Intermediate Microeconomics
Prof. David Bjerk
Extra Practice Questions for Midterm 1 (answers)
1 - Jay Lowe consumes only wine and cheese. Three of his indifference curves over wine
and cheese are shown below, along with Budget constraints for m = $20, m = $28, and m
= $36.
glasses
of wine
10
9
8
7
6
5
4
3
2
1
2
4
6
8 10 12 14 16 18 20
lbs. of cheese
(a) Sketch Jay’s Engel curve for Wine (label carefully).
A:
m
36
28
20
2
6
10
wine
(b) For Jay, is wine a normal good, an inferior good, or can’t we tell given the
information presented? (Briefly explain)
A: A normal good since demand increases as his income increases.
2 - Save the Bears Inc. care about saving Black Bears and Polar Bears in such a way that
their preferences are captured by the utility function U(qb,qp) = qb0.5 qp, where qb denotes
the number of Black Bears they save and qp denotes the number of Polar bears they save.
Suppose Save the Bears Inc. has an annual budget of $600 and it costs $10 to save each
Black Bear and $20 to save each Polar Bear,
(a) How many Black Bears and Polar Bears will Save the Bears Inc. optimally choose to
save?
A: Given Cobb-Douglas preferences, we know they demands will be
qb = 0.5/1.5*600/10 = 1/3*60 = 20
qp = 1/1.5*600/20 = 2/3*30 = 20
(b) Suppose the melting polar ice caps makes saving each Polar Bear more expensive.
Given their limited budget, this will cause Save the Bears Inc. to save not only fewer
Polar Bears, but also fewer Black Bears. True, False, or do we need more information?
(Briefly justify the answer you give)
A: False. Given the Cobb-Douglas preferences, Save the Bear’s demand function for
Black Bears will depend only on the overall budget and the price of saving Black Bears.
So a change in the price of saving a Polar Bear will not affect how many Black Bears are
saved.
3 –Consider a bundle with 10 pizza slices and 6 glasses of beer. Assume that Pippy’s
preferences exhibit a diminishing marginal rate of substitution and her marginal rate of
substitution at this {10,6} bundle is such that she would be willing to give up to 3 beers
for one more slice of pizza. If the current price of a glass of beer is $2 and a the price of a
slice of pizza is $4, would Pippy change her current consumption bundle to one with
more pizza and less beer, one with less pizza and more beer, or stay choose the bundle
{10, 6}? (Explain your answer carefully and use a graph if necessary).
A:
beer
Given Pippy has a diminishing Marginal
Rate of Substitution and at the bundle {10,
6} her MRS exceeds the price ratio (4/2 or
2/1) in magnitude, we know Pippy is willing
to give up more beer for another slice of
6
pizza than she would have to at current
prices. Therefore, if she was rational, she
would choose a bundle with more pizza and
less beer. This is shown on the graph to the
right.
Slope of indifference
curve at {10,6} = - 3
slope of budget
constraint = -2
10
pizza
4 - Bo and Luke live on Hazzard Island. There are two goods on Hazzard Island,
moonshine (m) and grits (g). Bo is endowed with 4 gallons of moonshine and 4 lbs. of
grits, while Luke is endowed with 6 gallons of moonshine and 4 lbs. of grits. The
Edgeworth Box below shows several indifference curves for Bo and Luke. (Bo’s are
solid, Luke’s are dotted).
gal moonshine
10 9 8 7 6 5 4 3 2 1
Luke
lbs.grit
8
7
1
endowment
2
point
6
3
5
allocation when Bo
4
and Luke optimize
4
given prices in (c)
5
3
6
2
allocation in (a)
1
7
8 lbs. grits
Bo
1 2 3 4 5 6 7 8 9 10
gal. moonshine
(a) Consider an allocation where Bo gets 7 gal. of moonshine and 3 lbs. of grits and Luke
gets 3 gal. of moonshine and 5 lbs. of grits. Will this allocation be Pareto Superior to the
allocation where each person consumes his endowment?
A: Yes, since it would put both Bo and Luke on an higher indifference curve.
(b) Given the indifference curves above, are there any allocations that appear to be Pareto
Efficient but are not Pareto Superior to the allocation where each person consumes his
endowment? If so, name one. If not, state why not.
A: Yes. The allocation that gives Bo the bundle {5, 1} and Luke the bundle {5,7}
(efficient but makes Bo worse off than endowment bundle) and the allocation that gives
Bo the bundle {7, 5} and Luke the bundle {3,3} (efficient but makes Luke worse off than
endowment bundle).
(c) Given the indifference curves show above, in equilibrium can it be the case that 1
gallon of moonshine can be traded for 1/2 lb. of grits (or equivalently 1 lb. of grits can be
traded for 2 gallons of moonshine)? (Use the Edgeworth Box above to help explain why
you give the answer that you do)
A: Yes. As shown in the Edgeworth Box above, these prices would imply a budget
constraint such that the amount of moonshine Bo would demand given this constraint
plus the amount of moonshine Luke would demand given this constraint would exactly
equal 10 gallons (the amount in the economy). The same would hold true for grits.
5. Suppose the price of a pound of beans $5 and the price of a pound of rice is $4.
Further, suppose the government is considering two tax programs. Program 1 is to
impose an additional sales tax of $13 on each lb. of rice sold. Program 2 is to make
everyone just pay $12 out of their endowment (assume this is possible).
(a) If Tatiana has an endowment of $50, and her preferences over the lbs. of beans (qb)
and the lbs. of rice (qr) she consumes are captured by the utility function u(qb, qr) = qb +
qr, what will be Tatina’s optimal bundle under each tax program? (Briefly explain your
answer)
A: This utility function reveals that Tatiana only cares about the total amount of food she
has, or in other words, rice and beans are perfect substitutes for her. This means she will
spend all her money on the cheaper good.
Under Program 1, beans are cheaper ($5/lb vs 4+13 = $17/lb), so Tatina would spend all
her money on beans, meaning she would choose the bundle with 50/5 = 10 lbs of beans
and 0 lbs of rice.
Under Program 2, rice is cheaper, so Tatiana would spend all her money left over after
the lump sum tax on rice, meaning she would choose the bundle with 38/4 = 9.5 lbs of
rice and 0 lbs of beans.
(b) How much will Tatiana pay in taxes if she gets to choose which tax program is
implemented (assuming Tatiana is rational when it comes to choosing tax programs)?
(Briefly explain your answer)
A: Tatiana’s utility from her optimal bundle under Program 1 is u = 10 + 0 = 10. Her
utility from her optimal bundle under Program 2 is u = 0 + 9.5 = 9.5. Therefore, she
would prefer Program 1 since it gives her higher utility. Given she chooses Program 1
she would buy no rice and therefore pay no taxes.
6. On January 1st of this year, Jimmy’s demand curve for coffee in a given week was
given by the graph below.
$pc
3
2
1
2 4 6 8 10 12 14 16 q coffee
On January 2nd, the government decided to raise the tax on cigarettes which caused an
increase in the price of cigarettes from $4/pack to $4.50/pack. However, on January 2nd
Jimmy’s favorite coffee store also decided to lower the price of a cup of coffee from
$2.00 to $1.50. If coffee and cigarettes are gross complements for Jimmy, we know that
he will demand exactly 10 cups of coffee per week after January 2nd. True, False, or can’t
we tell given the information above? (Briefly explain why you given the answer that you
do)
A: We can’t tell given the information given. The reason is that an increase in the price of
a gross complement for coffee (cigarettes) will shift back the demand curve for coffee. If
this shift back is big enough, Jimmy will demand less coffee than 10/week at a price of
$1.50 (see dotted demand curve). If the shift is only small, then Jimmy could demand
more than 10 coffees/week (see dashed demand curve).