Econ 101
Homework 3 Solutions
Fall 2005
Directions: The homework will be collected in a box before the lecture. Please place
your name, TA name and section number on top of the homework (legibly). Make sure
you write your name as it appears on your ID so that you can receive the correct grade.
Please remember the section number for the section you are registered, because you will
need that number when you submit exams and homework. Late homework will not be
accepted so make plans ahead of time. Good luck!
1.
a. This will be different for different people, but a good answer will have hours of
sleep per night on the horizontal axis over the range from 0 to 24. Utility will be
on the vertical axis and any range is acceptable (even negative numbers!). The
graph should probably be an upside down U shape with a maximum on the
preferred number of hours of sleep per night.
For example, if you prefer 7 hours of sleep per night and that gives you 100 utils
of utility, then you might have the following equation for your utility
U = -(S – 7)2 + 100
which is the same as
U = -S2 + 14S + 51,
where U is utility and S is sleep. This is shown in the graph below.
1
Utility of Sleep
150
100
Utility
50
0
Utility (utils) -50
-100
-150
-200
-250
0
6
12
18
24
Hours of sleep per night
b. The marginal utility is the change in utility per hour of sleep at every hour of
sleep. So it is just the slope of the Utility curve. In this case,
MU = -2S +14,
c.
Quantity of water drank
(cups per day)
0
1
2
3
4
5
6
7
8
Total Utility
0
10
18
24
28
30
30
28
24
Marginal
Utility
10
8
6
4
2
0
-2
-4
d. 5 or 6 cups or most likely, something in between. We look for the quantity that
maximizes utility. This should be where marginal utility equals zero, 6 cups in
this case. However since we are measuring marginal utility in discrete units it
equals zero somewhere between 5 and 6 cups.
2. See chart below for the plots.
2
a. BL1: QA = -3/5 * QB +12
b. BL2: QA = -3/10 * QB +6
c. BL3: QA = -6/5 * QB +12
d. BL4: QA = -3/10 * QB +12
e. BL5: QA = -3/5 * QB +12
f. BL1 is equal to BL5. This is because the price of both goods and the
income have all doubled. Therefore the budget line is unaffected.
14
13
12
11
10
Apples
9
8
BL4
7
6
BL3
5
BL2
4
BL1 and BL5
3
2
1
0
0
2
4
6
8
10
12 14
16 18
20 22 24
26 28
30 32
34 36
38 40
Bananas
3.
a. Indifference Curve C
b. See attached graph.
c. Yes, they are all satisfied.
d. See attached graph.
e. Tennis matches = y
Soccer matches = x
The y-intercept if 85, because when Paula consumes zero soccer matches, she can
consume a maximum of 85 tennis matches. The slope is -2 because for every
additional soccer match she wants to consume, she has to give up two tennis
matches. That gives us the equation of the budget line is: Y = 85 – 2 * X
3
f. 20 soccer matches and 45 tennis matches. This can be seen from the graph. The
optimal bundle is the point where the budget line is tangent to one of the
indifference curves.
g. –2. At the optimal bundle, we know that the marginal rate of substitution equals
the slope of the budget line.
GRAPH FOR QUESTION 3:
100
90
Tennis Matches per year
80
70
60
Indifference Curve 1
Indifference Curve 2
50
Indifference Curve 3
Budget Line
40
30
20
10
0
0
10
20
30
40
50
60
Soccer Matches per year
4. The equation of the line is :
P = -2*Q + 10
4
Demand for Movies
9
1, 8
Price of Movies
8
7
6
5
3, 4
4
3
2, 4
2
1
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Quantity of Movies
5.
a. Bill’s optimal choice of movies changes from 4 movie to 1 movies, for a
decrease of 3 movies.
b. A decrease of 2 movies.
c. A decrease of 1 movie.
d. A normal good. Income goes down and consumption of movies goes
down as well, therefore the good must be a normal good. (Same direction)
5