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ECON20022 Sample Exam

Microeconomics 4
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Answer the Question in Section A and TWO QUESTIONS in Section B
Section A counts for 40% of the exam mark; Section B counts for 60% of
the exam mark.
You are required to submit typed responses. Your exam responses will not be
accepted if it is not typed. You can include images of algebra or graphs if you
Where relevant, questions include word limits. These are limits, not targets.
Excellent answers can be shorter than the word limit. If you go beyond the word
limit the additional text will be ignored. Where a question includes a word limit
you HAVE to include a word count for your answer (excluding formulae). You
could use https://wordcounter.net to obtain word counts.
Candidates are advised that the examiners attach considerable importance to
the clarity with which answers are expressed
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© The University of Manchester, 2020
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Section A (This section counts for 40% of the exam mark)
Question 1
a) Answer each part of the following question. Show the appropriate mathematical
steps. You should also explain your answer and the process intuitively (you can
use diagrams too).
Suppose there are two consumers in an exchange economy, consumer A and
consumer B, who consume only two goods, X and Y, available in the economy.
There are 20 units of X available and 20 units of Y.
Assume A’s preferences are described by 𝑈𝐴 = 𝑋𝐴0.5 𝑌𝐴0.5 and B’s preferences
are described by 𝑈𝐵 = 2𝑋𝐵 𝑌𝐵 , where 𝑋𝐴 , 𝑌𝐴 , 𝑋𝐵 , and 𝑌𝐵 are the consumption of
X and Y by consumers A and B, respectively. Now derive an equation for the
contract curve. [Word limit: 50] [10 marks]
Suppose that consumer A has an initial endowment of 5 units of X and 15 units
of Y, and consumer B has the remainder of what’s available. Their preferences
are the same as in part (I). Show, using the concept of MRS and the Edgeworth
Box, that a trade could benefit both consumers. [Word limit: 50] [5 marks]
Given the same preferences, now assume the consumers can trade as much
as they like at the prices of 𝑃𝑋 = 1 and 𝑃𝑌 =1. Starting out with the same
endowments as in part (I), how much will each consumer want to buy/sell of
each good? Is the result a competitive equilibrium? [Word limit: 100] [5 marks]
b) As we discussed in the lecture, Vickrey auction (1961) is considered to be
demand revealing as each rational bidder’s dominant strategy is to bid their true
value. However, experimental studies document overbidding behaviour as
bidders could increase the probability of winning the auction by overbidding
without adding huge costs of losing (as they pay the second highest bid). Some
people criticise such results from lab experiments—they are not that sincere in
choosing their actions in the lab because they receive the monetary endowment
for free. To address such a concern, propose an experimental design that can
examine bidders’ sincere biding behaviour, given induced and independent
private values and Vickrey auction in the lab. [Word limit: 500] [20 marks]
The Vickrey auction is efficient in the case of private values6. To see this, note first that it is optimal--in fact, a dominant strategy--for buyer i to set bi =vi, i.e., to bid his true valuation.
In particular, bidding below vi does not affect buyer i’s payment if he wins (since his bid does not depend on his own bid); it just reduces his chance of winning—and so is not a good
strategy. Bidding above vi raises buyer i’s probability of winning, but the additional events in which he wins are precisely those in which someone else has bid higher than vi. In such
events buyer i pays more than vi, also not a desirable outcome. Thus it is indeed optimal to bid bi =vi, which implies that the winner is the buyer with the highest valuation, the
criterion for efficiency.
Unfortunately, the Vickrey auction does not remain efficient once we depart from private values.
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Section B (This section counts 60% of the exam mark)
Answer TWO questions from this section.
Question 2
a) [Word limit 500] Consider the following Public good game. There are 4 players in
a group and each player has £y as endowment. Player i’s pay-off function is given
by: 𝜋𝑖 = 𝑦𝑖 − 𝑔𝑖 + 𝑎 ∑4𝑗=1 𝑔𝑗 , where 𝑔𝑖 is player i’s voluntary contribution to the
public good, 𝑎 is the marginal per capita return from a contribution to the public
good and 0 < 𝑎 < 1 < 4𝑎. Following rational choice theory, if it is common
knowledge that every player is rational and self-interested and they can do
backward induction, the dominant strategy of each player is to give zero to the
public good (i.e. 𝑔𝑖 = 0). Suppose, a researcher conducts a finitely repeated public
good game with the randomly chosen players in each group over all rounds and
the same pay-off function described above.
What results would the researcher expect based on the results from the
existing literature (e.g. Fehr and Gächter 2000) ? [5 marks]
Explain intuitively whether an institution with pre-commitment of contribution
through an endogenous group formation can improve the outcome? Briefly
state how one can conduct an experiment to test this. [15 marks]
a) State and explain the Coase mechanism. Critically evaluate the relevance of
Coase mechanism [Word limit 500] [10 marks]
Question 3
a) Consider a model of voluntary incentive mechanism design for protecting
endangered species on private land. After a regulator has identified
endangered species on private land, she wants private landowners to retire the
land from production. The landowners suffer a monetary loss when they retire
land for species protection. They would voluntarily participate in the program of
species protection if they received monetary compensation from the regulator
to offset their loss. The regulator designs a contract to maximize social welfare
from species protection subject to the landowner’s participation constraint.
Social welfare is the utility of the individual landowner and social benefits from
species protection, minus the monetary compensation scaled by the social
value of public funds.
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 Each landowner has fixed land-endowment, i.e., 𝐴 acres, and 𝑖th landowner
retires 𝑎𝑖 (with 𝑎𝑖 ≤ 𝐴) acres of land
Suppose, there are only two types of landowners—high (who own high quality
land and that means they have higher opportunity costs of land retirement) and
Each landowner’s rent function from land is 𝜋𝑖 (𝐴 − 𝑎𝑖 , 𝜃 𝑖 ), where 𝜃 𝑖 denotes
land quality, 𝑖 = high, low. The rent function is increasing and concave; and
marginal-rent is increasing in types.
Also note that (i) 𝜋𝑖 (𝐴, 𝜃 𝑖 ) is the rent when a landowner does not participate in
the program; and (ii) landowners are risk neutral
𝑇 𝑖 denotes monetary transfer from the regulator to the landowner 𝑖
𝐵(𝑎) denotes social benefit from species protection when 𝑎 acres of land
retired. This function is concave in acres
Under conditions of complete information about the land quality, the
regulator knows the value of land and offers a contract specifying a
monetary compensation for the land’s retirement. Set up the objective
function and identify the constraints. Comment on the optimal transfer
the farmers would receive in this case. [Word limit 100] [5 marks]
Under asymmetric information about the quality of land, the regulator
cannot distinguish the types—she does not want to disincentives the
high-type by offering less money and does not want to pay higher than
the true opportunity costs for the low type (due to the opportunity costs
of public fund). The regulator seeks to maximize social welfare by
choosing an optimal contract, designed to extract private information
cost-effectively and protect the habitat efficiently. Set up the objective
function and identify the constraints. Assuming interior optimal solution,
comment on the optimal transfers that each type of farmers would
receive in this case. Explain why this would be a second-best solution.
[Word limit 150] [20 marks]
a) Explain (intuitively and with Edgeworth box diagram) the role of the Second
Welfare Theorem reaching a more equitable Pareto equilibrium. [Word limit
200] [10 marks]
Please Turn Over
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Question 4
b) Rational choice theory assumes that economic agents are rational and selfinterested. Based on the evidence from behavioural laboratory experiments
(e.g., dictator games), behavioural economists suggest that people are not
always self-interested, rather they have intrinsic preferences for others’ wellbeing (e.g., altruism, inequity aversion). However, some other studies in
behavioural economics investigate this further and disentangle the intrinsic
preferences into several other factors. Following the discussion in the lecture,
state two such studies that try to disentangle the true intrinsic preferences
based on dictator games in the lab. Explain clearly and briefly the following: (i)
what each study addresses; (ii) brief description of the experimental design;
and (iii) intuitive explanations. [Word limit: 600] [15 marks]
c) Write a brief summary of the following paper. In the summary, you may want to
include the main research questions, motivation, research designs, and main
findings of the paper. Next explain how the findings of this paper are
relevant/useful in reality by providing one real-world example (choose a
different example than the one used in the paper). [Word limit 600] [15 marks]
Allcott, H., 2011. Social norms and energy conservation. Journal of
public Economics, 95(9-10), pp.1082-1095.