Marginal utility, demand curves, Elasticity, Regression

Extracted Content from Question Files:

4.1 Marginal Utility. Complete the following table, which describes the de4.1 Complete
the following table, which describes the demand for goods:

Total Marginal Price/Marginal
Price Units Utility Utility Utility
o
$11 0 __ __ _

10 1 25
9 2 45
8 3 60
7 4 70
6 5 75

B. How does an increase in consumption affect marginal utility and the price/marginal utility
ratio?
C. What is the optimal level of goods consumption if the marginal utility derived from the
consumption of services costs .50 per util?

4.3 Optimal Consumption. Alex P. Keaton is an ardent baseball fan. The following table shows
the relation between the number of games he attends per month and the total utility he derives from
baseball game consumption:

Number of Baseball Games per Month Total Utility

0 0

1 50

2 90

3 120

4 140

5 150
A. Construct a table showing Keaton's marginal utility derived from baseball game consumption.
B. At an average ticket price of $10, Keaton is able to justify attending only one game per month.
Calculate his cost per unit of marginal utility derived from baseball game consumption at this
activity level.
C. If the cost/marginal utility trade-off found in part B represents the most Keaton is willing to
pay for baseball game consumption, calculate the prices at which he would attend two,
three, four, and five games per month.
D.. Plot Keaton's baseball game demand curve.

4.5 Demand Curves. KRMY-TV is contemplating a T-shirt advertising promotion. Monthly sales data
from T-shirt shops marketing the "Eye Watch KRMY-TV" design indicate that
Q = 1,500 – 200P

where Q is T-shirt sales and P is price.
A. How many T-shirts could KRMY-TV sell at $4.50 each?
B. What price would KRMY-TV have to charge to sell 900 T-shirts?
C. At what price would T-shirt sales equal zero?
D. How many T-shirts could be given away?
E. Calculate the point price elasticity of demand at a price of $5.

... ~ __________________ _ _______________ I ___

4.8 Income Elasticity. Ironside Industries, Inc. is a leading manufacturer of tufted carpeting under the Ironside brand.
Demand for Ironside's products is closely tied to the overall pace of building and remodeling activity and, therefore, is
highly sensitive to changes in national income. The carpet manufacturing industry is highly competitive, so Ironside's
demand is also very price-sensitive.

During the past year, Ironside sold 15 million square yards (units) of carpeting at an average wholesale price of $7.75
per unit. This year, disposable income per capita is expected to surge from $25,760 to $28,000 in a booming economic
recovery. Without any price change, Ironside's marketing director expects current-year sales to rise to 25 million units.
A.. Calculate the implied income arc elasticity of demand.
B.. Given the projected rise in income, the marketing director believes that current volume of 15
million units could be maintained despite an increase in price of .50 per unit. On this basis,
calculate the implied arc price elasticity of demand.
C.. Holding all else equal, would a further increase in price result in higher or lower total revenue?

5 .3 Demand Curve Analysis . Anathema Printers, Inc., is a leading supplier of high-speed color
p rinters. Average price and annual unit sales data are as follows:

1 998 1999 2000 2001 20002
Price ($) $9,000 $8,000 $6,000 $5,000 $3,000
Unit Sold 25,000 50,000 100,000 125,000 175,000

A. Complete the following table, and use these data to dreve intercept and slope coefficients for the
linear demand curve.

Year Price Quantity ∆Price ∆Quantity Slope=∆P/∆Q
1998 $9,000 25,000
1999 $8,000 50,000
2000 $6,000 100,000
2001 $5,000 125,000
2002 $3,000 175,000

B. Assuming that demand conditions are held constant, use the preceding data to plot a linear curve.

5.7 Correlation and Simple Regression. Market Research, Inc., has conducted a survey to learn the
relationship between income and age for a n = 15 sample of households in the affluent Minneapolis suburb
of Eden Prarie, Minnesota. Survey results were as follows:

Age Income Age Income
32 81 49 104
33 86 50 104
33 87 51 115
37 92 51 118
38 94 52 121
40 99 53 122
41 102 53 131
42 103

A. Interpret the coefficient of correlation between the AGE and INCOME variables of 94.0%.
B. Interpret the following results for a simple regression over this sample where INCOME is the
dependent Y variable and AGE is the independent X variable (t statistics in parentheses):

-
INCOMEj = $27.377 + $1.753 AGEi, = 87.4%, SEE = 5.261, F = 98.10
R^2

(3.49) (9.90)

5.10 Multiple Regression. In the third phase of the Ninja Pizza Inc., survey data analysis, the company
wishes to study a multiple regression model of pizza demand. The company thinks that it is likely that
the marginal influence of advertising depends upon the average price charged and income levels in the
market area. Similarly, the effects of these two latter independent variables are thought to depend upon
the level of advertising. Therefore, a multiplicative demand model has been estimated in log-linear
form as follows:

Predictor Coefficient Standard Deviation t Ratio p
Constant -13.637 3.2300 -4.22 0.001
LOGe P -0.6702 0.2002 -3.35 0.007
LOGe AD 1.2944 0.1424 9.09 0.000
LOGe Y 1.1467 0.3721 3.08 0.010

-
R^2
SEE = 0.05795, R^2 = 94.6%, = 93.1%, F statistic = 63.86 (p = 0.000)

A. Interpret the coefficient estimate for each respective independent variable.
B. Characterize the overall explanatory power of this log-linear regression model

7.1 Marginal Rate of Technical Substitution. The following production table provides
estimates of the maximum amounts of output possible with different combinations of
t wo input factors, X and Y. (Assume that these are just illustrative points on a spectrum
o f continuous input combinations.)

Units of Y used Estimated Output per Day
5 210 305 360 421 470
4 188 272 324 376 421
3 162 234 282 324 360
2 130 188 234 272 305
1 94 130 162 188 210
1 2 3 4 5

A. Do the two inputs exhibit the characteristics of constant, increasing, or decreasing marginal rates of
technical substitution? How do you know?
B . Assuming that output sells for $3 per unit, complete the following tables:

X Fixed at 2 Units

Units Y Used Total Product of Y Marginal Product Average Product Marginal Revenue
of Y of Y Product of Y
1
2
3
4
5

X Fixed at 3 Units

Units Y Used Total Product of Y Marginal Product Average Product Marginal Revenue
of Y of Y Product of Y
1
2
3
4
5

C. Assume that the quantity of X is fixed at 2 units. If output sells for $3 and the cost of Y is $120 per
day, how many units of Y will be employed?
D. Assume that the company is currently producing 162 units of output per day using 1 unit of X and 3
units of Y. The daily cost per unit of X is $120 and that of Y is also $120. Would you recommend a
change in the present input combination? Why or why not?
E. What is the nature of the returns to scale for this production system if the optimal input combination
requires that X = Y?

7.7 Optimal Input Level. The Route 66 Truck Stop, Inc., sells gasoline to both self-service and
full-service customers. Those who pump their own gas benefit from the lower self-service price of
$1.50 per gallon. Full-service customers enjoy the service of an attendant, but they pay a higher price of
$ 1.60 per gallon. The company has observed the following relation between the number of attendants
e mployed per day and full-service output:

Route 66 Truck Stop Inc.

Number of Attendants per Day Full-Service Output (gallons)
0 0
1 2,000
2 3,800
3 5,400
4 6,800
5 8,000

A. Construct a table showing the net marginal revenue product derived from attendant
e mployment.
B. How many attendants would Route 66 employ at a daily wage rate of $160 (including
wage and benefits)?
C. What is the highest daily wage rate Route 66 would pay to hire four attendants per day?

7.10 Production Function Estimation. Consider the following Cobb-Douglas production function for
bus service in a typical metropolitan area.

Q = b Lb1 Kb2 F b3
0

where
Q = output in millions of passenger miles
L= labor input in worker hours
K= capital input in bus transit hours
F= input in gallons

Each of the parameters of this model was estimated by regression analysis using monthly data over a
recent 3-year period. Results obtained were as follows (standard errors in parenthes):

b = 1.2: b = 0.28: b = 0.63: b = 0.12
0 1 2 3
The standard error estimates for each coefficient are:

σ = 0.4; σ = 0.15; σ = 0.12; σ = 0.07
b1 b2 b3
b0

A. Estimate the effect on output of a 4% decline in worker hours (holding K and F
constant).
B. Estimate the effect on output of a 3% reduction in fuel availability accompanied by a
4% decline in bus transit hours (holding L constant).
C. Estimate the returns to scale for this production system.