Homework 3
1. First we are going to look at your own utility curve.
a. What is your utility from sleep? Draw a graph or write an equation (or both) describing the satisfaction you personally get from consuming a certain number of hours of sleep per night. There is no "correct" answer, but try to be realistic. You can scale the utility axis however you would like.
b. Now graph or describe with an equation your marginal utility curve for hours of sleep per night. It should reflect your answer to part a.
c. Given the following utility schedule for water, give the schedule (a table) for the marginal utility of water.
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Quantity of water drank
(cups per day)
|
Total Utility
|
|
0
|
0
|
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1
|
10
|
|
2
|
18
|
|
3
|
24
|
|
4
|
28
|
|
5
|
30
|
|
6
|
30
|
|
7
|
28
|
|
8
|
24
|
d. What quantity of water would this person choose to consume? (Assume water is free.)
2. Beth consumes apples and bananas. Beth has an income of $120. Currently the price of apples is $10 per bag and the price of bananas is $6 per bunch.
a. Plot the equation describing Beth's budget line, and give the equation of that line. Label it BL1. (Put apples on the y-axis and bananas on the x-axis.)
b. Suppose that the price of apples doubles. On the same graph, plot the new budget line and give its equation. Label it BL2.
c. Suppose that the price of bananas doubles and the price of apples is $10. On the same graph, plot the new budget line and give its equation. Label it BL3.
d. Suppose that the price of apples doubles to $20 and the price of bananas is $6. In addtion, suppose Beth's income doubles to $240. On the same graph, plot the new budget line and give its equation. Label it BL4.
e. Suppose now that the price of apples doubles to $20 and the price of bananas doubles to $12. In addition, suppose Beth's income doubles to $240. On the same graph, plot the new budget line and give its equation. Label it BL5.
f. Which two of the budget lines have the same graph and equation? Why is this the case?
3. Paula likes to play soccer and tennis. The following table indicates pairs of soccer and tennis matches that are on the same indifference curve, for 3 different indifference curves.
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Indifference Curve A
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Indifference Curve B
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Indifference Curve C
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Soccer Matches
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Tennis Matches
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Soccer Matches
|
Tennis Matches
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|
Soccer Matches
|
Tennis Matches
|
|
10
|
60
|
|
10
|
90
|
|
10
|
120
|
|
20
|
30
|
|
20
|
45
|
|
20
|
60
|
|
30
|
20
|
|
30
|
30
|
|
30
|
40
|
|
40
|
15
|
|
40
|
22.5
|
|
40
|
30
|
|
50
|
12
|
|
50
|
18
|
|
50
|
24
|
|
60
|
10
|
|
60
|
15
|
|
60
|
20
|
a. Which indifference curve represents the highest level of utility?
b. Plot these three indifference curves on the same graph. Put soccer matches per year on the x-axis and tennis matches per year on the y-axis.
c. Are the four properties of indifference curves, which are discussed in the book, satisfied here? If not, which ones are not satisfied and why?
d. Paula has only a limited amount of time to play soccer and tennis matches during the year. In particular, she has 85 hours. If tennis matches take one hour and soccer matches take two hours, what is Paula's budget line? Plot this line on the same graph as the indifference curves.
e. What is the equation of the budget line?
f. Given the three indifference curves and the budget line, what is Paula's optimal choice of soccer and tennis matches?
g. What is the marginal rate of substitution at this bundle? Why?
4. Bill has $16 which he can spend on either movies or baseball games. Below is a graph that shows Bill's budget lines and Bill's consumer maximization points for each of the three budget lines. Using this information, derive Bill's demand curve for movies. Plot this demand curve and write it's equation. (Assume Bill's demand curve for movies is linear.)
5. Given below are two of Bill's indifference curves. When Bill's income is $16, the price of movies is $2 and the price of baseball games is $4, he has budget line BC1 and his optimal consumption point is A. When Bill's income stays at $16, the price of movies goes up to $8 and the price of baseball games stays at $4, he has budget line BC2 and his optimal consumption point is B. Budget line BC3 represents what Bill's budget line would be if he had income $32 and the price of movies was $8 and the price of baseball games was $4. In this case his optimal consumption point would be C.
a. What happens to the optimal quantity of movies when the price goes from 2$ to 8$?
b. What portion of this change is due to the substitution effect?
c. What portion of this change is due to the income effect?
d. Based on your previous answers, is movies a normal or inferior good for Bill?