HOMEWORK
PRODUCTION POSSIBILITIES MODEL: ANSWERS
1. Atlantis is a small, isolated island in the South Atlantic. The inhabitants grow potatoes and
catch fish. The accompanying table shows the maximum annual output combinations of
potatoes and fish that can be produced. Obviously, given their limited resources and available
technology, as they use more of their resources for potato production, there are fewer
resources available for catching fish.
Maximum annual
output options
A
B
C
D
E
F
Quantity of
potatoes
(pounds)
1000
800
600
400
200
0
Quantity of
fish
(pounds)
0
300
500
600
650
675
a) Draw a PPF with potatoes on the horizontal axis and fish on the vertical axis illustrating
these options, showing points A-F.
b) Can Atlantis produce 500 pounds of fish and 800 pounds of potatoes? Explain. Where
would this point lie relative to the PPF?
No because it is an unattainable combination (it lies outside the PPF)
c) What is the opportunity cost of increasing the annual output of potatoes from 200 to 400
pounds? What is the opportunity cost per unit of potatoes?
In order to produce 200 pounds more of potatoes, we have to give up 50 (650-600) pounds of
fish. The opportunity cost per pound of potatoes is equal to 0.25 (50/200).
d) What is the opportunity cost of increasing the annual output of potatoes from 600 to 800
pounds? What is the opportunity cost per unit of potatoes?
In order to produce 200 pounds more of potatoes, we have now to give up 200 (500-300)
pounds of fish. The opportunity cost per pound of potatoes is equal to 1 (200/200).
e) Explain why the answers to parts c and d are not the same. What does this imply about the
slope of the PPF?
As we move along the curve, opportunity costs increase, so this explains that at two different
points opportunity costs differ. This implies that the slope increases
2. Suppose that an economy has the PPF shown in the table below.
Possibility
A
B
C
D
E
Watches
0
200
300
350
400
Cameras
80
60
40
20
0
a) Plot these possibilities and draw the PPF (put watches on the x-axis)
90
80
70
Cameras
60
50
40
30
20
10
0
0
100
200
300
400
500
Watches
b) Identify each of the following combinations of the two goods as either efficient, inefficient
or unattainable and briefly explain why:
i)
60 cameras and 200 watches. Efficient, as it is ON the PPF
ii)
60 cameras and 80 watches. Inefficient, as it is INSIDE the PPF.
iii)
300 watches and 35 cameras. Inefficient, as it is INSIDE the PPF
iv)
300 watches and 40 cameras. Efficient, as it is ON the PPF
v)
58 cameras and 250 watches. Unattainable, as it is OUTSIDE the PPF.
c) Suppose the society is producing 200 watches and 60 cameras, but wishes to produce an
additional 100 watches (that is, move from possibility B to possibility C). How much output
of cameras must be sacrificed to enable these watches to be made? The opportunity cost per
unit of watches will be how many units of cameras?
In order to increase the production of watches by 100, 20 cameras have to be sacrificed. The
opportunity cost per unit of watches is 20/100=0.2.
d) If the economy moves from possibility C to possibility D, how much output of cameras
would need to be given up? The opportunity cost per unit of watches will be how many units
of cameras?
In order to increase the production of watches by 50, 20 cameras have to be sacrificed. The
opportunity cost per unit of watches is 20/50=2/5=0.4.
e) In general, what happens to the opportunity cost of watches as the output of watches
increases?
It increases.
f) In general, what happens to the opportunity cost of cameras as the output of cameras
increases?
It increases.
g) What do the results in parts e and f imply about resources?
Resources are specialized; they are not equally well suited for the production of both goods.
When resources are specialized the PPF is bowed outwards, like in this case.
h) If the PPF were a straight line, what would that imply about opportunity costs and
resources?
Opportunity costs would be constant and resources would be equally well suited for the
production of both goods.
3. What would happen to the PPF in problem 2 above if the following events occurred (each
is a separate event, unaccompanied by any other event)? Show diagrammatically how the PPF
would be affected.
a) A new energy source is discovered.
An outward parallel shift of the PPF (the PPF shifts to the right), representing an increase of
the production possibilities.
b) A new invention increases output per person in the watches industry but not in the cameras
industry.
Non-parallel outward shift of the PPF.
90
80
70
Cameras
60
50
40
30
20
10
0
0
100
200
300
400
500
600
Watches
c) A new law is passed compelling workers, who could previously work as long as they
wanted, to retire at age 60.
There is a decrease in the amount of resources available, so there is an inward parallel shift
of the PPF.