Question 1. Please initial that you understand each of the following statements. Failure to complete this will result in a one point deduction.
The assignment is open book/open note. Students may discuss this assignment with other students in the class, but must turn in legible, handwritten, and original answers. The posting of questions from this assignment to an online forum like Chegg, Coursehero, or Homeworkmarket will be considered cheating. Answers closely matching replies to such a post will be scrutinized. Students caught cheating will receive a zero on the assignment and may receive additional punishment under Faculty Senate Rule 49-20.
This assignment must be turned in at the beginning of class on Friday, October 21st. It will be considered late once the instructor starts lecturing. Late assignments will not be accepted and students will receive a score of zero on that assignment.
All work must be stapled, in the proper order, in the upper-left corner of the paper prior to being submitted. Four points will be deducted if the instructor staples or restaples the work for you.
Your name and Penn State Email must appear at the top of the first page.
Be sure to fully answer the entire question. Some questions have multiple parts which ask you to explain your reasoning. Providing the correct answer without an explanation (when asked for) will not earn students full credit.
Numbers should be rounded to two decimal places if needed.
Question 2. Don and Joan work in a high pressure Madison Avenue ad agency and smoke to relieve the pressure. Assume Don is willing to pay $10 for a pack of cigarettes, but Joan is only willing to pay $5. These valuations show that Don values smoking more than Joan at their current consumption levels. Draw one indifference curve for each individual through the bundle (1, 1) using the same set of axes for both consumers. Place packs of cigarettes on the x-axis and a composite of all other goods (AOG) on the y-axis. You may assume that the both items are "good" goods even though cigarettes have negative side-effects and externalities. You should also assume that Don's marginal rate of substitution of cigarettes for all other goods (MRSC,AOG) is constant while Joan's is strictly declining.
Question 3. Assume you have the following preferences and market conditions:
U = XY1/3 PX = 1, Py = 1, M =50
MUX = Y1/3
MUY = 1/3(X/Y2/3)
A. Solve for the optimal bundle given the above information.
B. Assume that the price of X increases to $2. Solve for the new optimal bundle.
C. What is the total effect of the price change?
D. What is the substitution effect of the price change?
E. What is the income effect of the price change?
F. Graph both of the optimal bundles, the budget constraint before and after the change in price, the point required to determine the income and substitution effects, and the consumer's indifference curves at both optimal bundles.
G. Derive the demand function for X, X = f(PX) holding all other factors constant:
4. Assume you have the following preferences and market conditions:
U = X0.5Y0.25 PX = 1, Py = 1, M = 100
MUX = 0.5(Y0.25/X0.5)
MUY = 0.25(X0.5/Y0.75)
A. Solve for the optimal bundle given the above information.
B. Assume that the price of X increases to $2 and the price of Y increases to $3. Solve for the new optimal bundle.
C. What is the total effect of the price changes?
D. What is the substitution effect of the price changes?
E. What is the income effect of the price changes?
F. Graph both of the optimal bundles, the budget constraint before and after the changes in price, the point required to determine the income and substitution effects, and the consumer's indifference curves at both optimal bundles.
G. Derive two demand functions for X, one where PY = $1 and PY = $3.
When PY = $1, X=f(PX):
When PY = $3, X=f(PX):
5. Assume you have the following preferences and market conditions:
U = X + 0.25Y PX = 1, Py = 1, M = 50
MUX = 1
MUY = 0.25
A. Solve for the optimal bundle given the above information.
B. Assume that the price of X decreases to $0.50. Solve for the new optimal bundle.
C. What is the total effect of the price change?
D. What is the substitution effect of the price change?
E. What is the income effect of the price change?
F. Graph both of the optimal bundles, the budget constraint before and after the change in price, the point required to determine the income and substitution effects, and the consumer's indifference curves at both optimal bundles.
G. What is the compensating variation associated with this price change?
6. Assume you have the following preferences and market conditions:
A. Solve for the optimal bundle given the above information.
B. Assume that the price of X decreases to $1. Solve for the new optimal bundle.
C. What is the total effect of the price change?
D. What is the substitution effect of the price change?
E. What is the income effect of the price change?
F. Graph both of the optimal bundles, the budget constraint before and after the change in price, the point required to determine the income and substitution effects, and the consumer's indifference curves at both optimal bundles.
G. What is the compensating variation associated with this price change?