Carnegie Mellon University Principles of Macroeconomics Exam Practice

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Principles of Macroeconomics (73-103): Fall 2021
Midsemester Exam #2
Friday, 11/12/2021
Instructions: There are 4 questions/problems in this exam. You must submit your exam by 10pm EST on
November 12th on Gradescope. There will be no extensions.
Write clear, complete, and accurate solutions that justify your answers. Use diagrams and equations if
useful and where appropriate. Include units with your answers where appropriate. Partial credit will be
awarded when possible. Show your work. Credit will not be assigned to calculated responses when work is
not shown.
This is an open book exam. If you have access to a printer, print the exam and put answers in the space
provided. We have provided quite a bit of space for you to answer the questions. Do not feel obliged to fill
up the space.
Good Luck!
First Name:
Last Name:
Andrew ID:
Midsemester Exam #2: 11/12/2021
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Principles of Macroeconomics (73-103): Fall 2021
This page is only for the use of the graders.
Question Number
Points Earned
Possible Points
1
10
2
15
3
15
4
15
Total
55
Midsemester Exam #2: 11/12/2021
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Principles of Macroeconomics (73-103): Fall 2021
1. (10 points) Question goal: Test your knowledge of the production function (using some real data from
the Penn World Tables).
You are sent to Colombia by the World Bank. You collect the following data:
Colombia, 2004
Colombia, 2014
POP (millions)
42.7
47.8
Y ($ 2011 billions)
314
602
L (millions of people)
18.6
24.6
K ($ 2011 billions)
1140
1822
Assume Colombia has a Cobb Douglas production function and that ? = 0.4.
a. (5 points) Compute a measure of Colombian TFP for the years 2004 and 2014. Compute a
measure of Colombian living standards for both years. Show all your work.
Answer:
Midsemester Exam #2: 11/12/2021
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Principles of Macroeconomics (73-103): Fall 2021
b. (5 points) Some useful facts about growth rates: You can calculate a growth rate using a log
difference: log xt+1 ? log xt . (Note: logs here are natural logs, often denoted ln on a calculator).
For data that is 10 years apart, you can calculate an average annual growth rates over the decade
1
by simply dividing the log difference by 10: 10
× (log xt+10 ? log xt ).
The Cobb Douglas production function implies:
GDP growth rate = TFP growth rate +
+
?×capital growth rate
|
{z
}
capital’s contribution to growth
(1??)×labor growth rate .
{z
}
|
labor’s contribution to growth
Using the data, the above formulas and the useful facts about growth rates, assess which made
the largest contribution to Colombian GDP growth: TFP, capital or labor. Give supporting
numbers and show all work.
Answer:
Midsemester Exam #2: 11/12/2021
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Principles of Macroeconomics (73-103): Fall 2021
2. (15 points) Question goal: Test your knowledge of the Solow Growth Model.
Consider the following equation for the evolution of capital Kt in an economy:
Kt+1 = Kt + sAKt? L1?? ? ?Kt .
|
{z
} |{z}
Term 1
Term 2
(a) Interpret the equation. What do the two terms on the right hand side (labeled Term 1 and Term
2) capture?
(b) Define the steady state level of capital. In doing so, state clearly what is needed for the capital
stock to be at steady state.
Midsemester Exam #2: 11/12/2021
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Principles of Macroeconomics (73-103): Fall 2021
(c) The diagram below shows the amount of depreciation and the amount of savings (on the y-axis)
for any amount of Capital (on the x-axis). Identify the steady state level of capital on the graph
Depreciation,
Savings 2
Depreciation
1.5
Savings
1
0.5
0
0
5
10
15
20
Capital Stock, Kt
(d) Suppose that a new government policy compels people to save a larger fraction of their income
so that s rises to a higher value. Draw the savings curve corresponding to savings under this
new policy in the figure above. Draw it sufficiently close to the old savings curve so that the
steady state is still on the picture and show where this steady state is.
(e) Do you think people are made better off by this policy? In answering distinguish between the
short and the long run effects. (Hint/Suggestion: You may assume that population is constant
and, for simplicity, equal to one. We often take GDP per capita as a guide to living standards.
But for this question, it is important to think about consumption per capita, which is the share
of output not saved).
Midsemester Exam #2: 11/12/2021
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Principles of Macroeconomics (73-103): Fall 2021
3. (15 points) Question Goal: Test your knowledge of the determinants of the labor demand curve.
(a) A firm has the production data in the following table. If the price of the firm’s good is $2,
complete the table:
L
0
Y = AF (K, L)
if K = 1
0
Y = AF (K, L)
if K = 2
0
1
5
10
2
9
18
3
12
24
4
14
28
5
15
30
Value of MPL if K = 1
Value of MPL if K = 2
(b) Suppose the market wage is $7 and the firm has 1 unit of capital (K = 1). How many workers
does the profit maximizing firm hire? (Briefly explain your answer in two sentences or less.)
(c) If the wage remains at $7 but the firm has 2 units of capital (K = 2), how many workers does
the firm hire? (Again, briefly explain.)
Midsemester Exam #2: 11/12/2021
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Principles of Macroeconomics (73-103): Fall 2021
(d) Relative to part (b), how does the increase in capital change the firm’s labor demand curve?
Show your answer by graphing the firm’s labor demand in part (b) and in part (c). Carefully
label your diagram. (Don’t worry if your graph looks like a staircase).
(e) Is the increase in capital use by firms (possibly motivated by the falling prices of automation,
robots, and other capital goods) likely to raise or lower wages of workers? Briefly explain your
answer.
Midsemester Exam #2: 11/12/2021
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Principles of Macroeconomics (73-103): Fall 2021
4. (15 points) Question goal: Test if you understand credit market functioning.
(a) Table 1 presents the demand and supply for credit by households and firms in the land of
Carnegia. The Carnegian government borrows nothing. Why does the credit demand curve
slope downwards? What is the equilibrium interest rate and credit level?
Interest
Rate (%)
2
4
6
8
10
12
14
Quantity of Credit
Demanded (billion $)
35
30
25
20
15
10
5
Quantity of Credit
Supplied (billion $)
5
10
15
20
25
30
35
Table 1: Demand and Supply for Credit in the Land of Carnegia
(b) Following an election, the new Carnegian government increases its spending by $5 billion and
reduces its tax revenues by $5 billion (The government does not create additional money).
Household and firm demand and supply for credit at each interest rate remain the same. What
will the new equilibrium interest rate be?
Midsemester Exam #2: 11/12/2021
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Principles of Macroeconomics (73-103): Fall 2021
(c) Suppose that the Carnegian people realize that in the future their government will have to raise
income taxes to pay off the debt the government is incurring now to finance its spending. How
might they respond now? And how does this effect your answer to part (b)?
Midsemester Exam #2: 11/12/2021
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Explanation & Answer:
4 Questions

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production functions

Principles of Macroeconomics

market intuition

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