Answered: Figure 7.11 Determining Parameters of…

Principles of Macroeconomics (MindTap Course List)

8th Edition

ISBN:9781305971509

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter5: Elasticity And Its Application

Section: Chapter Questions

Problem 4CQQ

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Question

In Example 7.1, two points on the demand curve were
given (see Figure 7.11).
a. Suppose three additional points are estimated by
Madison: (1) demand of 460 when price is $65,
(2) demand of 355 when price is $75, and
(3) demand of 275 when price is $85. With these
new points and the original two points, estimate
and interpret the best-fitting linear demand curve;
do the same for the best-fitting constant elasticity
demand curve.
b. Calculate the mean absolute percentage error
(MAPE) for each of the two fits, linear and constant
elasticity, where each MAPE is the average of the
absolute percentage errors for the five points. On the
basis of MAPE, which curve provides the better fit?

Figure 7.11 Determining Parameters of Demand Functions
D
E
F
H
K
L
M
1 Madison pricing model - finding demand funcitons
2
3 Two points on the demand curve (as esiimated by Madison)
4
Price
Demand
$70
400
$80
300
8
Linear demand curve
Constant elaslcity demand curve
9
450
450
10
400
400
11
350
350
12
300
300
13
250
250
14
y=-10x + 1100
y=4E+06x2.154
200
200
15
150
150
16
100
100
17
50
50
18
19
20
$68
$70
$72
$74
$76
$78
S80
$82
$68
$70
$72
$74
$76
$78
S80
$82
21
Price
Price
22
Demand
Demand

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