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.
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) / Total Utility / Marginal Utility
0 / 0
1 / 10 / 10
2 / 18 / 8
3 / 24 / 6
4 / 28 / 4
5 / 30 / 2
6 / 30 / 0
7 / 28 / -2
8 / 24 / -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.
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.
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
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:
4. The equation of the line is :
P = -2*Q + 10
5.
- Bill’s optimal choice of movies changes from 4 movie to 1 movies, for a decrease of 3 movies.
- A decrease of 2 movies.
- A decrease of 1 movie.
- A normal good. Income goes down and consumption of movies goes down as well, therefore the good must be a normal good. (Same direction)
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