1. Round to two decimal places throughout this problem if needed. Assume you have the following supply and demand equations:
QS = 40 + 2P
QD = 400-2P-0.5Wage
A. (What are the equilibrium price and quantity when the Wage is $20?
B. Calculate the price elasticity of demand at this initial equilibrium.
C. Calculate the income elasticity at the initial equilibrium.
D. Is this good a normal or inferior good? Explain how you know.
E. Assume the wage increases to $30. Is the good becoming more or less normal (or inferior)? Be sure to use specific numbers to explain how you know.
F. Continue to assume the wage has increased to $30. Use the general definition of the income elasticity and comparative statics to discuss why your answer to Part E is true.
G. Return to the initial value of the wage at $20 and the initial equilibrium. Now assume the government decides to implement a 5% ad valorem tax on the consumer. What are the new values for the market price and quantity?
H. ) Draw this market before and after the implementation of the ad valorem tax. Be sure to label all relevant curves, points, and axes. Making each box in the graph below worth 20 units will make the graph easier to draw.
2. JJ is confused about the price elasticity of demand and is asking for your help. To try to reach a few conclusions on his own, he created the following graph:
He knows that flatter demand curves are supposed to show more responsive, or elastic, behavior. To make sure, he calculated the price elasticity of demand at several points on each demand curve. His calculations are starting to confuse him even more. He's found values on each curve that range from close to zero to almost infinity. He is unsure how this can be true at the same time that D1 is more elastic than D2. He is starting to believe that it is impossible to tell whether one demand is more elastic than the other when both demands share the same elasticity values.
A. Is D1 more elastic than D2? Circle one: YES NO
B. Circle YES or NO. Is JJ's comment about the range of values for the price elasticity along each curve true?
YES NO
C. Use specific values and information from JJ's graph to prove that your answers to Parts A and B are possible.
3. Graph each of the following budget constraints in the following chart. Be sure to label all intercepts and clearly label each constraint.
A. Px = 10, Py = 5, M=100
B. Px = 10, Py = 25, M=100
C. Px = 10, Py = 5, M=150
4. List and define all of the key assumptions we will make about consumer preferences.
5. Penny and Ray enjoy books and movies, but Penny likes movies just a little bit more than Ray when they are given the same amount of each good.
A. What does this imply about Penny's marginal rate of substitution of books (MRSBM) relative to Ray's?
B. Which of the three classes of indifference curves we covered in class can be used to portray these preferences?
6. The graph below represents an indifference curve for someone with "kinky" tastes. It consists of two line segments which meet at a point where X=Y. An infinite number of other indifference curves exist and the one that is selected is just illustrative, except for the MRS. All indifference curves share the same MRS along both the upper and lower portions of the indifference curves.
A. Over what range of does this consumer choose only good Y?
B. Over what range of does this consumer choose only good X?
C. Over what range of does this consumer choose only one bundle where X=Y?
D. Over what range(s) of does the consumer have an infinite number of bundles to choose from at the optimum?
7. Please initial 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 will be considered cheating. Answers closely matching replies to such a post will be scrutinized. Students caught cheating will receive punishment under Faculty Senate Rule 49-20 and department guidelines.
____ This assignment must be turned in at the beginning of class on Wednesday, September 23rd. 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. Six points will be deducted if the instructor staples or restaples the work for you.
____ Your name and Penn State Access ID 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.