ECON 202 Microeconomics
Winter 2008
Economics Department
Faculty of Management Technology
Dr. Abdel-Hameed Nawar
German University in Cairo
Solution Key to Home Assignment 3
YOU HAVE ONE WEEK TO SOLVE THIS HOME ASSIGNMENT
DUE IN THE SECTION
:: Multiple Choice Questions ::
Suppose Mina enjoys classical (C) music but is irritated by Waw-Waw-Wa type of music
(W). Which of the following utility functions would best represent Mina's utility from
classical and Waw-Waw-Wa type of music?
A. U = W0.5 T0.5
B. U = C . T
C. U = C / W
D. U = W / C
•
Note that ܹ is bad.
ଵ
Hence, to account for bad in our preference analysis, we redefine it as ቀௐቁ so that now more of
ଵ
ቀ ቁ is preferred to less.
ௐ
•
A utility function that describes how much of one market basket is preferred to another is
called
A. an ordinal utility function.
B. a cardinal utility function.
C. a utility-maximizing function.
D. a definitive utility function.
•
Indifference curves cannot intersect because of the assumption that
A. marginal utility diminishes as more of that good is consumed.
B. indifference curves are negatively sloped.
C. preferences are transitive.
D. preferences are complete.
•
Indifference curves cannot slope upward because of the assumption that
A. MRS is in absolute value.
B. more is preferred to less
C. preferences are transitive.
D. preferences are complete.
•
If Karim's marginal rate of substitution of Fried Ice Cream for Pecan Custard Dessert is 2,
then we know that
A. he is willing to give up 2 units of Pecan Custard Dessert to get the next unit of Fried Ice
Cream.
B. he is willing to give up 2 units of Fried Ice Cream to get the next unit of Pecan Custard
Dessert.
C. 2 units of Pecan Custard Dessert are identical to 2 units of Fried Ice Cream.
D. he prefers to eat 2 units of Pecan Custard Dessert together with every unit of Fried Ice
Cream he eats.
•
The indifference curves of Nisf coins and Guineas are
A. negatively sloped straight lines.
B. nominal.
C. upward sloping.
D. L-shaped.
•
The indifference curves of salt and salad are
A. negatively sloped straight lines.
B. nominal.
C. upward sloping.
D. L-shaped.
•
Consider a consumer who spends his income on Goods (G) and Services (S). If the
consumer's budget line can be written as G = 300 – 2 S, then we know that:
A. Goods costs twice as much as Services.
B. the consumer's nominal income is 300 EGP.
C. Services costs twice as much as Goods.
D. the consumer's nominal income is 600 EGP.
•
Consider an average Egyptian consumer who spends his monthly income on Goods (G) and
Services (S). The consumer's budget line can be written as G = 300 – 2S. If we know that the
price of Goods is 1.35, then:
A. The price of services is 2.7.
B. The consumer's nominal income is 405 EGP.
C. The consumer's real income in terms of the price of services is 150 EGP.
D. All of the above.
Note that ܲீ = 1.35, from the budget line equation we know that:
௉ೄ
The slope is − ௉௉ೄ = − ଵ.ଷହ
= −2 , thus ܲௌ = 2.7 ,
ಸ
ூ
ூ
The y-intercept is ௉ = 300 = ଵ.ଷହ , thus ‫ = ܫ‬405
ಸ
ூ
The x-intercept is ௉ =
ೄ
ସ଴ହ
ଶ.଻
= 150
:: Discussion Questions ::
[1] In the theory of consumer behavior, more of a good is preferred to less. How do we
reconcile this theory with the concept of "bads," or products for which less is preferred
to more?
We have assumed all our commodities are “goods” There are commodities we don’t want more
of, however. These are called “bads” and for which less is preferred to more. Examples include
air pollution, asbestos, noise etc. In order to account for bads in the preference analysis, we
redefine the commodity to be clean air instead of air pollution and asbestos removal instead of
asbestos etc. In this way, the more will be preferred to less, which is consistent with the theory of
consumer behavior.
[2] Elaborate on the equilibrium condition that
ࡹࢁࢄ
ࡹࢁࢅ
=
ࡼࢄ
ࡼࢅ
, where X and Y are two goods.
The maximum satisfaction is obtainable only when the consumer’s ratio of marginal utilities of
X and Y indicated by the consumer preferences is the same as the ratio price of X and Y
determined by the market. (See also Making Sense of the Slopes in Sheet 7).
:: Problems ::
Mona consumes only Pizza Combo (X) and Turkey Combo (Y) while she is on campus. She
has a budget of EGP 240 to spend monthly on campus. Pizza Combo costs EGP 6 and
Turkey Combo costs EGP 8.
[1] Write down the budget line equation.
..
..
ܲ௑ ܺ + ܲ௒ ܻ = ‫ܫ‬
6 ܺ + 8 ܻ = 240
[2] If Mona spent her budget on Pizza Combo (X), how much could she buy?
6 ܺ + 8 (0) = 240
..
..
ܺ = 40
[3] If Mona spent her budget on Turkey Combo (Y), how much could she buy?
..
6 (0) + 8 ܻ = 240
..
ܻ = 30
[4] Graph the budget line.
[5] Calculate the slope of the budget line slope = ૟/ૡ = 3/4
Income Change: Graph the budget line with the change.
[6] If Mona’s budget increased from EGP 240 to EGP 300, what will happen to the budget
line, holding prices constant?
..
..
ܲ௑ ܺ + ܲ௒ ܻ = ‫ܫ‬
6 ܺ + 8 ܻ = 300
Price Change :Graph the budget line with the change.
[7] If the price of Pizza Combo (X) increases to EGP 8, holding other things constant, how
much she could buy? What is the slope of the budget line after this change?
..
8 ܺ + 8 ܻ = 300
8 ܺ = 300 8ܺ = 37.5 , 8 ܻ = 300 ܻ = 37.5 and slope = 8/8 = 1
..
[8] If the price of Turkey Combo (Y) further increases to EGP 12, holding other things
constant, how much she could buy? What is the slope of the budget line after this
change?
..
8 ܺ + 12 ܻ = 300
..
8 ܺ = 300 ܺ = 37.5 , 12 ܻ = 300 ܻ = 25 and slope = 8/12 = 2/3
[9] If the both the price of Pizza Combo (X) and Turkey Combo (Y) increase simultaneously
to EGP 9 and EGP 15 respectively, while holding income constant. How much she could
buy?
..
..
9 ܺ + 15 ܻ = 300
9 ܺ = 300 ܺ = 33.3 , 15 ܻ = 300 ܻ = 20 and slope = 9/15 = 3/5
:: Solve Problem 15 from the Textbook page 105 ::
Jane receives utility from days spent traveling on vacation domestically (ࡰ) and days spent
traveling on vacation in a foreign country (ࡲ), as given by the utility function (ࡰ, ࡲ) =
૚૙ࡰࡲ . In addition, the price of a day spent traveling domestically is $100, the price of a
day spent traveling in a foreign country is $400, and Jane’s annual travel budget is $4,000.
a.
Illustrate the indifference curve associated with a utility of 800 and the indifference
curve associated with a utility of 1200.
The indifference curve with a utility of 800 has the equation 10‫ = ܨܦ‬800, or
‫ = ܨܦ‬80, and hence ‫ = ܨ‬80ൗ‫ܦ‬. Choose combinations of D and F whose product
is 80 to find a few bundles.
The indifference curve with a utility of 1200 has the equation 10‫ = ܨܦ‬1200, or
‫ = ܨܦ‬120 , and hence ‫ = ܨ‬120ൗ‫ ܦ‬. Choose combinations of D and F whose
product is 120 to find a few bundles.
U=800
U=1200
D F=80/D
5 16.00
10 8.00
15 5.33
20 4.00
25 3.20
30 2.67
35 2.29
40 2.00
45 1.78
b.
D F=120/D
5
24.00
10 12.00
15
8.00
20
6.00
25
4.80
30
4.00
35
3.43
40
3.00
45
2.67
Graph Jane’s budget line on the same graph.
..
..
‫ܲ = ܫ‬஽ ‫ ܦ‬+ ܲி ‫ܨ‬
4000 = 100 ‫ ܦ‬+ 400 ‫ܨ‬
If Jane spends all of her budget on domestic travel, i.e. 4000 = 100 ‫ܦ‬, she can
afford 40 days. If she spends all of her budget on foreign travel, i.e. 4000 = 40 ‫ܨ‬,
she can afford 10 days. Combining the budget line and the indifference curves
together,
c.
Can Jane afford any of the bundles that give her a utility of 800? What about a
utility of 1200?
Yes she can afford some of the bundles that give her a utility of 800 as part of this
indifference curve lies below the budget line. However, she cannot afford any of
the bundles that give her a utility of 1200 as this whole indifference curve lies
above the budget line.
d.
Find Jane’s utility maximizing choice of days spent traveling domestically and days
spent in a foreign country.
The optimal bundle is where
the slope of the indifference curve is equal to the slope of the budget line, and
Jane is spending her entire income.
The slope of the indifference curve is the ratio of marginal utilities of
ܷ(‫ܦ‬, ‫ = ) ܨ‬10 ∗ ‫ܨ ∗ ܦ‬
..
..
‫ܷܯ‬஽ =
..
‫ܷܯ‬ி =
..
∆௎
∆஽
∆௎
∆ி
=
=
ଵ଴∗ (஽ା∆஽)∗ ஼ିଵ଴∗ ஽∗ ி
∆஽
ଵ଴∗ ஽∗ (ிା∆ி)ିଵ଴∗ ஽∗ ி
‫ = ܴܵܯ‬−
∆ி
ெ௎ವ
ெ௎ಷ
=−
= 10 ∗ ‫ܨ‬
= 10 ∗ ‫ܦ‬
ଵ଴∗ ி
ଵ଴∗஽
=−
ி
஽
The slope of the budget line is
−
..
..
Thus
௉ವ
௉ಷ
=−
‫= ܴܵܯ‬
ଵ଴
ସ଴
ெ௎ವ
ெ௎ಷ
..
or
‫=ܦ‬
We now have two equations and two unknowns:
=−
=
4‫ܨ‬
௉ವ
௉ಷ
ଵ
ସ
gives
..
‫ = ܦ‬4‫ܨ‬
..
4000 = 100 ‫ ܦ‬+ 400 ‫ܨ‬
ி
஽
ଵ
= ,
ସ
Solving the above two equations gives ࡰ = ૛૙ and ࡲ = ૞. Utility is ࢁ = ૚૙૙૙. This bundle
(૛૙, ૞) is on an indifference curve between the two previously drawn.