Maximizing Consumption on Limited Income: Bridgets Wine and Cheese Dilemma

Bridget has 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 added 40 units. a) Is Bridget making the utility-maximizing choice? Why or why not? In simplest terms wine is 50 units/$10 = 5 and cheese is 40 units/$4 = 10. Bridget is taking away dollars from cheese to buy wine.

Thus, she is not maximizing her choice. b) If not, what should she do instead? Why?

She should trade the bottle of wine for more cheese to maximize her choice.

Chapter 6: Applied Problem 1

In an article about the financial problems of USA Today, Newsweek reported that the paper was losing about $20 million a year.

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A Wall Street analyst said that the paper should raise its price from 50 cents to 75 cents, which he estimated would bring in an additional $65 million a year. The paper’s publisher rejected this idea, saying that circulation could drop sharply after a price increase; citing Wall Street Journal’s experience after it increased its price to $.75. What implicit assumptions are the publisher and analyst making about price elasticity?

The Wall Street Analyst is saying that the paper has low elasticity, or low price sensitivity. He thinks that the customers would not respond negatively to a price increase thus helping the paper raise revenue. The Wall Street Publisher thinks the opposite; he believes the paper has high elasticity and price sensitivity that will result in customers reacting negatively to a price increase.

The price increase will not be successful because they will also lose customers in the process.

Chapter 7: Applied Problem 1

Wilpen Company, a price setting firm, produces nearly 80 percent of all tennis balls purchased in the United States. Wilpen estimates the U.S. demand for its tennis balls by using the following linear specifications: Q = a + bP + cM + dPr

Where Q is the number of cans of tennis balls sold quarterly, P is the wholesale price Wilpen charges for a can of tennis balls, M is the consumer’s average household income, and Pr is the average price of tennis rackets.

a. Discuss the statistical significance of the parameter estimates a^, b^, c^, and d^ using the p-values. Are the signs of b^, c^, and d^ consistent with the theory of demand? The theory of demand says if the prices rise, then quantity sold will drop. The p-value associated with b is consistent with this claim. The theory of demand says when consumers have more income; they will probably purchase more tennis balls. The p-value associated with c is consistent with this claim. The theory of demand says that if Wilpen increases the price of their tennis rackets, then the consumers will buy less rackets and tennis balls. The p-value associated with d is consistent with this claim.

b) What is the estimate number of cans of tennis balls demanded? Q = a + b * P + c * M + d * Pr
Q = 425120 -37260.6 P + 1.46 * 24600 – 1456 Pr
Q = 425120 – 37260.6 * 1.65 + 1.46 * 24600 – 1456 * 110
Q = 239,396
c) At the values of P, M, and Pr given, what are the estimated values of the price (E^), income (E^m), and cross-price elasticity’s (E^xr) of demand? The estimate value for the price elasticity’s is:

E -37260.6 (1.65/Q) = -37260.6 (1.65/239396.01) = -0.257
The estimated values of the income (EM) of demand is:
EM = 1.46 (24600/Q) = 1.46 (24600/239396.01) = 0.150
The estimate values of the cross-price elasticity’s (EXr) of demand is: EXr = -1456.0 (110/Q) = -1456.0 (110/239396.01) = -0.669
d) What will happen, in percentage terms, to the number of cans of tennis balls demanded if the price of tennis balls decreases 15 percent? Q = E * % change in price = -0.257 * (-15%) = 0.04
The number of cans of tennis balls demanded will rise by 4%
e) What will happen in percentage terms, to the number of cans of tennis
balls demanded if the average household income increases by 20 percent? Q = EXR * % change in income = 0.150 * 20% = 0.03
The number of cans of tennis balls demanded will rise by 3%
f) What will happen, in percentage terms, to the number of cans of tennis balls demanded if the average price of tennis rackets increases by 20 percent? Q = EXR * % change in racket price = -0.669 * 25% = -0.167

The number of cans of tennis balls demanded will drop by 16%