Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Textbook Question
Chapter 17, Problem 17.9P
Precautionary saving and prudence The Query to Example 17.2 asks how uncertainty about the future might affect a person's savings decisions. In this problem we explore this question more fully. All of our analysis is based on the simple two-period model in Example 17.1.
a. To simplify matters, assume that
r=δ in Equation 17.15. If consumption is certain, this implies that
u′(c0)=u′(c1) or
c0=c1. But suppose that consumption in period 1 will be subject to a zero-mean random shock, so that
c1=cp1+x, where
cp1 is planned period- 1 consumption and
x is a random variable with an expected value of 0. Describe why, in this context, utility maximization requires
u′(c0)=E[u′(c1)] .
b. Use Jensen's inequality (see Chapters 2 and 7 ) to show that this person will opt for
cp1>c0 , if and only if
u' is convex-that is, if and only if
u‴>0 .
c. Kimball" suggests using the term "prudence" to describe a person whose utility function is characterized by
u‴>0 . Describe why the results from part (b) show that such a definition is consistent with everyday usage.
d. In Example 17.2 we showed that real interest rates in the U.S. economy seem too low to reconcile actual consumption growth rates with evidence on individuals willingness to experience consumption fluctuations. If consumption growth rates were uncertain, would this explain or exacerbate the paradox?
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Problem 3
You are given the following demand for European luxury automobiles:
Q=1,000 P-0.5.2/1.6
where P-Price of European luxury cars
PA = Price of American luxury cars
P, Price of Japanese luxury cars
I= Annual income of car buyers
Assume that each of the coefficients is statistically significant (i.e., that they passed the t-test).
On the basis of the information given, answer the following questions
1. Comment on the degree of substitutability between European and American luxury cars and
between European and Japanese luxury cars. Explain some possible reasons for the results in
the equation.
2. Comment on the coefficient for the income variable. Is this result what you would expect?
Explain.
3. Comment on the coefficient of the European car price variable. Is that what you would expect?
Explain.
Problem 2:
A manufacturer of computer workstations gathered average monthly sales figures from its 56 branch
offices and dealerships across the country and estimated the following demand for its product:
Q=+15,000-2.80P+150A+0.3P+0.35Pm+0.2Pc
(5,234) (1.29) (175) (0.12) (0.17) (0.13)
R²=0.68 SER 786 F=21.25
The variables and their assumed values are
P = Price of basic model = 7,000
Q==Quantity
A = Advertising expenditures (in thousands) = 52
P = Average price of a personal computer = 4,000
P.
Average price of a minicomputer = 15,000
Pe Average price of a leading competitor's workstation = 8,000
1. Compute the elasticities for each variable. On this basis, discuss the relative impact that each
variable has on the demand. What implications do these results have for the firm's marketing
and pricing policies?
2. Conduct a t-test for the statistical significance of each variable. In each case, state whether
a one-tail or two-tail test is required. What difference, if any, does it make to…
You are the manager of a large automobile dealership who wants to learn more about the effective-
ness of various discounts offered to customers over the past 14 months. Following are the average
negotiated prices for each month and the quantities sold of a basic model (adjusted for various
options) over this period of time.
1. Graph this information on a scatter plot. Estimate the demand equation. What do the
regression results indicate about the desirability of discounting the price? Explain.
Month
Price
Quantity
Jan.
12,500
15
Feb.
12,200
17
Mar.
11,900
16
Apr.
12,000
18
May
11,800
20
June
12,500
18
July
11,700
22
Aug.
12,100
15
Sept.
11,400
22
Oct.
11,400
25
Nov.
11,200
24
Dec.
11,000
30
Jan.
10,800
25
Feb.
10,000
28
2. What other factors besides price might be included in this equation? Do you foresee any
difficulty in obtaining these additional data or incorporating them in the regression analysis?
Chapter 17 Solutions
Microeconomic Theory
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