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Exam 2 Problems
1.
Demand Curve Estimation.
The Real Kool Toys Company manufactures and sells educational toys. An empirical demand function for one of the firm's products has been estimated over the last 21 quarters using regression analysis. The estimated demand function is:

Q
_{
Y
}
=

8,000

 5,000P
_{
Y
}

+ 192A

+ 120I

+ 2,000P
_{
X
}


(6,000)

(1,000)

(120)

(80)

(800)


R
_{
2
}
= 91%

Standard Error of the Estimate = 1,000

Here Q
_{
Y
}
is quantity (measured in units) of Product Y demanded in the current period, A is hundreds of dollars of advertising ($00), I is thousands of dollars of disposable income per capita ($000), and P
_{
X
}
is the price ($) of another toy manufactured by a competitor, ABC Toys. The terms in parentheses are the standard errors of the coefficients.

A.
How would you characterize the ability of this empirical demand function to explain demand for product Y?

B.
Currently, P
_{
Y
}
is $8, advertising is $25,000, disposable income per capita is $50,000 and P
_{
X
}
is $7. What are expected sales of Y in this period, and what range of sales would you specify for the current period if you wanted to establish a 99% confidence interval?

C.
What is the demand curve currently facing Real Kool for Product Y? (Note: Be careful to properly account for the units in which advertising and income appear in the estimated demand function.)

D.
What is the point price elasticity of demand for Y at the current price?

E.
Given the current price elasticity of demand, would a price reduction increase Real Kool profits? Explain.

F.
What demand curve would Real Kool face for Product Y if it raised advertising expenditures to $37,500?

2.
Incremental Costs.
Infinite Audio, Inc., manufactures car speakers which it sells to other resellers, who then customize and distribute the products to retailers which sell hifi auto equipment. The yearly volume of output is 300,000 pairs. The selling price and cost per unit are shown below:

Selling price


$150

Costs:



Direct material

$25


Direct labor

45


Variable overhead

20


Variable selling expenses

15


Fixed selling expenses

10

115

Unit profit before tax


$ 35


Management is evaluating the alternative of performing the necessary customizing to allow Infinite Audio to sell its output directly to car stereo retailers for $200 per unit under an inhouse marquee. Although no added investment is required in productive facilities, additional processing costs are estimated as:

Direct labor

$20 per unit

Variable overhead

$15 per unit

Variable selling expenses

$10 per unit

Fixed selling expenses

$300,000 per year


A.
Calculate the incremental profit Infinite Audio would earn by customizing its instruments and marketing directly to end users.

3.
Firm Supply.
The Copy Center specializes in highvolume printing and color copying for small businesses. This is a fiercely competitive market. The following relation exists between output and total production costs:

Total Output

Total Cost

0

$ 500

10,000

3,500

20,000

7,500

30,000

12,500

40,000

18,500

50,000

25,500

60,000

33,500

70,000

45,000


A.
Construct a table showing the marginal cost of production.

B.
What is the minimum price necessary for the company to supply ten thousand copies?

C.
How many copies would the company supply at industry prices of $5,500 and $7,000 per ten thousand?

4.
Perfectly Competitive Equilibrium.
Office building maintenance plans call for the stripping, waxing, and buffing of ceramic floor tiles. This work is often contracted out to office maintenance firms, and both technology and labor requirements are very basic. Supply and demand conditions in this perfectly competitive service market in St. Paul, Minnesota are:

Q
_{
S
}
= 20 + 2P

(Supply)

Q
_{
D
}
= 80  2P

(Demand)


where Q is thousands of hours of floor reconditioning per month, and P is the price per hour.

A.
Algebraically determine the market equilibrium price/output combination.

B.
Use a graph to confirm your answer.

5.
Competitive Market Equilibrium.
Syracuse Paper supplies printer paper in upstate New York. Like the output of other wholesale distributors, Syracuse Paper must meet strict guidelines and the printer paper supply industry can be regarded as perfectly competitive. Total and marginal cost relations are:

TC = $3,600 + $5Q + $0.01Q
^{
2
}

MC = ∂TC/∂Q = $5 + $0.02Q

where Q is cases of printer paper per day.

A.
Calculate the firm's optimal output and profits if prices are stable at $20 per case.

B.
Calculate optimal output and profits if prices rise to $25 per case.

C.
If Syracuse Paper is typical of firms in the industry, calculate the firm's equilibrium output, price, and profit levels.

Copyright 2008,
by the Contributing Authors.
Cite/attribute Resource
.
admin. (2009, January 27). Exam 2 Problems. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/economics/managerialeconomics/exam2problems.htm.
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