a. Lakshani has $200 to spend on sneakers and sweaters. Sneakers cost $50 per pair, and sweaters cost $20 each. She is thinking about buying 2 pairs of sneakers and 5 sweaters. She tells her friend that the additional utility she would get from the second pair of sneakers is the same as the additional utility she would get from the fifth sweater. (For this question, you have to consider MU/$. So, choose a number to represent MU. The problem states that the utility for the 2nd pair of sneakers is the same as the utility for the 5th sweater. Assign a random number to represent the MU and determine what the MU/$ would be. This will enable you to determine if it is optimal or not.)
b. Lakshani has $5 to spend on pens and pencils. Each pen costs $0.50 and each pencil costs $0.10. She is thinking about buying 6 pens and 20 pencils. The last pen would add five times as much to her total utility as the last pencil.
c. Lakshani has $50 per season to spend on tickets to football games and tickets to soccer games. Each football ticket costs $10 and each soccer ticket costs $5. She is thinking about buying 3 football tickets and 2 soccer tickets. Her marginal utility from the third football ticket is twice as much as her marginal utility from the second soccer ticket.
2. In the United States, 2007 was a bad year for growing wheat. As the wheat supply decreased, the price of wheat rose dramatically, leading to a lower quantity demanded (a movement along the demand curve). The accompanying table describes what happened to prices and the quantity of wheat demanded.
|
|
2006 |
2007 |
|
Quantity demand (bushels) |
2.2 billion |
2.0 billion |
|
Average price (per bushel) |
$3.42 |
$4.26 |
a. Using the midpoint
method, calculate the price elasticity of demand for winter wheat. (I've provided an example for you below.)
b. What is the total revenue for U.S. wheat farmers in 2006 and 2007? (For each year.)
c. Did the bad harvest increase or decrease the total revenue of U.S. wheat farmers? How could you have predicted this from your answer to part a?
3. A recent study determined the following elasticities for Volkswagen Beetles:
Price elasticity of demand = 2
Income elasticity of demand = 1.5
The supply of Beetles is elastic. Based on this information, are the following statements true or false? Explain your reasoning.
a. A 10% increase in the price of a Beetle will reduce the quantity demanded by 20%.
b. An increase in consumer income will increase the price and quantity of Beetles sold. Since price elasticity of demand is greater than 1, total revenue will go down. (Please address both statements for part b. They may both be false, both be true, or one true and one false.)
