Economics 102 Introductory Macroeconomics - Spring 2005, Professor J. Wissink
Problem Set 1 – DUE at the start of class on Monday Feb 7, 2005
Boxes will be removed ten minutes after the start of class.
Remember: We will NOT accept problem sets late. Period.
Thanks for minding this policy and not asking if you can hand it in late.
1. The small industrial town of Springfield produces two goods: rafts (produced with labor hours and
wood) and girders (produced with metal, machinery and labor hours). The production function (in
terms of labor, holding all other inputs constant) for each of these outputs is given in the tables below.
Springfield has 80 hours of labor, total, to allocate to these two output sectors.
Number of
Hours
0
10
20
30
40
50
60
70
80
Number of
Rafts
0
1
2
3
4
5
6
7
8
Number of
Hours
0
10
20
30
40
50
60
70
80
Number of
Girders
0
15
28
39
48
56
61
65
67
a) What is the Marginal Productivity of Labor (MPL) in the production of Rafts? What is the
Marginal Productivity of Labor (MPL) in the production of Girders?
b) Does the “Law of Diminishing Returns” apply in the production function of Rafts? How about in
the production of Girders? If you answer affirmatively, indicate where diminishing returns “set
in”.
c) Graph the production function for rafts and the production function for girders as labor hours vary
in each sector.
d) Graph the Production Possibilities Frontier (PPF) between rafts and girders. Put Girders on the
horizontal axis and rafts on the vertical axis. Assume that all units of measurement are
infinitely divisible, so you can smoothly connect points on your graph.
e) What is the Total Opportunity Cost of 4 rafts? What is the Marginal Opportunity Cost of the 4th
raft?
f) Time has passed since the first date in which this economic data was collected (the year 2000).
During this time there were substantial technological improvements in the production of girders,
making its production easier and making labor more productive. The following graph depicts the
actual amount of girders produced in Springfield over several years. By looking at this graph, can
you conclude that the Law of Diminishing Returns didn’t apply over the 2000-2008 period? Why
or why not.
Production of Girders over Tim e
400
350
2008
2006
Girders
300
250
200
2004
150
2002
100
50
2000
0
0
20
40
60
80
100
Labor
2. Two friends Claire and Thomas work for a textbook publisher. They have a day to write exercises for
the publisher’s new Math and Economics workbooks. Each one can allocate 8 hours that day to
writing (and solving) the exercises they dream up. The following table shows how many hours it
takes each of one of them to compose one exercise, based on the subject matter.
Claire
Thomas
Hours per
Math exercise
0.5
4
Hours per
Econ exercise
0.5
1
a) Who has the comparative advantage in writing Math exercises? Who in Econ? Give a brief
defense/explanation of why.
b) Who has the absolute advantage in writing Math exercises? Who in Econ? Give a brief
defense/explanation of why.
c) Draw Claire’s and Thomas’ PPF curves if they compose exercises separately. Put “Econ
exercises” on the horizontal axis and “Math exercises” on the vertical axis in each graph.
d) Suppose, as of now, each one of them is working separately and each one spends 4 hours working
for each course. Seeing Claire’s abilities and output, Thomas proposes that they work in team to
compose the exercises. Would you recommend the Claire accept his offer? Support your answer
by giving a numerical example based on the productivity information in the table above.
e) Irrespectively of what your advice might have been, Claire decides to accept Thomas’s offer.
Draw their joint PPF for writing Math and Econ exercises.
f) Adam is a friend of both Claire and Thomas. After seeing them working in a team, he proposes
to join their team. Adam can write a Math exercise in 4 hours and an Econ exercise in 2 hours.
Thomas initially opposes the idea, arguing that Adam has neither absolute nor comparative
advantage in any discipline and hence he wouldn’t add anything to the team. Claire disagrees and
accepts him into the team. Draw the new PPF that would arise by accepting Adam.
3. Consider an economy producing only corn and automobiles. Corn is produced with land and labor as
inputs, while automobiles are produced with capital and labor as inputs.
a) Draw the PPF assuming the usual “bowed-out” shape, putting corn in the horizontal axis and
automobiles in the vertical axis.
b) Draw the possible consequences of the following on the economy’s PPF. Assume each event
below occurs separately (and not in combination with other events noted), and use a separate
diagram for each answer.
i) A devastating natural disaster unexpectedly hits the country flooding the corn plantations and
killing thousands of people.
ii) The labor force grows over the next year due to lax immigration policy.
iii) Workers in the car plants strike and instead go and work at the plantations.
4. True or False and EXPLAIN: The law of diminishing returns implies that labor MUST be
heterogeneous.
5. True or False and EXPLAIN: The law of diminishing returns implies that an input's marginal product
must eventually be negative.
6. True or False and EXPLAIN: For a two country/two good world if County A has the absolute
advantage in both goods it must have the comparative advantage in both goods as well.
7. Multiple Choice:
1) The Law of Diminishing Returns is best described by which of the following statements:
a) Total output will decline if too much of an input is applied to a production process.
b) Extra output will decline as more of one input is added.
c) Additions to total output will increase as all inputs applied to a production process are increased
proportionately.
d) Additions to total output will decline as all inputs applied to a production process are increased
proportionately.
2) In a two-good economy, if the opportunity cost of producing a good decreases as more of that good is
produced, the economy’s Production Possibility Frontier will be:
a) “bowed outward” from the origin.
b) a straight line.
c) positively sloped.
d) “bowed inward” toward the origin.
3) Which of the following is primarily a normative statement?
a) Taxes will increase if the government guarantees drug benefits to all social security recipients.
b) The speed with which new drugs are developed will slow down if the government places price
controls on prescription drugs.
c) Infant mortality rates are higher in the United States than in most other developed countries.
d) Physicians’ incomes will decrease if national health insurance is instituted in the United States.
e) The government should provide health insurance for any individual who cannot afford it.