifies an effort level, a wage that is paid to the manger
when he chooses the right effort level and a punishment wage when he chooses
the wrong effort.
ii. Determine for any pL with 0 ≤ pL ≤ 3/4 the optimal contract if effort is ver-
ifiable. When you use results from the lecture describe intuitively why they
hold.
Answer: IR constraints are binding to induce high effort: wH = 82 = 64, to
induce low effort:wL = 62 = 36
3/4 · 200− 64 ≥ pL · 200− 36⇔ pL ≤ 61
100
The optimal contract will induce high effort whenever pL ≤ 61100 . In this case,
wH = 64 and (for example) wL = 0.
Otherwise, the optimal contract induces low effort and wL = 36 and wH = 0.
Intuition for binding constraints...
iii. What is the company’s profit as a function of pL?
Answer: For 0 ≤ pL ≤ 61100 the profit is
3/4 · x2 − wH = 3/4 · 200− 64 = 86
For 61
100
≤ pL ≤ 3/4 the profit is
pL200− 36

(b) Now turn to the case when effort is not verifiable.
i. Set up the hedge fund’s maximisation problem. Describe verbally the role of
the constraints.
Answer:
max
A∈{l,H},w1,w2
pA(200− w2) + (1− pA)(−w1) s.t.
pAw
2 + (1− pA)w1 ≥ v(eA) (IR)
pAw
2 + (1− pA)w1 − v(eA) ≥ p−Aw2 + (1− p−A)w1 − v(e−A) (IC)
With the following notation: A = L then −A = H and vice versa.
The IR constraint ensures that the manager agrees to the contract and the IC
constraint ensures that he chooses the right effort level.
ii. Suppose that pL = 1/4. Determine the optimal contract if effort is not verifiable.
Answer: We calculate the expected profit of the hedge fund for the best
contract that induces high effort. When we denote Ui =
√
wi, the binding IC
and IR constraint read:
Intuition why IR and IC must be binding...
U23/4 + U11/4− 8 = U21/4 + U13/4− 6
U23/4 + U11/4− 8 = 0
This yields U1 = 5 and U2 = 9. And correspondingly, w1 = 25 and w2 = 81
2
The hedge funds expected profit is then:
3/4 · (200− 81) + 1/4(−25) = 83.
This exceeds the profit from the optimal contract that induces low effort (this
is the same as in the SI case)
1/4 · 200− 36 = 14

A.2 (15 marks) Sarah bought a firework factory. The factory’s value is £1 million. After
paying this price she still has £1 million in her bank account (the interest rate is 0). She
does not have any further assets and is protected by limited liability.
Sarah’s plan is to develop a new ultra-explosive type of firework in her factory. The
development of this new type of firework is very risky. With probability 1/2 it will fail
and cause a huge fire destroying Sarah’s factory entirely but also damaging a neighbouring
factory which is owned by Bo.
If there is a fire, the damage to Bo’s factory will amount to £1.5 million. If the fire
occurs, Bo will claim this amount of money from Sarah.
If the development succeeds, Sarah will make a profit of £4 million and her factory will
remain its value.
Sarah’s Bernouli utility function with respect to wealth w is given by
√
w.
(a) What is Sarah’s wealth if she succeeds?
Answer: Value of her cash+ value of her factory +profits:
1 + 1 + 4 = 6

(b) What is Sarah’s wealth when she fails?[Hint: Take Sarah’s limited liability into
account]
Answer: When she fails the factory will be worth 0 and she will not make any
profits. She will be liable to Bo’s repairing cost claims of 1.5. Her available assets
in this situation will only be the cash in the bank: 1
Therefore she has to pay all her cash but is protected by limited liability from the
remaining claim. Her wealth in this situation will be 0.
(c) A insurance broker offers Sarah to insure her factory (only the factory, i.e. in case
of a fire the insurer pays out the value of the factory to Sarah) for the actuarially
fair premium.
Suppose Sarah buys this insurance and pays the premium: What is her wealth if the
development succeeds and what is her wealth after a fire?
Answer: The actuarially fair premium is given by the expected damage of Sarah’s
factory:
1/2 · 1 + 1/2 · 0 = 1/2.
So if Sarah buys the insurance her remaining cash holdings will be 1/2
If there is no fire her wealth will be: Cash + value of factory + profit:
1/2 + 1 + 4 = 5.5.
3
If there is a fire, the insurance will pay out the value of her factory. Before she meets
Bo’s claim her cash balance will be at 1.5. She can therefore completely pay out Bo
and will end up with a cash balance of 0. Since her factory will also be destroyed
and she will not make any profits her wealth will be 0.
(d) Should Sarah buy the insurance for her factory? Give an intuition for your answer!
Answer: Sarah should not buy the insurance despite being risk averse. As we
have seen above in the case of a fire her wealth will be 0 regardless of whether she
bought the insurance or not. And in the case of no fire, she will have strictly hire
wealth when she does not buy insurance. She can use the limited liability to default
on any claims from Bo that would lead to a negative wealth level. If she buys the
insurances she has more wealth in the case of a fire (the value of the factory) and
therefore Bo can claim more money from her so that Sarah does not profit from the
extra money she gets in the case of fire.

Part B
Answer one question from this part, either B.1 or B.2.
B.1 (50 marks)
Bo, a risk-neutral app developer, needs funding to create a new smartphone game. His
last project was a complete failure so he owns no assets today. For developing the game
he needs to invest a fixed amount of £1 million. If the game will be a success, Bo will
earn a revenue of £2 million. If it fails he will earn a revenue of £0.
After the investment, Bo can either put all the money in the development of the game or
he can embezzle a fraction of the money and use it for his own private consumption.
Embezzling would yield him a private benefit of B with £0 < B ≤ £1 million.
A potential lender cannot observe whether Bo embezzled money or not. If Bo enters a
contract with a lender he will be protected by limited liability.
If Bo allocates all the funds to the development of the game, the probability of it being
successful is pH with 1/4 ≤ pH ≤ 1. Otherwise, it is a success with probability pL = 1/4.
If Bo decides to dismiss the project and not invest he will earn £0.
There is only one potential lender. This lender is also risk-neutral and if the she does not
contract with Bo her outside option is £0.
Assume that both Bo and the potential lender accept the contract in the case that they
are indifferent between accepting the contract and taking their outside option.
(a) i. What is the Net Present Value (NPV) of the project when Bo does not embezzle
money? Express it as a function of pH .
Answer: The NPV of investing with no embezzlement is:
pHR
S − I = pH2− 1

ii. Suppose Bo had enough money to fund the investment on his own: When would
he prefer the investment without embezzlement over not investing?
Answer: The NPV is higher than the outside option if
pH ≥ 1/2
.
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iii. What is the Net Present Value (NPV) of the project with embezzlement? Ex-
press it as a function of B.
Answer: The NPV of investing with embezzlement is
pLR
S − I + B = 1/4 · 2− 1 + B = B − 1/2

iv. Suppose Bo had enough money to fund the investment on his own: When would
he prefer the investment with embezzlement over not investing?
Answer: The NPV is higher than the outside option, if
B ≥ 1/2

v. Suppose Bo had enough money to fund the investment on his own: What would
he do?
Answer: Investing with no embezzlement has a higher NPV than investing an
embezzling if:
2pH − 1 ≥ B − 1/2⇔ pH ≥ B/2 + 1/4
So we have to go over the following cases:
If B < 1/2 then not inversting dominates investing with embezzlement and we
have that Bo invests without embezzlement iff pH ≥ 1/2 and does not invest if
pH < 1/2.
If B ≥ 1/2 then investing with embezzlement dominates not investing so in
this case Bo invests without embezzlement if pH > B/2 + 1/4 and invests with
embezzlement if pH < B/2 + 1/4. In the case that pH = B/2 + 1/4 Bo is
indifferent between investing with or without embezzlement
(b) Now assume that Bo has no funds.
i. What type of asymmetric information is present in this model? Explain! What
does it mean that Bo is protected by limited liability? What does a contract
between Bo and a lender specify?
Answer:
There is moral hazard since the agent (Bo) can embezzle after the contract is
concluded (ex-post) and whether he embezzles is not verifiable. (The lender is
the principal.) Limited liability means that the Bo cannot be forced to pay more
than he owns. Since he has no initial funds Bo can never be forced to pay more
than the the revenue of the project in each case (failure success).
Since Bo has no initial assets the size of the investment must always be equal to
I. A contract specifies payments to the lender in the case of success and failure:
RSl , R
F
L and payments to Bo in the two cases: R
S
b , R
F
b .

ii. Write down the conditions every contract that is accepted by both parties, re-
spects limited liability, and induces Bo not to embezzle money has to fulfil.
Describe verbally what they mean.
Answer:
Limited liability: RXB ≥ 0 for X ∈ {S < F}: Bo can always default, since he
has no assets he can never be forced to pay an
Break even: pHR
S
l +(1−pH)RFl ≥ 1: The lender must break even in expectation
Individual rationality: pHR
S
b + (1− pH)RFb ≥ 0: Bo must agree to the contract
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IC for high effort (no embezzling): pHR
S
b +(1−pH)RFb ≥ pLRSb +(1−pL)RFb +B:
Bo must choose not to embezzle

iii. Assume that B < £1/2 million. Show that there cannot be a contract that
induces Bo to embezzle.
Answer: The lender’s participation constraint for a contract that induces
embezzlement reads:
pLR
S
l ≥ I ⇔ I − pLRSl ≤ 0
From above we know that if B < 1/2 the if Bo was having enough money he
would prefer not investing over investing and embezzling. That means:
pLR
S + B ≤ I.
Since B > 0 we have:
pLR
S < pLR
S + B ≤ I.
On the other hand,Since RSb ≥ 0 and RSl = RS −RSB we have that
pLR
S ≥ pLRSl ≥ I

iv. Argue verbally why Bo does not get any payment in the case of a failure.
Answer:
v. Assume that B < £1/2 million. Derive the formula for the minimal amount
of assets needed so that Bo can obtain funding for the game from the above
conditions on the contract.
Answer: From above we know that there can only be a contract that induces
no embezzlement. Every contract must therefore respect the IC constraint:
pHR
S
b ≥ pLRSB + B ⇔ RSb ≥
B
pH − pL
The lender’s participation constraint reads:
pHR
S
l ≥ I ⇔ RSl ≥
I − A′
pH
Plugging in RS = RSl + R
S
b yields:
A′ ≥ I + B
pH − pLpH −R
SpH = 1 +
B
pH − 1/4pH − 2pH = A¯

vi. Suppose that pH = 5/8. For which values of B can there exist a contract? Give
an intuition for your answer!
Answer:
Since Bo has no funds, A′ = 0 and it must hold that A ≤ 0. If we plug in
pH = 5/8 we arrive at:
1 +
B
5/8− 1/4 · 5/8− 2 · 5/8 ≤ 0⇔ B ≤ 3/20
If Bo is too skilfull in embezzling money, the incentives that the contract have
to offer him will come at such a high cost in terms of agency rent that the lender
cannot break even.
6
vii. Assume now that B = £1/10 million and pH = 5/8. Suppose Bo has only access
to one single lender. This lender is risk-neutral and can make a take-it-or-leave-
it offer. What contract will she propose? Argue verbally which constraints must
be binding.
Answer: The monopolist lender will propose the contract that is best for her.
... Binding IC constraint
pHR
S
b = pLR
S
b + B ⇔ RSb =
B
pH − pL = 1/10 · 8/3 = 4/15

(c) Suppose now that pH = 3/4. Assume that by taking a course in accounting Bo
can change his ability to embezzle money. More precisely, assume that B could be
chosen by Bo before he meets the potential lender. He is free to choose any B with
£0 million ≤ B < £1/2 million. The lender will observe which B Bo has chosen
before she makes a take-it-or-leave-it offer. What would be the optimal B for Bo.
Explain your answer also intuitively.
Answer: Bo’s expected profit is given by:
pH
B
pH − pL = 3/2B
and therefore increasing in B. From above we can derive that there will be a contract
iff
1 +
B
3/4− 1/4 · 3/4− 2 · 3/4 ≤ 0⇔ B ≤ 1/3
Therefore the optimal B will be B = 1/3.
B.2 (50 marks)
A risk-neutral company employs a specialist to construct a more efficient machine for the
production of one of its products. Let t denote the time that the specialist spends on
developing this new machine with t = 1 meaning that the specialist works the whole year
on the machine (1 is the maximal amount of time he can choose to work on the machine).
If the specialist spends time t on developing the new machine, the company’s profits will
increase by t million $.
Since the machine is constructed on the company’s premises the company can log how
much time the specialist spends on building the machine during the year he is employed.
The logs are verifiable.
The specialist is an expected utility maximiser. When he spends time t on building the
machine and receives a wage of w (in million $) his utility is given by
U(w)− kiv(t),
with
U(w) =
√
w,
and disutility from working time:
v(t) = t.
There are two types of specialists. The workaholic type G does not suffer as much as the
leisure type B from spending time at work. Assume that 1/
√
2 < kG < kB.
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The probability that the specialist which the company faces is a workaholic (type G) is
1/2. The specialist is protected by limited liability. This means that the company can
never enforce a negative wage: w ≥ 0. The company can compose a menu of contracts
and offer them to the specialist in a take-it-or-leave-it manner. Each contract can be
contingent on verifiable outcomes.
When the specialist does not work for the company his utility is given by U = 0.
(a) i. Who is the principal and who is the agent? What are the risk preferences of the
specialist? Explain your answer.
Answer: The company is the principal: she writes the contract and can commit
to it. The specialist is the agent. He is better informed than the principal. He
is risk averse since his Bernoulli utility function is strictly concave:
U ′′(w) < 0

ii. What type of asymmetric information is present in this situation? Explain your
answer!
Answer: There is asymmetric information in form of adverse selection because
before the specialist signs the contract he knows his type the parameter ki. This
asymmetric information is ex-ante.
(b) Derive the optimal contract (for the company). Use the knowledge from the lecture
for these derivations.
i. Suppose (for this part only) that the company could observe the specialist’s type
(symmetric information).
Set up the company’s maximisation problems for both types and solve for the
optimal contracts.
If you assume that constraints bind give a small verbal intuition for why this is
the case in the optimum.
Answer: Given a specialist with type i the companies maximisation reads
max
ti∈[0,1],wi≥0
ti − wis.t.√wi − kiti ≥ 0
We can assume that the IR constraint of both types is binding, otherwise we
could lower the wage.
Plugging the binding IR constraint into the objective yields:
max
ti
ti − k2i t2i
FOC yield:
1− k2i 2ti = 0⇔ ti =
1
2k2i
This is interior if ki > 1/
√
2.
SOC
−2k2i < 0,
the problem is concave. So this is a maximiser. The corresponding wi =
1
4k2i

8
ii. Show that the two optimal contracts from the symmetric information case do
not comprise an incentive-compatible menu when the specialist’s type are not
observable (asymmetric information).
Answer: The good type has incentive to misrepresent his type since when he
does so his expected utility is given by√
1
4k2B
− 1
2k2B
kG =
1
2kB
(1− kG
kB
) > 0 = U
This exceeds his expected utility from reporting his type truthfully.
iii. Set up the maximisation problem for the case that the type is not contractible
(asymmetric information). State and briefly describe the different constraints
in this problem.
Answer:
max
wG,wB ,tG.tB
1/2(tG − wG) + 1/2(tB − wB)s.t.
√
wG − kGtG ≥ √wB − kGtB (IC-G)√
wB − kBtB ≥ √wG − kBtW (IC-B)√
wG − kGtG ≥ 0 (IR-G)√
wB − kBtB ≥ 0 (IR-B)
IC-G makes sure that G prefers his contract over the contract for B and does
not try to mimic B.
IC-B makes sure that B prefers his contract over the contract for G and does
not try to mimic G.
IR-G makes sure that G prefers his contract over not contracting
IR-B makes sure that B prefers his contract over not contracting

iv. Suppose from now on that kG = 3/4 and kB = 1. Solve for the optimal menu of
contracts. [Hint: Use your knowledge from the lecture and problemsets. Assume
first that certain constraints are binding and verify that the resulting solution
also fulfils the remaining constraints]
Answer: As usual we assume that IC−B and IC−G is binding and will then
verify that the solution fulfils IC −B and IR-G
Binding IB-B gives us:
√
wB = kBtB ⇔ wB = k2Bt2B
Plugging this in the binding IC-G constraint yields:
√
wG − kGtG = kBtB − kGtB ⇔ wG = (kGtG + (kB − kG)tB)2
Plugging the wages into the objective yields
1/2[tG − (kGtG + (kB − kG)tB)2] + 1/2[tB − k2Bt2B]
FOCs w.r.t to tG yields:
1/2(1− 2kG(kGtG + (kB − kG)tB) = 0⇔ tG = 8/3− 17/3tB
FOCs w.r.t to tG yields:
tB = 8/3− 3tG
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Solving this together gives us:
tB = 1/3, tG = 7/9
It follows that:
wB = 1/9, wG = (3/4 · 7/9 + 1/4 · 1/3)2 = 4/9
We need to verify IC-B
√
wG − tGkB = −0.1111 < 0 = U
which is by the binding IR constraint what B gets if he chooses his contract.
We need to verify IR-G:
√
wG − tGkG = 0.83333 > 0 = U

(c) Suppose from now on that kG = 3/4 and kB = 1. Suppose now that the company
has the opportunity to send the specialist to an assessment centre before contracting.
There are two assessment centres available but the company can only partner with
one of them. The assessment centres differ in what test they will conduct on the
specialist.
Assessment centre 1 conducts a test on the specialist which type G can always pass
whereas type B will fail. In contrast, assessment centre 2 conducts a test which type
B can always pass whereas type G always fails.
When the company partners with one of the assessment centres, she can send the
specialist to this centre and the centre reports back whether the specialist passed or
failed the test.
With which assessment centre is the company going to partner and how much money
would she be willing to pay for the opportunity to send the specialist to the centre
before contracting?
Answer: The two SI contracts are given by: wSIG = 4/9, t
SI
G = 8/9 and w
SI
B =
1/4, tSIB = 1/2
We know from above that the SI contract cannot be implemented under AI since
IC-G is violated: √
wSIG − 3/4tG = 0 ≥
√
wB − kGtB = 1/8
We observe that IC-B is fulfilled:√
wSIB − kBtSIB = 0 ≥
√
wSIG − kBtSIW = −2/9X
Therefore if the company partners with Assessment centre 2 they can implement
the two SI contracts: The company offers the contract (wSIG , t
SI
G ) to the specialist
without any conditions. But if the specialist wants to have the contract (wSIB , t
SI
B )
the company sends this specialist to Assessment centre 2 and only offers (wSIB , t
SI
B )
if the specialist passed the test and therefore proofed to be type B.
Since B has no incentive to mimic G and with the test from Assessment centre 2 G
can no longer mimic B this implements the first best SI menu of contracts.
The company therefore is willing to pay the difference between her expected profit
in the SI and AI model:
V SI − V AI = 5/72