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ECON 207: Intermediate Microeconomic Theory
HW#2
DUE DAY 9 at 9:30 a.m.
1.
Jill's MRSF,C = 3/2, no matter how many units of each she is currently consuming. Draw several of her
indifference curves. If her income is $100, the price of food is $5 and the price of clothing is $10,
draw her budget line on the same graph. What is her budget equation? What will her utility
maximizing bundle be?
2.
A student living in a house off-campus would like to have music in each room. Music comes from a
compact disk player and two speakers. Assume that it is impossible to connect more than two
speakers to each player. Show the indifference curves of the student over compact disk players and
speakers, (with disk players on the horizontal axis) Write down the utility function which generates
these indifference curves. Next write down the students' Marshallian demand functions for disk
players and the Marshallian demand function for speakers.
3.
On a given evening A.J. enjoys the consumption of Cigars (C ) and Brandy (B) according to her utility
function: U(C,B) = 20C -C2 + 18B - 3B2 .
(a) How many cigars and glasses of brandy does she consume during an evening? (Assume that cost
is no object)
(b) Recently, AJ's doctor has advised her that she should limit the sum of glasses of brandy and cigars
to 5 per evening. What is her optimal consumption of Cigars and Brandy under the health
constraint? (Again assume that cost is no object).
4.
Mr. Weirdo enjoys two goods X and Y according to the following utility function:
U ( X ,Y )  ( X 2  Y 2 )
Calculate Mr. Weirdo's utility maximizing bundle if the price of X is $3 and the price of Y is $4.
Assume that Mr. Weirdo's income is $50. Graph Mr. Weirdo's indifference curve and its point of
tangency with the budget constraint. Have you found a true maximum? Explain why or why not.
5. . Sharon has the following utility function:
U ( X ,Y ) 
X  Y
where X is her consumption of candy bars, with price P X = $1, and Y is her consumption of
espressos, with PY = $3.
a. Derive Sharon’s demand for candy bars and espressos.
b. Assume that her income I = $100. How many candy bars and how many espressoswill Sharon
consume?
c. Calculate the numerical value of the marginal utility of income?