Bridget’s Consumption Choice

QUESTION

1. Bridget has a limited income and consumes only wine and cheese. Her current consumption choice is four bottles of wine and 10 pounds of cheese. The price of wine is $10 per bottle and the price of cheese is $4 per pound. The last bottle of wine added 50 units to Bridget’s utility, while the last pound of cheese added 40 units.
   1. Is Bridget making the utility maximizing choice? Why or why not?
   2. If not what should she do instead? Why?
2. The owner-manager of Good Guys Enterprises obtains utility from income (profit) and from having the firm behave in a socially conscious manner, such as making charitable contributions or civic expenditures. Can you set up the problem and derive the optimization conditions if the owner-manager wishes to obtain a specific level of utility at the lowest possible cost? Do these conditions differ from the utility maximizing conditions?
3. The Dallas Morning News reported the findings of a study by the Department of Transportation that examined the effect on average airfares when new, low priced carriers, such as Southwest Airlines or Vanguard Airlines, entered one of the three city-pair markets: Baltimore-Cleveland, Kansas City-San Francisco, or Baltimore-Providence. Use the following excerpts from the newspaper article to calculate the arc elasticity of demand for each of the three city-pairs. How do the three computed elasticizes compare? Based on the computed elasticizes, describe “travelers” responsiveness to the reduction in airfares.
   1. “(In) Baltimore and Cleveland for example, …just 12,790 people between those cities in the last three months of 1992, at an average fare of $233. Then Dallas-based Southwest Airlines entered the market. In the last three months of 1996, 115,040 people flew between the cities at an average fare of $66.”
   2. “(On) Kansas City-San Francisco connection… during the last quarter of 1994 some 35,960 people made the trip at an average fare of $165. Two years later, after the arrival of Vanguard Airlines, fares had dropped to an average of $107 and traffic had nearly doubled to 68,100.”
   3. On the Baltimore-Providence, R. I., route, where the average fare fell from $196 to $57, …the number of passengers carried jumped from 11,960 to 94,116.”
4. Rubax, a U.S. manufacturer of athletic shoes, estimates the following linear trend model for shoe sales.
   1. Is there sufficient statistical evidence of an upward trend in shoe sales?
   2. Do these data indicate a statistically significant seasonal pattern of sales for Rubax shoes? If so, what is the seasonal pattern exhibited by the data?
   3. Using the estimated forecast equation, forecast sales of Rubax shoes for 2014(III) and 2015(II)
   4. How might you improve this forecast equation?

ANSWER