# Econ 301 problem set perl

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University of Wisconsin-Milwaukee
Department of Economics
Problem Set-1
296:301 Prof. J. Peoples
Problem Set 1: Due Friday, February 12 (Upload you answer sheet in the ‘Assignments’
Module in Canvas)
LATE WORK WILL NOTE BE ACCEPTED WITHOUT ADMINISTRATIVE
APPROVAL
This problem set is partitioned into two sections. Section I require the application of
consumer theory to analyze consumer choice. Section II requires the use of consumer
theory to derive the consumer’s Marshallian demand curve.
Section I: Consumer Behavior and Individual Demand (50 points)
The Wisconsin Department of Transportation is considering building a new highway.
John Marshall lives and works near the site of the proposed new highway. He makes a
number of trips each month between Whitewater and Milwaukee. If the new highway
were built it would reduce the cost of each trip from 30 cents to 20 cents. The graph
below shows Mr. Marshall’s individual demand curve for trips between Whitewater and
Milwaukee.
John Marshall’s Demand Curve
Price per trip
(in cents)
30 (10, 30)
20 (20, 20)
10
10 20 Number of trips per month
As indicate, John Marshall would make 10 trips per month when the price of a trip is 30
cents.

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A state legislator asks John Marshall whether he favors the construction of the
new highway. Marshall replies that it would save him \$1 per month, since he makes 10
trips per month between Whitewater and Milwaukee, and the savings per trip is 30 cents
minus 20 cents, or 10 cents. Thus, he says that the most that he would be wiling to pay is
\$1 per month in taxes to support the new highway. If he is not asked to pay more than
this amount, he favors the construction of the new highway. Otherwise he opposes it.
Do you agree with Jon Marshall’s reasoning? If not, what changes would you make in
his argument.
You must use the figure above when answering this question to receive full credit.
I do not agree with Mr. Marshall’s reasoning because according to his
demand curve, if his cost of travel decreases, then his number of trips will
increase from 10 to 20, if the cost is reduced from 30 cents to 20 cents. He will
earn \$2 per month extra because:
Money saved = # of trips * reduction in cost
= 20 * 10 cents = \$2
If he pays \$1 in taxes, then he will still save \$1.
Section I: Application of consumer utility (50 points)
Tom Brady’s utility function is as follows:
U= 10X
1/2
Y
1/2
Where, X, is the quantity of good X consumed, Y, is the quantity of good Y consumed
and, U, is Tom’s utility function.
A. If Tom spends all of his income, B, on goods X and Y what is the general form
of his budget constraint? (Hint: the budget constraint should be specified such
that budget is the sum of the expenditures on good X and Y.) Also note that
you should use notation such that, P
X
, is the unit price of good X, and P
Y
, is
the unit price of good Y. (5 points)
Budget line: I = X.Px + Y.Py
B. What is Tom’s marginal rate of substitution? Note his respective marginal
utilities are MU
X
=5X
-1/2
Y
1/2
and MU
Y
= 5X
1/2
Y
-1/2
. Please show all of your
work to receive full credit. (10 points)
MRS = MUx / MUy = (5X
-1/2
Y
1/2
) / (5X
1/2
Y
-1/2
) = Y / X
C. Now suppose that Toms income is \$1000, and that the price of good X is 1
and the price of good Y is 4 what is the optimal amount of good X and good Y
that he should purchase? Use the information from above to help answer this
Budget line: 1000 = X + 4Y

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University of Wisconsin-Milwaukee Department of Economics Problem Set-1 296:301 Prof. J. Peoples Problem Set 1: Due Friday, February 12 (Upload you answer sheet in the ‘Assignments’ Module in Canvas) LATE WORK WILL NOTE BE ACCEPTED WITHOUT ADMINISTRATIVE APPROVAL This problem set is partitioned into two sections. Section I require the application of consumer theory to analyze consumer choice. Section II requires the use of consumer theory to derive the consumer’s Marshallian demand curve. Section I: Consumer Behavior and Individual Demand (50 points) The Wisconsin Department of Transportation is considering building a new highway. John Marshall lives and works near the site of the proposed new highway. He makes a number of trips each month between Whitewater and Milwaukee. If the new highway were built it would reduce the cost of each trip from 30 cents to 20 cents. The graph below shows Mr. Marshall’s individual demand curve for trips between Whitewater and Milwaukee. John Marshall’s Demand Curve Price per trip (in cents) 30 (10, 30) 20 (20, 20) 10 10 20 Number of trips per month As indicate, John Marshall would make 10 trips per month when the price of a trip i ...
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