NAME & SECTION:
Problem Set #2
Micro I – Winter Term 2009
Instructor: Gul Andaman
DUE DATE: Wednesday, October 7
1. (Consumer choice) Suppose that Fiza consumes two goods, apples (A) and bananas
(B) and that he has an equal preference for the following five combinations (bundles) of
A and B:
Group I Bundles:
Good
Bundle I1
A
10
B
2
Bundle I2
6
3
Bundle I3
4
4
Bundle I4
3
6
Bundle I5
2
10
Suppose also that the following 5 bundles are equally preferred to each other:
Group II Bundles:
Good
Bundle II1
A
20
B
4
Bundle II2
12
6
Bundle II3
8
8
Bundle II4
6
12
Bundle II5
4
20
a. Plot the Group I and the Group II bundles, where the quantity of apples is on the
horizontal and quantity of bananas is on the vertical axis. Connect the bundles
that are equally preferred. Label these indifference curves I and II.
b. Suppose that the income of Rs. 150, the price of apples is Rs10 per unit, and the
price of bananas is Rs10 per unit. Draw Fiza’s budget constraint on the same
graphs as the indifference curves (constructed for part a above). Identify the
bundle at which Fiza maximizes his utility and label it “X.”
c. What is the marginal rate of substitution (MRS) between apples and bananas at
the point X? How did you determine the MRS?
d. Suppose that, instead of the data given at the beginning of the problem, Ameen’s
set of Group II bundles are:
Alternate Group II Bundles:
Good
Bundle II1
Bundle II2
A
7
6
B
1
3
Bundle II3
4
8
Bundle II4
3
12
Bundle II5
2
18
Plot Group I and the new Group II bundles on a new graph. Would these two
indifference curves be consistent with our assumptions about preferences? Why or
why not?
2. (Consumer choice) Shaheen receives a monthly allocation of pocket money (income)
of Rs 4000, which she spends each month on movies (Rs. 200) and dinners. She finds
that she maximizes her utility (is most happy) by spending half of her pocket money on
dinners, and the other half on movies. Her marginal rate of substitution (MRS) at this
bundle of goods is 0.4 (measured with movies on the horizontal axis).
a. Given this information, what is the cost of dinners? Show your work.
b. Write an equation for Shaheen’s budget constraint.
c. What is the opportunity cost, in terms of movies, of an additional dinner?
3. Every week, Ibrahim buys tea and biscuits to sustain his late night study habits.
Suppose bundle “A” consists of 10 packages of biscuits and 10 cups of tea. Using the
concept of marginal rate of substitution (MRS), answer the following questions
(assuming packages of biscuits are on the horizontal axis):
a. Suppose the slope of Ibrahim’s indifference curve through the bundle A is -2.
Consider bundle B which consists of 9 packages of biscuits and 11 cups of tea.
Does Ibrahim prefer bundle A, bundle, B, or is he indifferent between the two?
Explain.
b. If the slope of the indifference curve is -1/2 instead of -2, would your answer to
part a change? Explain.
4. The utility that Meredith receives by consuming food F and clothing C is given by
u(F,C) = FC. Suppose that Meredith’s income in 1990 is $1,200 and the prices of food
and clothing are $1 per unit for each. However, by 1995 the price of food has increased
to $2 and the price of clothing to $3. Let 100 represent the cost of living index for 1990.
Calculate the ideal and the Laspeyres cost-of-living index for Meredith for 1995. (Hint:
Meredith will spend equal amounts on food and clothing with these preferences.)
5. Connie has a monthly income of $200, which she allocates between two goods: meat
and potatoes.
a.
Suppose meat costs $4 per pound and potatoes cost $4 per pound. Draw her budget
constraint.
b.
Suppose also that her utility function is given by the equation u(M, P) = 2M + P.
What combination of meat and potatoes should she buy to maximize her utility?
(Hint: Meat and potatoes are perfect substitutes.)
c.
A bumper crop of potatoes lowers the price of potatoes to $2 per pound. What does
her budget constraint look like now? What combination of meat and potatoes
maximizes her utility?
6. Debra usually buys a soft drink when she goes to a movie theater, where she has a
choice of three sizes: the 8 ounce drink costs $1.50, the 12 ounce drink, $2.00, and the
16 ounce drink, $2.25. Describe the budget constraint that Debra faces when deciding
how many ounces of the drink to purchase. Put “ounces of soda” on the horizontal axis
and “$ spent on all other goods” on the vertical axis. Also assume that the total amount
spent is $2.25. HINT: The budget line is kinked.
7. Janice Doe consumes two goods, X and Y. Janice has a utility function given by the
expression:
U = 4X.5Y.5.
The current prices of X and Y are 25 and 50, respectively. Janice currently has an
income of 750 per time period.
a.
Calculate the optimal quantities of X and Y that Janice should choose, given her
budget constraint. Graph your answer.
b.
Suppose that the government rations purchases of good X such that Janice is limited
to 10 units of X per time period. Assuming that Janice chooses to spend her entire
income, how much Y will Janice consume?
c.
d.
Construct a diagram that shows the impact of the limited availability of X on the
budget constraint. Is Janice satisfying the usual conditions of consumer equilibrium
while the restriction is in effect?
Calculate the impact of the ration restriction on Janice's utility.
8. You are managing a $300,000 city budget in which monies are spent on schools and
public safety only. You are about to receive aid from the federal government to support a
special anti-drug law enforcement program. Two programs that are available are (1) a
$100,000 grant that must be spent on law enforcement; and (2) a 100 percent matching
grant, in which each dollar of local spending on law enforcement is matched by a dollar
of federal money. The federal matching program limits its payment to each city to a
maximum of $100,000.
a. Complete the table below:
Schools
$0
$50,000
$100,000
$150,000
$200,000
$250,000
$300,000
Safety (no
government aid)
Safety (with
program 1)
Safety (with
program 2)
$0
$100,000
$0
b. Draw the budget constraints of the three options: no aid, Program 1, and Program 2.
Place the safety expenditures on the horizontal axis.
c. Which program would you (the manager) choose if you wish to maximize the
satisfaction of the citizens if you allocate $50,000 of the $300,000 to schools? What
about $250,000?
9. (Corner Solution) Mary’s utility function is U = b + 10c – c2, where b is the number of
silver bells in her garden and c is the number of cockle shells. She has 50 square feet in
her garden to allocate between silver bells and cockle shells. Silver bells each take up 1
square foot and cockle shells each take up 11 square feet. She gets both kinds of seeds
for free.
a. Draw the indifference curve for U=25
b. To maximize utility, how many silver bells and cockle shells should she plant?