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Midterm Exam with 7 Questions - Intermediate Microeconomic Analysis | ECO 3306, Exams of Microeconomics

Baylor University (BU)Microeconomics
Prof. Charles M. North

Material Type: Exam; Professor: North; Class: Intermediate Microeconomic Analysis; Subject: Economics; University: Baylor University; Term: Spring 2005;

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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ECO 3306 – MIDTERM EXAMINATION – SPRING 2005 – Page 1
ECO 3306 Name:
Spring 2005
Dr. Charles M. North
MIDTERM EXAMINATION
Answer all questions in your bluebook. SHOW ALL WORK! Only answers showing work
will receive any credit, partial or full. This examination is worth 100 points, all of which must
be earned.
1. A consumer’s preferences are represented by the utility function 2
2
121 ),( xxxxu =.
a. (1 point) Derive the consumer’s marginal rate of substitution as a function of 1
x
and 2
x.
b. (2 points) Write down another utility function that represents the same
preferences. Prove that your utility function has the same marginal rate of
substitution that you found in part (a).
c. (10 points) Find the consumer’s generalized demand functions for goods 1 and 2,
),,(* 211 mppx and ),,(* 212 mppx .
d. (1 point) What is the consumer’s optimal bundle if )300,4,5(),,( 21 =mpp ?
e. (10 points) Suppose that the price of good 2 goes up to 5
2=
′
p, while p1 and m
remain at the same levels as in part (d). Calculate the substitution and income
effects of the price change on consumption of good 2.
f. (4 points) Sketch a graph of your answer to part (e), and label it completely.
2. Another consumer’s preferences are represented by 2121 23),( xxxxu +
=
.
a. (3 points) What is the consumer’s optimal bundle if )81,3,9(),,( 21 =mpp ?
b. (3 points) What is the consumer’s optimal bundle if )81,3,3(),,( 21 =
′
mpp ?
c. (4 points) Calculate the substitution and income effects of the change in the price
of good 1 from part (a) to part (b). Explain.
3. A third consumer’s preferences are represented by 2
2121 )8)(4(),( −−= xxxxu .
a. (8 points) Find the consumer’s generalized demand functions for good 1 and 2,
),,(* 211 mppx and ),,(* 212 mppx .
b. (4 points) Are these preferences homothetic? Explain.
pf3

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Download Midterm Exam with 7 Questions - Intermediate Microeconomic Analysis | ECO 3306 and more Exams Microeconomics in PDF only on Docsity!

ECO 3306 Name: Spring 2005 Dr. Charles M. North

MIDTERM EXAMINATION

Answer all questions in your bluebook. SHOW ALL WORK! Only answers showing work will receive any credit, partial or full. This examination is worth 100 points, all of which must be earned.

  1. A consumer’s preferences are represented by the utility function u ( x 1 , x 2 )= x 12 x 2.

a. (1 point) Derive the consumer’s marginal rate of substitution as a function of x 1 and x (^) 2. b. (2 points) Write down another utility function that represents the same preferences. Prove that your utility function has the same marginal rate of substitution that you found in part (a). c. (10 points) Find the consumer’s generalized demand functions for goods 1 and 2, x 1 (^) * ( p 1 , p 2 , m )and x (^) 2 * ( p 1 , p 2 , m ). d. (1 point) What is the consumer’s optimal bundle if ( p 1 (^) , p 2 , m )=( 5 , 4 , 300 )? e. (10 points) Suppose that the price of good 2 goes up to p 2 ′ (^) = 5 , while p 1 and m remain at the same levels as in part (d). Calculate the substitution and income effects of the price change on consumption of good 2. f. (4 points) Sketch a graph of your answer to part (e), and label it completely.

  1. Another consumer’s preferences are represented by u ( x 1 , x 2 )= 3 x 1 + 2 x 2.

a. (3 points) What is the consumer’s optimal bundle if ( p 1 (^) , p 2 , m )=( 9 , 3 , 81 )? b. (3 points) What is the consumer’s optimal bundle if ( p 1 ′ , p 2 , m )=( 3 , 3 , 81 )? c. (4 points) Calculate the substitution and income effects of the change in the price of good 1 from part (a) to part (b). Explain.

  1. A third consumer’s preferences are represented by u ( x 1 , x 2 )= ( x 1 − 4 )( x 2 − 8 )^2.

a. (8 points) Find the consumer’s generalized demand functions for good 1 and 2, x 1 (^) * ( p 1 , p 2 , m )and x (^) 2 * ( p 1 , p 2 , m ). b. (4 points) Are these preferences homothetic? Explain.

  1. (10 points) Brad consumes two food items: chicken dinners and sodas. His preferences over the two goods are represented by the utility function u ( C , S )= C ⋅ S , where C is the number of chicken dinners he eats each month and S is the number of bottles of soda he drinks. Brad has $180 per month to spend on chicken dinners and sodas. At present, the price of a chicken dinner is $3, and the price of a bottle of soda is $2. However, the price of each bottle of soda includes a $1 per bottle tax. The government is considering eliminating the per-bottle tax in favor of having Brad write a check each month in the amount he currently pays in soda tax. Does Brad favor this change? Explain your answer, including a discussion of Brad’s well-being under each proposal.
  2. Millicent and Gertrude have both won a contest in which the prize is an opportunity to attempt a 30-yard field goal during halftime of the Super Bowl. The prize for a successful kick is $1 million, and missing the kick yields no prize at all. Both women have a chance at the $1 million prize, but the prize is paid only to a successful kicker.

Both women have been practicing their kicking, and on average each woman makes 40% of the 30-yard field goals she attempts. Millicent’s risk preferences are represented by the von Neumann-Morgenstern utility function v ( ci )= c^1 i /^2 , where c (^) i is the amount of money she wins in the contest. In contrast, Gertrude’s risk preferences are represented by the von Neumann-Morgenstern utility function v ( ci )= ci^2 /^3.

a. (2 points) Find each woman’s expected utility. b. (6 points) For each woman, find the minimum amount of money she would have to be paid to give up the chance to kick the field goal. c. (2 points) Suppose that the right to attempt the field goal could be sold. Would either woman be willing to purchase the other’s field goal attempt? If so, which one, and what is the range of prices at which a voluntary sale could be made? Explain.

  1. A charity is planning a fund-raising dinner. There are two types of people likely to attend: city dwellers and suburbanites. The city dwellers’ demand for tickets to the dinner is represented by QC = 1000 − 10 PC , while the suburbanites’ demand is represented by QS = 2000 − 25 PS. Qi represents the quantity demanded by all members of group i , and Pi represents the price charged to group i. Assume that members of both groups will be charged the same price.

a. (4 points) What is the total market demand function that combines demand for both city dwellers and suburbanites?

b. (4 points) Calculate ε ( P ), the price elasticity of the market demand function as a

function of P , the price charged to all dinner attendees. c. (2 points) In the past, the charity has set P = $40. What is the price elasticity of demand at this price? Assuming the charity seeks to maximize the revenue generated by the dinner, how do you know that P = $40 is not optimal? d. (5 points) Assuming that the charity seeks to maximize revenue from the dinner, find the optimal price to charge all attendees.