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Microeconomics I
Homework #2
Fall, 2006
I. Multiple choices.(45%)
＊請將答案寫在本大題最後面的表格之中，否則不與計分。
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Which of the following functional forms for utility suggests the greatest income effect
when starting at the point where PX = PY
a. U = min (X, Y)
c. U = x1/2y1/2
b. U = X + Y
d. U = x1/4y3/4
If the income effect is in the opposite direction as the substitution effect but the
substitution effect dominates then the good is
a. normal
b. inferior but not Giffen
c. Giffen
d. There is not enough information to answer.
Suppose a person’s utility is only a function of their consumption of diet soda and they do
not care which brand, Diet Coke (DC) or Diet Pepsi (DP) they consume. Suppose further
that PDC < PDP. If PDC rises to a point where PDC > PDP then the consumption of DC
a. Falls from a positive amount to zero
b. Falls from a positive amount to another positive amount.
c. rises.
d. stays at zero.
The lump sum principle suggests that the tax that reduces utility the least is
a. a tax on income
b. a tax on one good, not all goods
c. an equal tax on all goods, not income
d. an unequal tax on all goods, not income
Suppose three goods (steak, Russet potatoes, and Redskinned potatoes) provide
consumers with utility so that U = steak1/2(Russet and Redskinned)1/2. Suppose a price
index, based on consumption patterns is specified as PI = PsteakPRussetPRed. Suppose that in
the base year PRusset = PRed. Suppose the next year PRusset rises more than PRed, the price
index will
a. overstate the impact on consumer happiness.
b. understate the impact on consumer happiness.
c. accurately state the impact on consumer happiness.
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If a good is inferior and its price increases,
a. the income effect will be positive and the substitution effect will be positive.
b. the income effect will be negative and the substitution effect will be negative.
c. the income effect will be positive and the substitution effect will be negative.
d. the income effect will be negative and the substitution effect will be positive.
Suppose and the price of X is 1, the price of Y is 1 and income is $12. If the price of X
increases to 2, the income effect (in terms of X) is
a. 2
c. 0
b. -1
d. -2
The relationship between changes in income and purchase of a good indicates
a. whether the good is a luxury or necessity.
b. whether the good is normal or inferior.
c. whether the good is a complement or substitute.
d. Both a and b.
9. At any price, the market demand curve
a. is flatter than the flattest individual demand curve.
b. has a slope that is the average of the individual demand curve slopes.
c. is steeper than the steepest individual demand curve.
d. has a horizontal intercept equal to the average of the individual demand curve
horizontal intercepts.
10. Suppose demand can be written as PQ = 1000. The elasticity of demand is
a. increasing as price rises.
b. decreasing as price rises.
c. constant regardless of prices and perfectly elastic.
d. constant regardless of prices and unit elastic.
11. If the income elasticity of demand is -1/2, the good is
a. a luxury.
b. a normal good (but not a luxury).
c. an inferior good.
d. a Giffen good.
12. In Heterogenia everyone is different. Each person has a demand for apples that is
P = Ai -BiQ. The market demand for apples is
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b.
c.
d.
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13. Suppose the “poor” and “rich” have identical demand functions but only differ in income
(I).
The price elasticity of their individual demand curves is such that
a. the rich person’s demand is more elastic than the poor person’s.
b. the poor person’s demand is more elastic than the rich person’s.
c. the poor person’s demand is as elastic as the rich person’s.
14. The market demand curve for any good is
a. independent of individuals’ demand curves for the good.
b. the vertical summation of individuals’ demand curves.
c. the horizontal summation of individuals’ demand curves.
d. derived from the firm’s marginal cost of production.
15. If the demand for a product is elastic, then a rise in price will
a. cause total spending on the good to increase.
b. cause total spending on the good to decrease.
c. keep total spending the same, but reduce the quantity demanded.
d. keep total spending the same, but increase the quantity demanded.
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Ⅱ. Problems.(55%)
＊ 答案請寫在題目下面的空白處，並標明題號。(共四題)
＊ 只有答案而無計算過程或理由以及圖形的刻度標示不清者，一率不予計分。
1.
The Jones family spends all its income on food and shelter. It derives maximum utility
when it spends two-thirds of its income on shelter and one-thirds of its income on food.
a.) Use this information to calculate the demand functions for shelter and food. Show
that demand is homogeneous with respect to changes in all prices and income.
b.) Graph the demand curves for shelter and food for the Jones family if family income
is $20,000.
c.) Show how the demand curves for shelter and food would shift if income rose to
$50,000.(Plot the graph in part b.)
d.) Explain why a change in food prices does not affect shelter purchases in this problem.
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2.
Tom, Dick, and Harry constitute the entire market for scrod. Tom’s demand curve is given
by
Q1=100－2P
for P  50. For P>50, Q1=0. Dick’s demand curve is given by
Q2=160－4P
for P  40. For P>40, Q2=0. Harry’s demand curve is given by
Q3=150－5P
for P  30. For P>30, Q3=0. Using this information, answer the following：
a.) How much scrod is demanded by each person at P=50? At P=35? At P=25? At P=10?
And at P=0?
b.) What is the total market demand for scrod at each of the prices specified in part a?
c.) Graph each individual’s demand curve. (only plot one graph and label each demand
curve clearly)
d.) Use the individual demand curves and the results of part b to construct the total
market demand for scrod. (plot another graph)
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3.
Suppose that the demand curve for gummy bears is given by
Q= 200－20P
, where Q is pounds of gummy bears bought per week and P is the price in dollars per
pound.
a.) How many gummy bears will be bought at P=0?
b.) At what price does the quantity demanded of gummy bears become 0?
c.) Calculate total expenditures (PQ) for gummy bears of each whole dollar price
between the prices identified in part a and part b.
d.) What price for gummy bears yields the highest total expenditures?
e.) Suppose the demand for gummy bears shifted to Q=300－20P. How would your
answers to part a through part d change? Explain the difference intuitively and with
a graph.
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4.
【The last problem in HW1】(20% in HW1)
Sometimes it is convenient to think about the consumer’s problem in its “dual” form. This
alternative approach asks how a person could achieve a given target level of utility at
minimal cost.
a.) Develop a graphical argument to show that this approach will yield the same choices
for this consumer as would the utility-maximizing approach.
b.) Returning to problem 2.3（ U  C  D ）, assume that Paul’s target level of utility is
U=10. Calculate the costs of attaining this utility target for the following boundless of
goods:
i.
C=100, D=1
iv.
C=20, D=5
ii.
C=50, D=2
v.
C=10, D=10
iii.
C=25, D=4
vi.
C=5, D=20
c.) Which of the bundles in part b provides the least costly way of reaching the U=10
target? How does this compare to the utility-maximizing solution found in problem
2.3?
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