Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN: 9781305506381
Author: James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher: Cengage Learning
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Question
Chapter 4, Problem 2E
(a)
To determine
To estimate: the demand function using the linear regression model.
(b)
To determine
The coefficient of determination. Significance of the
(c)
To determine
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The Pilot Pen Company has decided to use 15 test markets to examine the sensitivity of demand for its new product to various prices, as shown in the following table. Advertising effort was identical in each market. Each market had approximately the same level of business activity and population.
Complete the following worksheet and then estimate the demand function for Pilot's new pen using a linear regression model.
Test Market
Price Charged
Quantity Sold
(cents)
(Thousands of Pens)
ii
xixi
yiyi
xixiyiyi
xi2xi2
yi2yi2
1
50
20
1,000
2,500
400
2
50
21
1,050
2,500
441
3
55
19
1,045
3,025
361
4
55
19.5
1,072.5
3,025
380.25
5
60
20.5
1,230
3,600
420.25
6
60
19
1,140
3,600
361
7
65
15.5
1,007.5
4,225
240.25
8
65
15
975
4,225
225
9
70
14.5
1,015
4,900
210.25
10
70
15.5
1,085
4,900
240.25
11
80
13
1,040
6,400
169
12
80
14
1,120
6,400
196
13
90
11.5
1,035
8,100
132.25
14
90
11
990
8,100
121
15
40
17
680
1,600
289
Total
980
246
?…
Suppose that an economist has been able to gather data on the relationship between demand and price for a particular product. After analyzing scatterplots and using economic theory, the economist decides to estimate an equation of the form Q= aPb, where Q is quantity demanded and P is price. An appropriate regression analysis is then performed, and the estimated parameters turn out to be a = 1000 and b = - 1.3. Now consider two scenarios: (1) the price increases from $10 to $12.50; (2) the price increases from $20 to $25. a. Do you predict the percentage decrease in demand to be the same in scenario 1 as in scenario 2? Why or why not? b. What is the predicted percentage decrease in demand in scenario 1? What about scenario 2? Be as exact as possible.
The 2008 sales and profits of seven companies were given as follows Firm Sales ($ Billions) Profit ($ Billions) Fiat 5.7 0.27 Honda 6.7 0.12 BP 0.2 0.01 Toyota 0.6 0.04 Apple 3.8 0.05 IBM 12.5 0.46 Phillips 0.5 0.02 The estimated value for the company’s Profit can be estimated using the equation; Y ̂i = α ̂ + β ̂Xi……………………………………………………………………Eqn.1 Where; Y = Companies Profit X = Companies Sales α ̂ and β ̂ are estimated parameters in the model Calculate the sample regression line, where profit is the dependent variable (Y) and sales is the independent variable (X)
Chapter 4 Solutions
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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