January 2022 Exam
EC1A3
Microeconomics I
2021/22 syllabus only – not for resit candidates
Instructions to candidates
This paper contains seven questions. Answer all questions.
Time Allowed
Writing Time:
2 hours
You are supplied with:
No additional materials
You may also use:
No additional materials
Calculators:
Calculators are allowed in this exam
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SECTION A: Answer all questions.
There are 5 questions. Each question carries 6 points.
Choose the correct answers, no explanation needed.
For each question, there might be more than one correct answer.
All correct answers get proportionate points. For example, if there is only one correct answer to a question,
the correct answer gets 6/1=6 points; if there are two correct answers to a question, each correct answer
gets 6/2=3 points; if there are three correct answers to a question, each gets 6/3=2 points; if there are four
correct answers to a question, each gets 6/4=1.5 points; and so on.
If one or more wrong answers to a question are chosen, 0 points are given for the whole question no matter
how many correct answers are also chosen.
Question 1 [6 marks]
Consider a Cournot competition between two identical firms facing the market demand curve p=16-2Q
where p is price and Q is quantity demanded. Each firm’s total cost curve is C(q)=4q where C(q) is total cost
and q is quantity produced. Then in the Nash (Cournot) equilibrium:
a. Profit maximizing level of output is 3.
b. The quantity each firm will produce is lower than that if they were to compete in prices.
c.
The profit of each firm is 12
d. The profit of each firm is 8
e. Profit of each firm is higher than if they were to compete in prices.
__________________________________________________________________________________________________________
Question 2 [6 marks]
Which of the following statements are true?
a. A rational CEO of a firm will always maximise profits.
b. The model of rationality is a mathematical model we use in economics to make predictions about
how individuals behave in economic situations.
c. The model of rationality is a mathematical model we use in economics to make recommendations
about how individuals should behave in economic situations.
d. Transitivity of an individual’s preferences implies that the individual can always compare between
any two alternatives in their set of alternatives.
e. Completeness of an individual’s preferences implies that the individual can always compare
between any two alternatives in their set of alternatives.
__________________________________________________________________________________________________________
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Question 3 [6 marks]
Consider the following game. Which of the statements below are true for this game?
L
M
R
2,2
-1,-1
1,1
M -1,-1
1,1
1,-2
D
-2,1
-1,-1
U
1,1
a. The Row player has a strictly dominated action.
b. The Column player has a strictly dominated action.
c. There is no Nash equilibrium for this game.
d. The row player playing D and the column player playing R constitutes a Nash equilibrium of this game.
e. There are two pure strategy Nash equilibria to this game.
f. There is no mixed strategy equilibrium in this game.
__________________________________________________________________________________________________________
Question 4 [6 marks]
You are an aspiring monopolist and planning to sell a new gadget you have developed. The demand in the
LSE campus for this gadget is given by Q=50-2p and your marginal cost of producing each gadget is 10.
Which of the following statements are true about the short run?
a. As a simple monopolist you will sell 15 gadgets.
b. As a simple monopolist you will sell each gadget for 10 pounds.
c. As a simple monopolist you will sell each gadget for 25 pounds.
d. As a fully discriminating monopolist you will make a profit of 225 pounds.
e. As a fully discriminating monopolist you will make a profit of 450 pounds.
__________________________________________________________________________________________________________
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Page 3 of 6
Question 5 [6 marks]
You are thinking about investing in one of the following three projects. Project A costs 20k pounds today
and pays off 30k pounds in two years. Project B costs 40k pounds today and pays off 60k pounds in two
years. Finally, Project C involves paying nothing today and receiving no payments in the future. Which of the
following statements are true?
a. Whatever the interest rate, the net present value (NPV) of project C is zero.
b. Suppose that there are no credit markets so you cannot borrow or save. You surely prefer project A
as it costs half as much as project B.
c. Suppose that credit markets are perfect. There is an interest rate level so that for each interest rate
higher than that level you would prefer Project A to Project B.
d. Suppose that credit markets are perfect. There is an interest rate level so that for each interest rate
higher than that level you would prefer Project B to Project A.
e. Suppose that credit markets are perfect. Either you prefer projects A and Project B to Project C or
you prefer Project C to projects A and B or you are indifferent between the three projects.
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Page 4 of 6
SECTION B: Answer the following TWO questions
Each question carries 35 points.
Question 6 [35 marks]
Consider the following strategic situation that has been enacted in a recent experiment: Participants are grouped
into groups of n participants. Participants sit, each in front of their own computer, in the lab and decide about
whether to volunteer or not. Each group was given two minutes to decide, with the experiment ending as soon as
someone volunteered. If no one volunteered, each group member received a payment of $1. Anyone who
volunteered received $1.75, while the other group members who have not volunteered each received $2.
a.
b.
c.
d.
e.
f.
Translating this situation into a simultaneous move game, write the primitives of the model, the set of
players, the set of actions for each player and the preferences of each participant on profiles of actions by
all players. [5 marks]
Assume that n=2, write this game in a matrix form. [6 marks]
Find a pure strategy Nash equilibrium in the game you found in (b). Explain and prove your answer. [6
marks]
Find a mixed strategy Nash equilibrium of the game you found in (b). Explain and prove your answer. [6
marks]
Assume now that n=3. Find a pure strategy Nash equilibrium of this game. Explain and prove your answer.
[6 marks]
Economists ran these experiments in groups of two and had participants play in many rounds where they
were able to see the gender of the other participant in their group. The economists measured the
proportion of time participants volunteered. The economists noticed that when the groups were
composed of only women or only men, there was no difference between proportion of volunteering
between men and women and these proportions were strictly between one and zero. But when they ran
the experiment with groups composed of both males and females, they found big gender differences.
Indeed, they found that the proportion of times men volunteered was almost zero and that of the women
was close to one. Use your analysis of this game, specifically the equilibria you found above to support the
claim that “this experiment dispels the notion that women are different than men when it comes to
volunteering, or that women are more inclined to volunteer, rather it is the beliefs and expectations in
society that make women volunteer more because men expect them to do so more often, and woman
know that men expect this”. [6 marks]
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Page 5 of 6
Question 7 [35 marks]
You eat only Pink lady apples, 𝑥! , or Granny smith apples, 𝑥" . You are comparing two local supermarkets,
Weightrose and Senseberries. In Weightrose the price of Pink lady apples is £2 and the price of Granny
smith apples is £3. In Senseberries the price of Pink lady apples is £3 and the price of Granny smith apples
is £2. Your utility from a consumption bundle (𝑥! , 𝑥" ) is given by 𝑈(𝑥! , 𝑥" ) = 𝑥! # 𝑥"!$# . You have £60 to
spend.
a. Compute the MRS between 𝑥! and 𝑥" . [6 marks]
b. Write the formula for the budget constraint in each of the supermarkets. Draw the budget constraints
you have found. [5 marks]
c. Compute the optimal consumption bundle (𝑥! , 𝑥" ) in each supermarket as a function of θ. [6 marks]
d. Assume that θ=0.6. On the same graph, show the optimal consumption at each supermarket. By
looking at your drawing or by doing some calculations can you tell which supermarket would you
prefer to do your shopping in? Explain your answer. [6 marks]
e. Assume that θ=0.4. On the same graph, show the optimal consumption at each supermarket. By
looking at your drawing or by doing some calculations can you tell which supermarket would you
prefer to do your shopping in? Explain your answer. [6 marks]
f. For what value of θ would you be indifferent as to which supermarket would you prefer to do your
shopping in? Explain your answer. [6 marks]
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