# Principles of Microeconomics_Homework 1 Sec3

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```					BRAC University
Department of Economics & Social Sciences
ECO 101-3: Principles of Microeconomics                                   THN, Fall 2010
Problem Set 1 (Due by 5:00PM on September 28)                                Total: 60 pts

1. Calculate the slope of the straight line in the following ﬁgure.                  (5 pts)

2. Atlantis is a small, isolated island in the South Atlantic. The inhabitants grow potatoes
and catch fresh ﬁsh. The accompanying table shows the maximum annual output combi-
nations 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         Quantity of potatoes       Quantity of ﬁsh
output options             (pounds)                (pounds)
A                      1,000                      0
B                       800                     300
C                       600                     500
D                       400                     600
E                       200                     650
F                        0                      675

(a) Draw a production possibilities frontier with potatoes on the horizontal axis and ﬁsh
on the vertical axis illustrating these options, indicating points A–F .      (5 pts)
(b) Can Atlantis produce 500 pounds of ﬁsh and 800 pounds of potatoes? Explain. Where
would this point lie relative to the production possibility frontier?      (5 pts)

1
(c) What is opportunity cost of increasing the annual output of potatoes from 600 to 800
pounds?                                                                     (5 pts)
(d) What is opportunity cost of increasing the annual output of potatoes from 200 to 400
pounds?                                                                     (5 pts)
(e) Can you explain why the answers to parts (c) and (d) are not the same? What does
this imply about the slope of the production possibility frontier?       (5 pts)

3. Draw the graphs for the following two equations:

(a) y = f (x) = 3x + 6                                                           (5 pts)
(b) y = a, where a > 0                                                           (5 pts)

4. Solve for x and y using the following system of equations:                    (10 pts)

3x − y = −4         and       x + 3y = 12

5. Find Y and C from the following:                                              (10 pts)

Y = C + I0 + G0
Y
C = 30 +
2
I0 = 16
G0 = 14

2

```
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