ECO 336Y
Sample Questions
4
Please answer
the following questions. They should
help to give you an idea of the types of question that will appear on the term
test.
1. Person A will trade two loaves of bread for
five apples and remain equally happy. At the same time, Person B will gladly exchange three loaves of
bread for ten apples. Is the allocation
of loaves and apples between Persons A and B Pareto-efficient? Please justify your answer. [Two sentences.] (2 points)
2 Explain why Monte-Carlo experiments are
useful in determining the properties of estimators. [Aside: an estimator is a statistical 'recipe' that is applied to
data in order to obtain estimates.
Least squares is perhaps the most widely used estimator.] In answering this question, you should focus
on the case of the least squares estimator, and specifically whether it gives
unbiased estimates or not, depending on whether the error term is uncorrelated
with the explanatory variables. (8 points)
Question 3 (17 points)
Suppose a firm faces a
horizontal demand curve, with price P = $4.
The firm’s total cost curve is given by
C = Q2,
where Q is the firm’s
output.
3a) Does the firm have any market power? Please explain. [One
sentence.] (2 points)
3b) Write down a general expression (in terms of Q) for this
firm’s profit level. (3 points)
3c) Solve for the firm’s optimal output choice, showing your
workings. [Hint: your answer should
give Q* equal to some number.] (6
points)
3d) What is the firm’s marginal cost at the optimal output
level? (2 points)
3e) In the absence of externalities, does this firm produce at the
socially optimal output level? Please
explain. [Two sentences.] (4 points)
Question 4 (worth 12 points)
A number of social
scientists have studied the impact of police expenditures on the level of crime
to see whether higher expenditures lower the crime rate significantly. Here, we repeat the standard type of
analysis, collecting data on a random sample of communities. Our data set includes, for each community i,
the crime rate (Ci), the level of police expenditures (Ei), and the level of
unemployment (Ui). Suppose that the unemployment rate takes on
just two values: 0.1 in low-unemployment communities, and 0.2 in
high-unemployment communities. We
estimate the following model using ordinary least squares:
Ci = a0 + a1 Ui + a2 Ei + epsiloni
where a0, a1, and a2 are our coefficient
estimates, and epsiloni is a random error term.
4a) Consider the least squares line that corresponds to these
estimates, drawn with crime expenditures on the horizontal axis and the crime
rate on the vertical axis. Is the
intercept of this line in the low-unemployment community higher or lower than
in the high-unemployment community? And
does this make sense? Please explain. [Three sentences.] (6 points)
4b) Suppose our actual estimates are: a0 = 5, a1 = 2, and a2 = -1. Predict the average
crime rate in high-unemployment areas if police expenditures = 2 per year. Please set out your working. (6 points)
5A. Suppose a firm takes prices as given, and
the price it faces for its product is $6.
Let the firm's
total cost function be given by
C(Q) = Q^2,
where Q is
output (and ^2 denotes 'raising to the power 2').
i. Write down the firm's profit function.
ii. Solve for the firm's profit maximizing
output level. What is it?
iii. At this output level, what is the firm's
average revenue, marginal revenue, and marginal cost?
5B. Now suppose that the firm has market
power. By selling more output, the firm
is forced to lower its price.
Let the firm's
demand curve be given by
P = 6 - Q.
The firm still
faces the same cost function as in part A.
i. Write down a general expression for the
firm's total revenue.
ii. Write down a general expression for the
firm's profit.
iii. Solve for the firm's profit maximizing
output level. What is it?
iv. At this output level, what is the firm's
marginal cost and the firm's average revenue?
v. Is this level of output efficient (in the
sense that the extra cost to society equals the extra benefit)? If not, please calculate the efficient level
of output, explaining your reasoning carefully.
vi. Intuitively, what is the problem with
monopoly from society's point-of-view? [two sentences]
vii. Why does monopoly create a potential role
for government? [two sentences]