|
|
U8216
Microeconomics and Policy Analysis 1.
Grete, Mary, and Dan are a family that
does everything together, including making decisions.
They have to decide what to do for their vacation.
There are three possibilities: stay at home, sit on the porch and
watch birds and squirrels (call
this “home”); make a pilgrimage to Fatima (call this “Fatima”); or
visit the Power Tool Hall of Fame (call this “buzz”).
Their preferences are: Grete: Home is best, Buzz is next, Fatima is worst. Mary: Fatima is best, Home is next, Buzz is worst. Dan:
Buzz is best, Fatima is next, Home is worst. a.
Suppose they use the following decision making procedure: each
writes down (truthfully, since they are all very sincere creatures,
especially Grete) their ranking (1 for the best, 2 for next, 3 for worst).
The scores for each option are added up, and the family goes to the
one with the lowest score. In
the event of ties, what Grete wants prevails, since she’s the furriest
and can jump the highest. If
they use this procedure, what will there decision be? b.
After they make up their minds, they find out that the Power Tool
Hall of Fame has been closed for the season.
They re-vote, but without Buzz.
What will they do now? c.
Does decision-making by this household, using this procedure, obey
the assumptions that economists make about rational preferences?
Why or why not? d.
What does this tell you about saying that universities, clubs,
households, corporations, Congress, or society has preferences? 2.
Each day Paul, who is in third grade, eats lunch at school.
He likes only Twinkies (t) and
Orange Slice (s), and these
provide him with a utility of U
= ts. a.
If Twinkies cost a dime each, and Slice costs a quarter per cup,
how should Paul spend the dollar his mother gives him to maximize his
utility? b.
If the school tries to discourage Twinkie consumption by raising
the price to 40˘, by how much will Paul’s mother have to increase his
lunch allowance to provide him with the same level of utility he had in
part (a)? How many Twinkies and cups of Slice will he buy now (the
school allows fractional purchases)? Suppose that prices are as in
(b), that Paul’s mother in fact gives him the extra allowance, but that
the school now prohibits fractional purchases. Will this encourage
or discourage Paul’s Twinkie purchases? Will it make students
better off? c.
Suppose that all is as in part (b), but that the school now
prohibits fractional purchases. Will this encourage or discourage Paul’s Twinkie habit? 3.
Every evening JP enjoys the consumption of cigars (c)
and brandy (b) according to the
function: U(c,b)
= 20c - c2 + 18b
- 3b2. a.
How many cigars and glasses of brandy does he consume during an
evening? (Cost is no object to JP.) b.
Lately, however, JP’s doctors have advised him to limit the sum
of brandy and cigars consumed to 5. How much of each will he consume
under these circumstances? 4.
Ms. Caffeine enjoys coffee (c)
and tea (t) according to the function U(c,t)
= 3c + 4t. If coffee and tea cost $3 each and she has $12 to spend,
how much coffee and tea will she buy to maximize her utility? Draw
the graph of her indifference curves and the budget constraint, and show
that the utility-maximizing point is a boundary solution at which the
usual utility-maximizing condition does not hold. Under what prices would
the usual condition hold? Would the maximizing point be unique under
these circumstances? 5.
David gets an allowance of $3 per month as an allowance to spend
any way he pleases. Since he likes only peanut butter and jelly
sandwiches, he spends the entire amount on peanut butter (at a nickel an
ounce) and jelly (at a dime an ounce). Bread is provided free of
charge by a concerned neighbor. David is a particular eater and
makes his sandwiches with exactly 1 oz of peanut butter and 2 oz of jelly.
He is set in his ways and will never change these proportions. a.
How much peanut butter and jelly will David buy with his $3
allowance in a week? b.
Suppose the price of jelly were to rise to 15˘ an ounce.
How much of each commodity would be bought? c.
By how much should David's allowance be raised to compensate him
for the rise in the price of jelly? d.
In what sense does this problem involve only a single commodity:
peanut butter and jelly sandwiches? 6.
"As far as charities in this country are concerned, raising
income tax rates on upper-income families would be the worst possible way
to close the deficit. Charities depend on rich people for their
support; taking money away from rich people will drastically curtail the
amount they give to charity. That’s why we need to cut income tax
rates by 15%." Think about charitable contributions as a good
for the donor – if they are not a good, no one would make them.
Recall that charitable contributions are tax deductible, while other
expenditures aren’t. Think about the "price" of a
charitable contribution, and Mr Slutsky. Under what circumstances is
the speaker right? Wrong? 7.
Remember Bill Clinton University from
Problem Set 1? It turns out
that the people who run the university act as if they were maximizing the
“university utility function”: U(f,i) = .4 ln
i + .6 ln f Where i denotes number of interns hired and f denotes number of fellowships awarded. a.
Before the donor appears on the scene and BCU has only a million a
year, how many fellowships does it award?
How many interns are hired? b.
If the donor gives an unrestricted grant that generates an
additional $500,000 a year in income for BCU, how many fellowships will it
award? How many interns will
be hired? c.
If the donor explicitly states that BCU must use all of her money
for fellowships, how many fellowships will it award?
How many interns will be hired? d.
Suppose the donor states that she will match $5 for every $11 that
BCU spends on fellowships, but that the donation will be unrestricted: the
university can do whatever it wants with the money.
How many fellowships will BCU offer?
How much will it cost the donor per year? e.
Suppose the donor gets more enthusiastic about matching grants and
promises to match whatever BCU spends on fellowships at a rate of $2 for
every dollar BCU spends, but only up to a maximum of $500,000 a year.
How many fellowships will BCU offer? f.
All the donor cares about is the number of fellowships that BCU
students receive. She has never taken micro, though, and so she doesn’t know
what to do. She calls you for
advice. If you are really her
friend, what advice will you give her?
If you are really an undercover operative working for the
administration of BCU, what will you tell her? 8.
(optional) Giuseppi
owns a vineyard in northern Italy. He provides food and shelter for
the grape growers, who make the wine and pay Guiseppi a fixed amount of
wine. The worker’s rent is Giuseppi’s only source of income.
Giuseppi consumes some of the wine and sells the rest for income to
purchase a second good, good 2 (whose price is 1). Suppose that the
price of wine, Pw,
rises. Will Giuseppi consume less wine? Explain, using
diagrams. 9.
(optional) In July 1990,
the Czechoslovakian government reduced agricultural subsidies and allowed
food prices (which were still state-controlled) to rise. It used the
entire amount of money it saved on subsidies to increase family
allowances. Assume that all Czechoslovakian families are the same.
Did the combination of the two changes make the representative
Czechoslovakian worse off, better off, or leave her indifferent?
Explain. 10.
(optional) Rufus
lives in a small town and buys everything through mail order, everything
being food and clothes. Initially one jumpsuit costs $1 and one loaf
$1. He consumes 7 loaves and 3 jumpsuits. Now there is a cloth
shortage and the government issues 5 clothing coupons to each individual.
With the coupon, the price of jumpsuits remains $1, but without the coupon
the price rises to $1.50. Rufus’s friend George tells him that for
the right bribe, he can get Rufus 5 more coupons. How much is Rufus
willing to pay for each extra coupon? 11.
(optional) Assume that
consumers are choosing between housing services measured in square feet
and consumption of other goods aggregated and measured in dollars. a.
Show the utility-maximizing position in a diagram. b.
Now, suppose the government agrees to subsidize consumers by paying
50% of their housing costs. How will the budget line change?
Show the new utility-maximizing point. c.
Show in the diagram the minimum amount of income support the
government would have to give to make consumers just as well of as they
were in situation (b) without the housing subsidy. d.
Show that this is less than the housing subsidy the government is
paying in situation (b).
|
