Intermediate Microeconomic Theory (3550)
Homework 2 - Answers
Due Thursday, September 18, 2008
Please answer clearly, concisely and in complete sentences. Your work must be legible to receive
credit. This homework assignment is based on Chapter 3 of your Landsburg text Price Theory.
1.
Define the “marginal value of pencils in terms of pens.”
The marginal value of pencils in terms of pens is the number of pens for which the
consumer would be willing to trade one pencil.
2.
Think of two goods you typically consume. Imagine that you have only those two goods to
choose between and you must spend all your income. What is the equation for your budget
line? (Hint: this requires that you make up goods and income.)
Your answer should resemble mine. If I consume only Coke and Oreos on my weekly
budget of $20: Income = PCoke * Cokes + POreos * Oreos which gives:
$20 = ($1.00)(7) + ($3.25)(4).
3.
Draw the graph that reflects your answer to question 2 and include your indifference curve.
(Be sure to label your graph.) Keeping in mind the properties of indifference curves,
explain why your indifference curve is where you have drawn it.
Oreos
6.15
4
7
20
Coke
I prefer about an equal amount of Coke to Oreos; the more Coke I have, the more I’m
willing to give one up to get more Oreos and vice versa. Because preferences normally are
convex, my graph adequately represents my preferences.
4.
(From Landsburg Chapter 3, Question 3). Draw your indifference curves between nickels and
dimes, assuming that you are always willing to trade 2 nickels for 1 dime or vice versa.
What is the marginal value of nickels in terms of dimes?
The indifference curves are parallel lines with slope – ½ (if nickel is on the horizontal
axis). The marginal value of a nickel is ½ dime.
Dimes
5
10
5.
Nickels
Arthur spends his income on bread and chocolate. He views chocolate as a good but is
neutral about bread, in that he doesn’t care if he consumes it or not. Draw his indifference
curve map.
If the neutral product, bread, is on the vertical axis, the indifference curves are parallel
vertical lines. If the neutral product, bread, is on the horizontal axis, the indifference
curves are parallel horizontal lines.
6.
(From Landsburg Chapter 3, Question 11). Recently the price of cheese has risen from $4 per
pound to $6 per pound, the price of meat has fallen from $5 per pound to $2 per pound, and
Susan’s income has stayed fixed at $22 per week. Since the price changes, Susan has been
buying 3 pounds of cheese and 2 pounds of meat every week. Is Susan happier now than she
was before? Explain.
Susan’s old and new bundle lines both pass through (3,2). [3 cheese * $4 each + 2 meat *
$5 each = $22; now, 3 cheese * $6 + 2 meat * $2 = $22]. Her new budget line is tangent
to an indifference curve at that point; her old budget line cuts through the tangency and
is therefore tangent to a higher indifference curve at a point to the northwest of (3,2)
assuming cheese is on the horizontal axis. She is worse off after the price change.
11
meat
4.4
Original I-curve
Point
(3,2)
Original budget
line
New I-curve
7.
3.6
5.5
cheese
(From Landsburg Chapter 3, Question 12). Suppose that you consume nothing but beer and pizza.
In 2007, your income is $10 per week, beer costs $1 per bottle, pizza costs $1 per slice, and
you buy 6 bottles of beer and 4 slices of pizza per week. In 2008, your income rises to $20
per week, the price of beer rises to $2.50 per bottle, and the price of pizza rises to $1.25 per
slice.
a.
In which year are you happier? Better off in 2008.
b.
In which year do you eat more pizza? Justify and illustrate your answer with
indifference curves. Eat more pizza in 2008.
Pizza
 2008 Budget Line
2007
I = 10
Pb = 1
Pz = 1
B=6
Z=4
2008
I = 20
Pb = 2.50
Pz = 1.25
2007: PbB + PzZ = 10
1(6) + 1(4) = 10
10
New I-curve above old
2008: PbB + PzZ = 20
2.50(6) + 1.25(4) = 20
(6,4)
Budget line is steeper due to higher increase
in price of beer, so indifference curve in 2008
must lie to the left of 2007 indifference curve
tangency.
4
6
8.
We know you can buy the same amount in
2008 as in 2007, so both budget lines must
pass through (6,4).
10
Beer
(From Landsburg Chapter 3, Question 22). John buys shoes for $1 a pair and socks for $1 a pair.
His annual income is $20.
a.
Draw John’s budget line. (Carefully label all parts of the graph.)
b.
Now suppose the government institutes two new programs: first, it taxes shoes, so
that shoes now cost John $2 a pair. Second, it gives John an annual cash gift of $10.
Draw his new budget line.
c.
Suppose that with the new programs in place, John chooses to buy 10 pairs of socks
and 10 pairs of shoes. Has the pair of government programs made him better off,
worse off, or neither?
d.
Socks
 Compensated Demand Line
B
20
A
10
John’s Budget Line (Original)
10
20
Shoes
Budget Line after the tax on shoes
The scenario is that with the new program in place, John chooses to buy 10 pairs of shoes and
10 pairs of socks. That means that the point (10,10) is the best he can do with the new budget
line. If the indifference curve is as drawn, John could be at any point between B and A, but
he has chosen not to be at such a point, so we know that the indifference curve has a shape
other than that drawn.
To determine whether John is better or worse off, consider where the indifference curve must
have been on the initial budget line. To avoid indifference curve crossings (remember these
are all John’s curves so they don’t change when the budget line does), the initial indifference
curve must have been tangent to the initial budget line somewhere between A and the
horizontal axis. That would then place the tangency with the initial budget line above the
tangency with the new budget line. This means the pair of programs must make John worse
off.
9.
Your compensated and uncompensated demand curves for bubble gum are likely to be very
similar to each other, but your compensated and uncompensated demand curves for college
tuition might be very different. Why? [Students do not have to answer this one!]
Bubble gum is a very small portion of one’s income. The income effect of a price change
would be small. (It would take little money to compensate one for an increase in the
price of gum). Because tuition is a much larger expense, any change in price would
cause a large change in compensation to keep the same utility as was attained on the
original optimal bundle.
10. What do you find to be the single most difficult concept in this chapter? Explain carefully.
This can be anything in the chapter, but must be answered for credit.