# Utility-maximizing choice; price elasticity, Wilpen Company

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Managerial Economics.

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.

(a) Is Bridget making the utility-maximizing choice? Why or Why Not?

(b) If not, what should she do instead? Why?

2) In an article about the financial problems of USA Today, Newsweek reported that the paper was losing about $20 million a year. A Wall Street analyst said that the paper should raise its price from 50 cents, which he estimated would bring in an additional $65 million a year. The paper's publisher rejected the idea, saying that circulation could drop sharply after a price increase, citing the wall street journal's experience after it increased its price to 75 cents. What implicit assumptions are the publisher and the analyst making about price elasticity?

3) 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 specification:

E = b x P/Q

Em = c x M/Q

Exr = d x Pr/Q

Q= a+bp+ cM+ dPr

a= 425120.0, b= -37260.6, P = 1.65, c = 1.49, M = 24,600, d = -1456, and Pr = 110.

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. The regression results are as follows:

Dependent Variable: Q R-Square F- Ratio P-Value on F

Observations: 20 0.8435 28.75 0.001

Variable Parameter Standard

Estimate Error T-Ratio P-Value

Intercept 425120.0 220300.0 1.93 0.0716

P - 37260.6 12587 -22.96 0.0093

M 1.49 0.3651 4.08 0.0009

PR -1456.0 460.75 -3.16 0.0060

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?

Wilpen plans to charge a wholesale price of $1.65 per can. The average price of a tennis racket is $110, and consumers' average household income is $24,600.

b)What is the estimated number of cans of tennis balls demanded?

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?

d)What will happen, in percentage terms, to the number of cans of tennis balls demanded if the price of balls decreases 15 percent?

e) What will happen, in percentage terms, to the number of cans of tennis balls demanded if average household income increase by 20 percent?

f)What will happen, in percentage terms, to the number of cans of tennis balls demanded if the average price of tennis rackets increases 25 percent?

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Managerial Economics.

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.

(a) Is Bridget making the utility -maximizing choice? Why or Why Not?

No. Bridget is not making the utility maximizing choice. At utility maximizing combination, the marginal utility per unit of money spent is equal for each good.

MU wine = 50 Pwine = 10 So,

Marginal utility per unit of money for wine =MU wine / Pwine = 50/10 = 5.00

MU cheese = 40 Pcheese = 4 So,

Marginal utility per unit of money for cheese= MU cheese / Pcheese = 40/4 = 10.00

Since the two are not equal, we are not at the utility maximization point.

(b) If not, what should she do instead? Why?

She should increase the consumption of cheese. As she increases the consumption of cheese, the marginal utility from the last unit of money spent on cheese will decrease from 10. At the same time, she should decrease the consumption of wine. As she is decreasing the consumption of wine, the marginal utility from the last unit of money spent on wine will increase from 5. She should continue doing so till the utility derived from the last unit of money spent on wine and cheese are equal.

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

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