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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 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.

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

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

, is the unit price of good X, and P

, 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

=5X

-1/2

1/2

and MU

= 5X

1/2

-1/2

. Please show all of your

work to receive full credit. (10 points)

• MRS = MUx / MUy = (5X

-1/2

1/2

) / (5X

1/2

-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

question. Please show all of your work to receive full credit. (10 points)

• 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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