ECO208 L0101
TERM TEST 1
OCTOBER 25, 2022, 4:10pm-5:50pm
E-mail:
___________________________________@mail.utoronto.ca
Surname
(last name):
Given name
(first name):
UTORID:
(e.g. lihao8)
Instructions:
•
You have 100 minutes. Keep these test papers closed on your desk until the start of the
test is announced.
•
There are 5 questions (some with multiple parts) with varying point values worth a total
of 100 points.
•
Read each question carefully before attempting to answer.
•
Write your answers clearly, completely and concisely in the designated space provided
immediately after each question. No extra space/pages are possible. You cannot use
blank space for other questions. Your entire answer must fit in the designated space
provided immediately after each question.
o Write in pencil and use an eraser as needed. This way you can make sure to fit
your final answer (including work and reasoning) in the appropriate space.
o All questions give more blank space than is needed to answer. Follow the
answer guides and avoid excessively long answers.
•
Clearly show your work. Make your reasoning clear. Make all extra assumptions that you
consider necessary but make sure to state them clearly. Make sure to label all your
diagrams appropriately.
•
This test has 9 pages. You must write your answers in the designated space provided
immediately after each question. Answers written on scratch paper will not be graded.
Question 1: [20 points] Assume an economy with a coal company, a steel company, and some
consumers (but no government). The coal company produces 15 million tonnes of coal and sells
it for $5 per tone, and pays $50 million in wages to consumers. The steel company uses 25
million tonnes of coal as an input to steel production, all purchased at the same 5$/tonne price.
Of these 25 million tonnes, 15 million are purchased from the domestic coal company and 10
million are imported from abroad. The steel company produces 10 million tonnes of steel and
sells it for $20 per tonne. Domestic consumers buy 8 million tonnes of steel and the remaining 2
million tonnes are exported. The steel company pays $40 million on wages. All profits earned by
the coal and steel companies are distributed to domestic consumers are dividends. Using this
information, calculate the following. Make sure to show your work!
(a) [4 points] GDP using the product approach.
(b) [4 points] GDP using the expenditure approach.
Question 1, continued
(c) [4 points] GDP using the income approach.
(d) [3 points] The current account surplus.
(e) [2 points] GNP.
(f) [3 points] How would your answer to part (e) change if the coal company was owned by
foreigners rather than domestic consumers?
Question 2: [14 points] Suppose that government deficit is 12, interest on government debt is 4,
taxes are 37, government expenditures are 32, consumption expenditures are 73, net factor
payments are 11, the current account balance is +4, and national saving is 25. Calculate the
following, not necessarily in the order given [2 points each].
• Private disposable income
• Transfers from the government to the private sector
• Gross national product
• Gross domestic product
• The government surplus
• Net exports
• Investment expenditures
Question 3: [45 points] Consider the representative consumer’s problem from Chapter 4. The
consumer has standard preferences given by 𝑈(𝐶, 𝑙) = log 𝐶 + 𝜂 log 𝑙 and faces the standard
time constraint 𝑙 + 𝑁 𝑠 = ℎ. However, suppose that the government levies a proportional tax of
rate t on the representative consumer’s labor income instead of a lump-sum tax. That is, the
consumer’s budget constraint is 𝐶 = 𝑤(1 − 𝑡)𝑁 𝑠 + 𝜋.
(a) [1 point] Combine the budget and time constraints to obtain a single constraint for the
consumer’s problem.
(b) [2 points] Write down the representative consumer’s formal optimization problem. Explicitly
label (i) choice variables, (ii) the objective function, and (iii) the constraint.
(c) [5 points] Substitute the constraint from (b) into the objective function to eliminate C. Write
down the resulting unconstrained optimization problem that has only l as a choice variable.
(d) [5 points] Write down the first-order condition associated with this problem.
Question 3, continued: [45 points]
(e) [6 points] Use the FOC to find a closed-form solution for l as a function of the exogenous
parameters (which are 𝑤, 𝜋, 𝜂, ℎ, 𝑡).
(f) [3 points] Find a closed-form solution for C as a function of the exogenous parameters (not
l!). This should be easy to do given your answers to (b) and (f).
(g) [8 points] Calculate the partial derivatives of the closed-form solutions for l and C you found
in (f) and (g) with respect to the tax rate t.
Question 3, continued
(h) [15 points] Suppose now that the government decides to replace the income tax with a lumpsum tax (i.e., the standard setup in Chapter 4). Assume that the lump-sum tax is chosen to
generate the same amount of revenue as the proportional tax. In other words, if 𝑙 ∗ is the
consumer’s optimal choice of leisure under the proportional tax, then lump-sum tax is given
by 𝑇 = 𝑤𝑡(ℎ − 𝑙 ∗ ). Show that this policy change would make the consumer better off.
Question 4 [21 points] Consider the firm’s problem from Chapter 4 with one modification: the
firm has a minimum level of employment, denoted by 𝑁 ∗ , that is required to operate (e.g. a
restaurant that must have at least one cook). In other words, if the firm’s labor input is less than
𝑁 ∗ , it produces nothing. If it has labor of at least 𝑁 ∗ , then it produces according to the usual
production function 𝑌 = 𝑧𝐾 𝛼 (𝑁 𝑑 )1−𝛼 . Formally, the firm chooses either not to operate at all
(𝑁 𝑑 = 0), or to solve the following constrained profit maximization problem if it can earn nonnegative profits:
{𝑧𝐾 𝛼 (𝑁 𝑑 )1−𝛼 − 𝑤𝑁 𝑑 } subject to 𝑁 𝑑 ≥ 𝑁 ∗
max
𝑑
𝑁
(a) [5 points] Graph the firm’s revenue function, with labor demand on the x-axis and revenue
on the y-axis.
(b) [5 points] Let 𝑤 ∗ denote the highest possible wage at which the firm can operate without
losing money, which is given by 𝑤 ∗ 𝑁 ∗ = 𝑧𝐾 𝛼 (𝑁 ∗ )1−𝛼 . Graph the firm’s variable cost
function associated with this wage, 𝑤 ∗ 𝑁 𝑑 . Use the same graph for both (a) and (b).
Question 4, continued
(c) [5 points] What is the firm’s labor demand when the wage equals 𝑤 ∗ ? In this situation, is the
firm’s marginal product of labor higher than, lower than, or equal to 𝑤 ∗ ? Explain.
(d) [6 points] Plot the firm’s labor demand curve.