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Microeconomics Course E

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Title: Microeconomics Course E

1
Microeconomics Course E
• John Hey

2
Examinations
• Go to http//www.luiss.it/hey/microeconomia/esami.
htm
.htm
• Check on Aide/Memoire
• Check on grids

3
Aide-Memoire
4
Grids 1
5
Grids 2
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Example 2 of Exams Appello 2 Traccia 1
• 1-4 demand and supply
• 5-7 Edgeworth Box
• 8,9 inferring preferences
• 10,11 competitive firm
• 12,13 compensating and equivalent variations
• 14,15 risk
• 16,17 game theory

8
1-4 demand and supply
• Consider a market for a hypothetical good in
which there are a number of buyers and sellers,
each of which wants to buy or sell one unit of
the good. Assume that a buyer who is indifferent
indifferent about selling always sells. The
reservation prices are given below, first for the
buyers and then for the sellers.
• Buyers 6, 9, 10, 5, 8, 4, 8. Sellers 2, 6, 5,
3, 4, 4, 3.

9
Question 1 What is the maximum total surplus
generated in the market? (a) 28 (b) 23 (c) 22 (d)
25 Question 2 What is the maximum number of
trades (not necessarily with the same price)? (a)
6 (b) 7 (c) 5 (d) 8 Question 3 What price would
the buyers choose if they could? (a) 4 (b) 8 (c)
0 (d) 4 Question 4 What price would the sellers
choose if they could? (a) 10 (b) 5 (c) 8 (d) 4
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Questions 5-7
• Consider, in an Edgeworth Box, exchange between
two individuals, Individual A and Individual B,
with preferences as specified below, endowed with
two goods, Good 1 and Good 2. (Consider only
competitive equilibrium in which at least one
individual is better off compared to the initial
position.)
• Individual A has Perfect Complement preferences
with parameter a 0.5. Individual B has Perfect
Substitute preferences with parameter a 1.
Total endowment of good 1 is 8 and that of good 2
is 6.
• Individual A's endowment of good 1 is 0 and that
of good 2 is 1.

13
Question 5 What is the competitive equilibrium
price ratio? (a) 1.00 (b) 1.50 (c) 1.33 (d)
3.50 Question 6 What is the quantity exchanged
of good 1 to reach the competitive
equilibrium? (a) 4.00 (b) 2.00 (c) 3.00 (d)
1.00 Question 7 What is the quantity exchanged
of good 2 to reach the competitive
equilibrium? (a) 1.00 (b) 1.50 (c) 2.00 (d) 3.00
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Questions 8 and 9
• In the next two questions you will be asked to
consider an individual who has the following
demands. You will be asked to infer his or her
preferences, which will be either Perfect
Substitutes with parameter a, Perfect Complements
with parameter a, or Cobb-Douglas with parameter
a.
• With income 10.00 and at prices 1.00 and 2.00 the
demands were 3.33 and 3.33. With income 20.00 and
at prices 1.00 and 0.50 the demands were 6.67 and
26.67. With income 20.00 and at prices 2.00 and
2.00 the demands were 3.33 and 6.67.
• Question 8 What are the individual's
preferences?
• Perfect Substitutes
• There is not enough information
• Cobb-Douglas
• Perfect complements
• Question 9 What is the value of the parameter a?
• 0.25
• 0.50
• 1.00
• 0.33

22
Questions 8 and 9
• Remember the following
• With PS preferences the individual (except in one
special case) spends all his or her income on the
relatively cheaper of the two goods and spends
nothing on the other.
• With PC preferences the ratio of the quantities
q2/q1 bought is always equal to the parameter a.
• With CD preferences the amount spent on Good 1
p1q1 is always a fraction a of income.

23
Questions 10 and 11
• In the next two questions you will be asked to
consider a competitive firm which has a cost
function C(y) a by cy2 where a, b and c
are given below.
• a 20.0, b 0.0, c 1.0. Suppose that the
price of the firm's output is 40.
• Question 10 Determine the optimal output of the
firm.
• 60.00
• 40.00
• 20.00
• 0.00
• Question 11 What is the firm's profit?
• 380.00
• 0.00
• 800.00
• 1,619.76

24
Questions 12 and 13
• In the next two questions you will be asked to
evaluate the compensating and equivalent
variations for an individual facing a price rise
in the price of a good. The preferences of the
individual over the good and money are stated
below (note that the price of money is 1).
• The individual has Perfect Substitute preferences
over the good and money with parameter a 0.50.
The individual has income 30 and faces a price
2.00 for the good. Suppose the price of the good
rises by 0.10.
• Question 12 What is the compensating variation?
• 0.20
• 0.30
• 0.10
• 0.00
• Question 13 What is the equivalent variation?
• 0.40
• 0.20
• 0.00
• 0.30

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Questions 14 and 15
• In the next two questions you will be asked to
consider an individual, taking decisions under
conditions of risk, with Expected Utility
preferences and utility function u(x) x0.5
(that is, the utility of x is the square root of
x). Suppose the individual is faced with two
lotteries P and Q as specified below. A lottery
is denoted by (a,bp,1-p) and means that the
outcome is a with probability p and b with
probability 1-p.
• The lotteries are P (25,160.25,0.75) Q
(1,360.25,0.75)
• Question 14 Does the individual prefer P or Q?
• P
• Q
• We cannot say.
• The individual is indifferent
• Question 15 What is the individual's certainty
equivalent for P?
• 27.25
• 18.25
• 22.5625
• 18.0625

30
Questions 16 and 17
• In the next two questions you will be asked to
consider a game played simultaneously, and
without communication between two players, 1 and
2, each of whom can choose one of two options A
and B. The payoffs to the two players are given
below, the first for Player 1 and then for Player
2. The order of the payoffs is AA, AB, BA, BB
where XY indicates the outcome when Player 1
plays X and Player 2 plays Y.
• Player 1 5, 1, 6, 8. Player 2 10, 4, 8, 8.
• Question 16 Specify ALL the Nash Equilibria in
pure strategies.
• There are not any
• AB
• BA
• BA BB
• Question 17 Specify ALL other outcomes (not a
Nash Equilibrium) that Pareto dominate any of
these.
• AA dominates BB
• BB e AA dominate AB
• BB dominates AA
• There are none

31
Tips!
• Remember that you get 2 marks for a correct
answer and lose 1 mark for an incorrect.
• DO NOT GUESS!
• Take coloured pencils and pens.
• Take a rubber.
• Do NOT apply MAGIC formulae.
• Good Luck!!