This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ' “‘9” "ROBLEM SET 1, For each of the following events, consider how you might react.
What things might you consume more or less of? Would you
work more or less? Would you increase or decrease your saving?
Are your responses consistent with the discussion of household
behavior in this chapter? a. Tuition at your college is cut 25 percent. b. You receive an award that pays you $300 per month for the
next 5 years. c. The price of food doubles. (If you are on a meal plan, assume .. a ‘ that your board charges double.) d. A new business opens up nearby offering parttime jobs at i $20 per hour. 2. The following table gives a hypothetical total utility schedule for
the Cookie Monster (CM): Number of Cookies Total Utility 0 0
100
200
275
325
350
360
360 \IOWJKUJNb—d Calculate the CM’s marginal utility schedule. Draw a graph of
total and marginal utility. If cookies cost the CM 5 cents each, what is the maximum number of cookies he would most likely
eat? ' a 3. Kamika lives in Chicago but goes to school in Tucson, Arizona. 1 For the last 2 years, she has made four trips home each year. i " During 2001, the price of a roundtrip ticket from Chicago to Tucson increased from $350 to $600. As a result, Kamika bought ﬁve fewer CDs that year and decided not to drive to Phoenix with friends for an expensive rock concert. a. Explain how Kamika’s demand for CDs and concert tickets
can be affected by an increase in air travel prices. b. By using this example, explain why both income and substi
tution effects might be expected to reduce the number of
trips home that Kamika takes. 4. Sketch the following budget constraints: 3 ' PX PY Income
a. $20 $ 50 $1,000
b. 40 50 1,000
c. 20 100 1,000 .1 d. 20 50 2,000
e. .25 .25 7.00
f. .25 .50 7.00
g. .50 .25 7.00 @311 January 1, Professor Smith made a resolution to lose some
Weight and save some money. He decided that he would strictly
budget $100 for lunches each month. For lunch he has only two
Choices: the faculty club, where the price ofa lunch is $5, and
Alice’s Restaurant, where the price of a lunch is $10. Every day
that he does not eat lunch, he runs 5 miles. , My” 1, ,.,._ .. i ,M ..»,..._. . .. ...~ Hmwort 4+ 4 r 3. Assuming that Professor Smith spends the entire $100 each
month at either Alice’s or the club, sketch his budget con
straint. Show actual numbers on the axes. b. Last month Professor Smith chose to eat at the club 10 times
and at Alice’s 5 times. Does this choice ﬁt within his budget
constraint? c. Last month, Alice ran a halfprice lunch special all month. All
lunches were reduced to $5. Show the effect on Professor
Smith’s budget constraint. 6. Steve Forbes, Republican candidate for President during the pri
mary elections in the year 2000, advocated cutting tax rates
across the board, thus raising take—home pay for all taxpayers.
The purpose was in part to encourage work and increase the
supply of labor. People will respond by working longer hours
(supplying more labor) as long as income effects are greater
than substitution effects. Do you agree or disagree? Explain your
answer. 7. Assume that Mei has $100 per month to divide between dinners
at a Chinese restaurant and nights at Zanzibar, a local pub.
Assume that going to Zanzibar costs $20 and eating at the
Chinese restaurant costs $10. Suppose that Mei spends two
nights at Zanzibar and eats six times at the Chinese restaurant.
a. Draw Mei’s budget constraint and show that she can afford six dinners and two nights at Zanzibar. b. Assume that Mei comes into some money and can now spend
$200 per month. Draw her new budget constraint. c. As a result of the increase in income, Mei decides to spend
eight nights at Zanzibar and eat at the Chinese restaurant
four times. What kind of a good is Chinese food? What kind
of a good is a night at Zanzibar? d. What part of the increase in Zanzibar trips is due to the
income effect, and which part is due to the substitution
effect? Explain your answer. .Say whether you agree or disagree with each of the following
statements, and explain your reason: a. “If the income effect of a wage change dominates the substi~
tution effect for a given household, and the household works
longer hours following a wage change, wages must have
risen.” b. “In product markets when a price falls, the substitution effect
leads to more consumption, but for normal goods, the
income effect leads to less consumption.” 9. Suppose that the price ofX is $5 and the price of Yis $10 and a
hypothetical household has $500 to spend per month on goods
X and Y. a. Sketch the household budget constraint. b. Assume that the household splits its income equally between
X and Y. Show where the household ends up on the budget
constraint. c. Suppose that the household income doubles to $1,000. Sketch
the new budget constraint facing the household. d. Suppose after the change the household spends $200 on Y
and $800 on X. This implies that X is a normal or inferior
good? What about Y? 10. For this problem, assume that Joe has $80 to spend on books
and movies each month, and that both goods must be fl gwrr II: Di
‘3
.4.
'93.
1
E :q 3.!" f 195:: no: 130 Part 2 Microeconomics: Consumers and Firms This is the same rule derived in our earlier discussion without
using indifference curves. We can describe this rule intuitively
by saying that consumers maximize their total utility by equat
ing the marginal utility per dollar spent on X with the mar—
ginal utility per dollar spent on Y. If this rule did not hold, util i ity could be increased by shifting money from one good to
; the other. DERIVING A DEMAND CURVE FROM INDIFFERENCE . CURVES AND BUDGET CONSTRAINTS
» We now turn to the task of deriving a simple demand curve from indifference curves and budget constraints. A demand
curve shows the quantity of a single good, X in this case, that a ' consumer will demand at various prices. To derive the demand
’ curve, we need to confront our consumer with several alterna
3 tive prices for X while keeping other prices, income, and pref
': erences constant. 1. An indiﬁ‘erence curve is a set of points, each point represent
ing a combination of goods X and Y, all of which yield the
same total utility. A particular consumer’s set of indifference
curves is called a preference map. 2. The slope of an indifference curve is the ratio of the marginal
utility of X to the marginal utility of Y, and it is negative. indifference curve A set of points, each
point representing a combination of goods X
and Y, all of which yield the same total
utility. 127 PROBLEM SET 1. Which of the four assumptions that were made at the beginning
of the Appendix are violated by the indifference curves in
Figure 1? Explain. 2. Assume that a household receives a weekly income of $100. If
Figure 2 on p. 131 represents the choices of that household as
the price of X changes, plot three points on the household
demand curve. @f Ann’s marginal rate of substitution of onr X is S—that is, MUX/MUY = S—the price ofX is $9.00, and the price of Yis marginal rate of substitution M UX/M UY;
the ratio at which a household is willing to
substitute good Y for good X. 127 Figure 5AA shows the derivation. We begin with price P}.
At that price, the utility—maximizing point is A, where the con—
sumer demands X1 units of X. Therefore, in the right—hand
diagram, we plot P; against Xx. This is the first point on our
demand curve. Now we lower the price ofX to P)? Lowering the price
expands the opportunity set, and the budget constraint shifts
to the right. Because the price of X has fallen, if our consumer
spends all of the income on X, the individual can buy more of
it. Our consumer is also better off, because of being able to
move to a higher indifference curve. The new utility—maximiz
ing point is B, where the consumer demands X2 units of X.
Because the consumer demands X2 units of X at a price of P3,
we plot Pﬁ against X2 in the right—hand diagram. A second
price cut to P; moves our consumer to point C, with a
demand of X3 units of X, and so on. Thus, we see how the
demand curve can be derived from a consumer’s preference
map and budget constraint. 3. As long as indifference curves are convex to the origin, utility
maximization will take place at that point at which the indif
ference curve is just tangent to—that is, just touches—the budget constraint. The utility—maximizing rule can also be
written as M UX/PX = M UY/Py. preference map A consumer's set of
indifference curves. 127 $2.00, she is spending too much of her income on Y. Do you
agree or disagree? Explain your answer using a graph. *4. Assume that Jim is a rational consumer who consumes only two
goods, apples (A) and nuts (N). Assume that his marginal rate
of substitution of apples for nuts is given by the following
formula: MRS = MUN/MUA = A/N *Note: Problems marked with an asterisk are more challenging. ...
View
Full Document
 Summer '08
 xasdf
 Microeconomics

Click to edit the document details