Intermediate Microeconomics

Take-home assignment
Section A
Questions
1. Argue that if the utility that a given consumer obtains from the expected
prize of a lottery is higher than the expected utility he would enjoy from
the lottery itself, then it must be the case that the certainty equivalent of
the lottery is lower than the expected prize.
2. Consider a game between two players, where both players have a domi-
nant strategy. De?ne dominant strategy equilibrium and Nash equilibrium
carefully and argue that the dominant strategy equilibrium is a special case
of Nash Equilibrium.
3. Which assumption about consumer preferences does each of the following
individuals violate?
(a) Jack likes rugby more than football; football more than cricket and
cricket more than rugby.
(b) Anne prefers apple juice to orange juice but cannot decide how she
feels about grape juice.
(c) Ben likes superhero comic books but prefers 5 comic books to 10
comic books.
4. Explain, also with the aid of a diagram, how consumers in an economy can
be made better o¤ if their marginal rates of substitution are not equal.
5. What are production externalities and how can they be eliminated through
a merger? Explain, also with the aid of an example illustrated by a dia-
gram.
2
Section B
Problems
6. Two oligopolistic alluminium manufacturers are engaged in bitter compe-
tition with one another. The biggest ?rm, Big Alluminium Giant (BAG)
is deciding whether to expand capacity or hold the line. The smallest ?rm,
Little Alluminium Giant (LAG), is also considering expansion. The table
below shows payo¤s for the ?rms under various scenarios:
LAG n BAG Don?t expand Expand
Don?t expand 3, 4 2, 3
Expand 4, 2 1, 1
(a) De?ne a dominant strategy and determine if any of the two players
above have a dominant strategy.
(b) De?ne Nash equilibrium and determine what is (are) the Nash equi-
librium(a) in this game.
(c) Suppose now that the game is played sequentially, with BAG moving
?rst. Draw the extensive form of the game.
(d) Does the sequential game in (c) lead to the same equilibrium(a) you
found in the simultaneous move game? Does BAG have a ?rst mover
(e) Would your answer change if it was LAG to move ?rst?
7. Suppose that consumers value a high-quality used laptop computer at a
price of 400, while they value a low-quality used laptop at 100. The supply
of high-quality laptops is QH = PH ??100, while the supply of low-quality
laptops is QL = 2PL ?? 50. Potential buyers cannot tell the di¤erence
between high-quality and low-quality laptops when purchasing one.
(a) Assume that buyers believe there is a 50% probability that a used
laptop will be of high quality. What would be the price that buyers
are willing to pay for any used laptop?
(b) If the price determined in (a) is o¤ered in the market for used laptops,
how many high-quality laptops will be made available in the market?
How many low-quality laptops will be available in the market? Are
buyers correct in their assumption that 50% of the used laptops for
sale are of high quality? Explain.
(c) What would you expect to happen over time as information about the
true odds of buying a high-quality laptop becomes known? Explain.
(d) Argue that providing a guarantee against laptop faults may improve
the outcome.
3
8. Philippa is a farmer, with a utility function of U = pI, where I is her
income. If the weather is good, she will earn 100,000. If there is a hail-
storm, she will earn only 50,000. The probability of a hailstorm in any
given year is 30%.
(a) What is Philippa?s expected income? And her expected utility?
(b) Suppose a crop insurer makes the following o¤er to Philippa: In years
when there is no hailstorm, Philippa pays the insurer 16,000. In years
when there is a hailstorm, the insurer pays Philippa 34,000. What is
Philippa?s expected income? And her expected utility?
(c) Commen on the following statement referring to your answers to
part (a) and (b): “The insurance agreement in (b) reduces Philippa?s
expected income. Therefore, it must make her worse o¤”.
(d) Suppose instead that the insurer o¤ers Philippa the following: In
years when there is no hailstorm, Philippa pays the insurer 10,000;
in years when there is a hailstorm, the insurer paus Philippa 20,000.
How does Philippa?s expected income and expected utility compare
to the uninsured outcome in (a) and the insured outcome in (b)?
(e) Argue that contracting insurance between a risk averse agent and a
risk neutral insurance company constitutes a Pareto improvement.
9. A pizza chain recently o¤ered the following special promotion: “Buy one
pizza at full price and get your next three pizzas for just 5 pounds each!”.
Assume that the full price of pizza is 10, your daily income 40 and the
price of all other goods 1 pound per unit.
(a) Draw budget constraints for pizza and all other goods which re?ect
your situations both before and during the special promotion.
(b) How is this special o¤er likely to alter your buying behaviour?
(c) How might your answer to (b) depend on the shape of your indi¤er-
ence curves?
(d) Argue that you are not made worse o¤ by the promotion.
4
10. Chris and Pat like both co¤ee and biscuits. Chris views cups of co¤ee and
packets of biscuits are perfect one-to-one substitutes. Pat believes that
co¤ee and biscuits are perfect complements, and always consumes them
in one-to-one proportions (one cup of co¤ee and a packet of biscuits).
Initial endowments are as follows: Chris has 3 cups of co¤ee and 3 packets
of biscuits; Pat has 1 cup of co¤ee and 2 packets of biscuits.
(a) Construct an Edgeworth box for Chris and Pat.
(b) Draw their indi¤erence curves through the endowment point and ar-
gue that there is scope for Pareto improving trades.
(c) Derive the contract curve.
(d) How would you construct the utility possibility frontier for this small
?economy??
5
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Intermediate Microeconomics

Take-home assignment
Section A
Questions
1. Argue that if the utility that a given consumer obtains from the expected
prize of a lottery is higher than the expected utility he would enjoy from
the lottery itself, then it must be the case that the certainty equivalent of
the lottery is lower than the expected prize.
2. Consider a game between two players, where both players have a domi-
nant strategy. De?ne dominant strategy equilibrium and Nash equilibrium
carefully and argue that the dominant strategy equilibrium is a special case
of Nash Equilibrium.
3. Which assumption about consumer preferences does each of the following
individuals violate?
(a) Jack likes rugby more than football; football more than cricket and
cricket more than rugby.
(b) Anne prefers apple juice to orange juice but cannot decide how she
feels about grape juice.
(c) Ben likes superhero comic books but prefers 5 comic books to 10
comic books.
4. Explain, also with the aid of a diagram, how consumers in an economy can
be made better o¤ if their marginal rates of substitution are not equal.
5. What are production externalities and how can they be eliminated through
a merger? Explain, also with the aid of an example illustrated by a dia-
gram.
2
Section B
Problems
6. Two oligopolistic alluminium manufacturers are engaged in bitter compe-
tition with one another. The biggest ?rm, Big Alluminium Giant (BAG)
is deciding whether to expand capacity or hold the line. The smallest ?rm,
Little Alluminium Giant (LAG), is also considering expansion. The table
below shows payo¤s for the ?rms under various scenarios:
LAG n BAG Don?t expand Expand
Don?t expand 3, 4 2, 3
Expand 4, 2 1, 1
(a) De?ne a dominant strategy and determine if any of the two players
above have a dominant strategy.
(b) De?ne Nash equilibrium and determine what is (are) the Nash equi-
librium(a) in this game.
(c) Suppose now that the game is played sequentially, with BAG moving
?rst. Draw the extensive form of the game.
(d) Does the sequential game in (c) lead to the same equilibrium(a) you
found in the simultaneous move game? Does BAG have a ?rst mover
(e) Would your answer change if it was LAG to move ?rst?
7. Suppose that consumers value a high-quality used laptop computer at a
price of 400, while they value a low-quality used laptop at 100. The supply
of high-quality laptops is QH = PH ??100, while the supply of low-quality
laptops is QL = 2PL ?? 50. Potential buyers cannot tell the di¤erence
between high-quality and low-quality laptops when purchasing one.
(a) Assume that buyers believe there is a 50% probability that a used
laptop will be of high quality. What would be the price that buyers
are willing to pay for any used laptop?
(b) If the price determined in (a) is o¤ered in the market for used laptops,
how many high-quality laptops will be made available in the market?
How many low-quality laptops will be available in the market? Are
buyers correct in their assumption that 50% of the used laptops for
sale are of high quality? Explain.
(c) What would you expect to happen over time as information about the
true odds of buying a high-quality laptop becomes known? Explain.
(d) Argue that providing a guarantee against laptop faults may improve
the outcome.
3
8. Philippa is a farmer, with a utility function of U = pI, where I is her
income. If the weather is good, she will earn 100,000. If there is a hail-
storm, she will earn only 50,000. The probability of a hailstorm in any
given year is 30%.
(a) What is Philippa?s expected income? And her expected utility?
(b) Suppose a crop insurer makes the following o¤er to Philippa: In years
when there is no hailstorm, Philippa pays the insurer 16,000. In years
when there is a hailstorm, the insurer pays Philippa 34,000. What is
Philippa?s expected income? And her expected utility?
(c) Commen on the following statement referring to your answers to
part (a) and (b): “The insurance agreement in (b) reduces Philippa?s
expected income. Therefore, it must make her worse o¤”.
(d) Suppose instead that the insurer o¤ers Philippa the following: In
years when there is no hailstorm, Philippa pays the insurer 10,000;
in years when there is a hailstorm, the insurer paus Philippa 20,000.
How does Philippa?s expected income and expected utility compare
to the uninsured outcome in (a) and the insured outcome in (b)?
(e) Argue that contracting insurance between a risk averse agent and a
risk neutral insurance company constitutes a Pareto improvement.
9. A pizza chain recently o¤ered the following special promotion: “Buy one
pizza at full price and get your next three pizzas for just 5 pounds each!”.
Assume that the full price of pizza is 10, your daily income 40 and the
price of all other goods 1 pound per unit.
(a) Draw budget constraints for pizza and all other goods which re?ect
your situations both before and during the special promotion.
(b) How is this special o¤er likely to alter your buying behaviour?
(c) How might your answer to (b) depend on the shape of your indi¤er-
ence curves?
(d) Argue that you are not made worse o¤ by the promotion.
4
10. Chris and Pat like both co¤ee and biscuits. Chris views cups of co¤ee and
packets of biscuits are perfect one-to-one substitutes. Pat believes that
co¤ee and biscuits are perfect complements, and always consumes them
in one-to-one proportions (one cup of co¤ee and a packet of biscuits).
Initial endowments are as follows: Chris has 3 cups of co¤ee and 3 packets
of biscuits; Pat has 1 cup of co¤ee and 2 packets of biscuits.
(a) Construct an Edgeworth box for Chris and Pat.
(b) Draw their indi¤erence curves through the endowment point and ar-
gue that there is scope for Pareto improving trades.
(c) Derive the contract curve.
(d) How would you construct the utility possibility frontier for this small
?economy??
5
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