Tutorial 4: Asymmetric Information
and Externalities
Matthew Robson
University of York
Microeconomics 2
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Question 1
Which of the following statements is false?
a) Adverse selection is an outcome of an informational deficiency.
b) Adverse selection will necessarily lead to market inefficiency.
c) Signalling is an effective way to improve information and
therefore helps cure the problem of adverse selection.
d) Asymmetric information could lead to moral hazard problem.
e) None of the above.
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Question 1
a)
Adverse selection is an outcome of an informational deficiency.
True, e.g Market for Lemons
• Buyers do not know the type of the car, a lemon or a peach
b) Adverse selection will necessarily lead to market inefficiency.
True, e.g. Different Quality Umbrellas
•
Can lead to a situation where the whole market is destroyed, no trading takes place
c)
Signalling is an effective way to improve information and therefore helps cure
the problem of adverse selection.
True, e.g. Qualifications
•
Firms receive a signal from a qualification, and can operate a separating equilibrium
d)
Asymmetric information could lead to moral hazard problem.
True, e.g. Health Insurance
•
Ex-Ante Moral Hazard can’t track if individual is being more risky (smoking, skiing)
•
Ex-Post Moral Hazard excess use of hospital services (unnecessary doctor visits)
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Question 1
Which of the following statements is false?
a) Adverse selection is an outcome of an informational deficiency.
b) Adverse selection will necessarily lead to market inefficiency.
c) Signalling is an effective way to improve information and
therefore helps cure the problem of adverse selection.
d) Asymmetric information could lead to moral hazard problem.
e) None of the above.
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Question 2
200 used cars for sale. The fraction of peaches is 𝑝 and the fraction of
lemons is 1 − 𝑝, where 𝑝 ∈ [0, 1]. Owners are willing to sell a lemon at
the price of 300. For peaches, it is 1,100. Buyers are willing to pay 400
for a lemon and 2,100 for a peach. Buyers do not know which car is lemon
or peach but sellers know. Which of the following statements is correct?
a)
b)
c)
d)
e)
The only equilibrium is all lemons sell for the price of 400.
Equilibrium only exists when 𝑝 = 1/2 .
An equilibrium: all cars sell for 1,100 when 𝑝 ≥ 7/17.
An equilibrium: lemon for 300 and peach for 1,100.
An equilibrium: lemon for 400 and peach for 2,100.
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Question 2
A buyer’s expected value is (at most):
𝐸𝑉 = 𝑝 × 2100 + 1 − 𝑝 400
𝐸𝑉 = 1700𝑝 + 400
If there is only 1 price, then buyers will pay that price only if:
𝐸𝑉 ≥ Price
If Pri𝑐𝑒 = 1100:
1700𝑝 + 400 ≥ 1100
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𝑝 ≥
17
Therefore (c).
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Question 3
Bob’s utility function is 𝑦 − 𝑥 2 , where 𝑦 is income and 𝑥 is hours worked per
day. He can work in the city for 8 hours per day, earning $100 a day. Alternatively,
he can rent a small farm from Mrs. Incencont. If he rents the farm, he can work
as many hours a day as he wishes. If he works 𝑥 hours per day, he can sell the
crops for a total of $20𝑥 per day, but he must pay Mrs. Incencont a daily rent of
$𝑅. Mrs. Incencont wants to charge the highest rent $𝑅 that she can and still be able
to have Bob rent from her. What is the highest rent she can charge?
a)
b)
c)
d)
e)
A penny less than $18.
A penny less than $32.
A penny less than $50.
A penny less than $64.
A penny less than $100.
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Question 3
Bob’s reservation value by working in the city is:
𝑢𝐶 = 𝑦 − 𝑥 2 = 100 − 82 = 36
On the farm, Bob’s income is revenue minus rent:
𝑦 =𝑓 𝑥 −𝑅
As Bob wants to maximise his utility, he maximises:
𝑢𝐹 = 𝑓 𝑥 − 𝑅 − 𝑐 𝑥
The farmer (Mrs. Incencont)’s problem is:
max 𝑅 ,
𝑠. 𝑡. 𝑢𝐹 = 𝑢𝐶
Now we use the rental contract and consequently:
𝑓 𝑥 − 𝑐 𝑥 − 𝑅 = 𝑢𝐶
⇒ 𝑅 = 20𝑥 − 𝑥 2 − 36:
The farmer maximizes R, by calculating the 𝐹𝑂𝐶: 20 − 2𝑥 = 0. So, 𝑥 = 10.
Hence, 𝑅 = 64, and the correct answer is (d).
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Question 4
There are two types of bicycles to be manufactured: H and L. Buyers value a
type H bicycle at $240 and an L bicycle at $180. Buyers cannot tell the type of a
bicycle before buying it but producers (i.e. sellers) know. The cost of producing an
H bicycle is $230, and the cost of producing an L bicycle is $190. Which of the
following statements is correct?
a) There can exist a market equilibrium in which only H bikes are traded.
b) The market has no equilibrium.
c) There does not exist a market equilibrium for H bikes to be traded, but there
exists a market equilibrium in which only L bikes are traded.
d) There can exist a pooling market equilibrium in which both H and L bikes are
traded at the price of $210.
e) There can exist multiple equilibria in this market.
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Question 4
• A buyer’s expected value is:
𝐸𝑉 = 𝑝 × 240 + 1 − 𝑝 × 180 = 60𝑝 + 180
60𝑝 + 180 ≥ 230
𝑝 ≥
5
6
• But then a high-quality seller can switch to making low-quality and
increase profit further on each bicycle sold.
• Since all sellers reason this way, the fraction of high-quality sellers
will shrink towards zero - but then buyers will pay only $180, which
is lower than the cost of $190.
• So there is no equilibrium in the market.
• So (b) is correct.
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Question 5
A labour market has two types of workers: H (for high ability) and
L (for low ability). An H worker’s marginal product is 100, and an L
worker’s marginal product is 60. There are 30% of all workers
belong to type H. So 70% is the fraction of L workers. Workers can
acquire education as a credible signal for high ability. Education
costs an H worker 2 per unit of education and costs an L worker 4
per unit.
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Question 5
Which of the following statements is false?
a)
If there exists a separating equilibrium, it necessarily requires every H worker to
obtain an education level higher than 10.
b) There is a separating equilibrium where every H worker obtains education level
15 and is paid a wage of 100, and every L worker obtains education level 10
and is paid a wage of 60.
c) There is a pooling equilibrium where every worker is paid a wage of 72 and the
education level that all workers get is less than 3.
d) There is a pooling equilibrium where every worker is paid a wage of 72 and
every worker has zero education level.
e) None of the above.
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Question 5
• The expected marginal product is 100 × 3 + 60 × 7 = 72. Since
72 < 100, the H workers have incentive to get a credible signal to
differentiate them from L workers. An H worker will do so if:
𝑤𝐻 − 𝑤𝐿 = 𝑎𝐻 − 𝑎𝐿 > 𝑐𝐻 𝑒
100 − 60 > 2𝑒
20 > 𝑒
And:
𝑤𝐻 − 𝑤𝐿 = 𝑎𝐻 − 𝑎𝐿 < 𝑐𝐿 𝑒
100 − 60 < 4𝑒
10 < 𝑒
• Which implies that 10 < 𝑒 < 20, so (a) is correct.
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Question 5
• For the pooling equilibrium, we know:
𝑤𝑝 = 72
ℎ 𝑎𝐻 − 𝑎𝐿
𝑒≤
𝑐𝐿
0.3 100 − 60
𝑒≤
4
𝑒≤3
• So, (c) and (d) are correct.
• Finally, (b) is false because this is not an equilibrium as L workers
would be better off by not obtaining any education unit.
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Question 6
Externalities:
a)
are not reflected in market prices, so they can be a source of economic
inefficiency;
b) do become reflected in market prices, so they can be a source of economic
inefficiency;
c) are not reflected in market prices, so they do not adversely affect economic
efficiency;
d) do become reflected in market prices, so they do not adversely affect economic
efficiency;
e) may or may not become reflected in market prices, but do not have an impact
on economic efficiency in either event.
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Question 6
Externalities:
a) are not reflected in market prices, so they can be a source of economic
inefficiency;
b) do become reflected in market prices, so they can be a source of economic
inefficiency;
c) are not reflected in market prices, so they do not adversely affect economic
efficiency;
d) do become reflected in market prices, so they do not adversely affect economic
efficiency;
e) may or may not become reflected in market prices, but do not have an impact
on economic efficiency in either event.
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Question 7
Dry cleaning of clothing produces air pollutants. Therefore, in the
market for dry cleaning services, equilibrium price
a)
b)
c)
d)
e)
and output are too low to be optimal;
and output are too high to be optimal;
is too low to be optimal, and equilibrium quantity is too high;
is too high to be optimal, and equilibrium quantity is too low;
is optimal, but there is an excess supply.
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Question 7
Dry cleaning of clothing produces air pollutants. Therefore, in the
market for dry cleaning services, equilibrium price
a)
b)
c)
d)
e)
and output are too low to be optimal;
and output are too high to be optimal;
is too low to be optimal, and equilibrium quantity is too high;
is too high to be optimal, and equilibrium quantity is too low;
is optimal, but there is an excess supply.
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Question 8
“Improved information may not generally improve gains to trade
of the market, but in some cases it does help improve the market
efficiency.” Is this claim true? If yes, justify your answer by two
relevant examples. If not, provide explanation.
• Yes, it’s true. Signalling in labour market is an example showing
that improved information need not change the output, while
education is costly. So it actually worsened the market’s efficiency.
• On the contrary, for second-hand car market, improved
information can restore the market, and therefore, improve market
efficiency.
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Question 9
The farmer Mrs. Incencont hires a worker Bill. The farmer can gain
revenue $20𝑥 per day where 𝑥 is hours worked by Bill per day. Bills
utility function is 𝑦 – 𝑥 2 , where 𝑦 is income and 𝑥 2 is the cost
function. Bill’s reservation value is $10. What optimal wage
contract can you design for Mrs. Incencont?
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Question 9
Suppose that Bill’s reservation value is 10. The farmer (Mrs. Incencont)’s problem is:
max 20𝑥 − 𝑠 . ,
𝑠. 𝑡. 𝑠 . − 𝑥 2 = 10
As, 𝑠(. ) = 𝑥 2 + 10, the problem becomes:
max 20𝑥 − 𝑥 2 − 10
𝑥
FOC = 20 − 2𝑥 = 0 ⇒ 𝑥 = 10
Mrs. Incencont can get 20 × 10 − 102 − 10 = 90 (at most) when Bill works 10
hours. Hence, similar to rental contract, here the optimal contract will be:
𝑠 . = 20𝑥 − 90
By doing this, Mrs. Incencont secures
20𝑥 − (20𝑥 − 90) = 90
Of course, in order to provide a positive incentive, here we take 89.99 so that the
net utility is 10.01 for Bill, which is higher than his reservation value 10. That is, the
optimal contract is 𝑠 . = 20𝑥 − 89.99.
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Question 9
There are 3 types of farmer, who can earn $𝑝𝑥:
$10𝑥,
$20𝑥,
$30𝑥
There are 3 types of workers, with reservation prices $𝑟:
$0,
$10,
$20
We have the farmers problem:
max 𝑝𝑥 − 𝑠 . ,
𝑠. 𝑡. 𝑠 . − 𝑥 2 = 𝑟
For farmers calculate your maximisation problem, and find your optimal wage
contract, for a given 𝑟.
For workers, find the minimum wage contract you would accept.
Find others who will take up a contract with you… Calculate your profit.
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