Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Question
Chapter 2, Problem 2.14P
(a)
To determine
The proof of
(b)
To determine
The proof of
(c)
To determine
The proof of
(d)
To determine
The proof of
(e)
To determine
- The proof that
f ( x ) = 2 x − 3 x ≥ 1
F ( x ) E ( x ) - The proof that Markov’s inequality holds for this function
(f)
To determine
- The proof that
f ( x ) = x 2 3 − 1 ≤ x ≤ 2
- The value of
E ( x )
- The probability that
− 1 ≤ x ≤ 0
- The value of
f ( x | A ) A 0 ≤ x ≤ 2
- The value of
E ( x | A )
- Intuitive explanation of the results
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Exercise 3
An individual lives two periods, 0 and 1. The income is 14,000 in period 0 and 5,000 in period 1.
The individual's marginal utility is: K- Co in period 0 and d8(K – C1) in period 1, where C is the
consumption in period 0, C1 the consumption in period 1 and d a discount rate. K is a constant
(higher than the consumption in each period). Suppose that the person can save or borrow from
the bank from period 0 to period 1 with a 25% interest rate. Set the discount rate & to 0.8.
a) How much will the individual consume in the two periods? How much will she save?
b) A National Insurance scheme (pension system) is established. The individual must pay 4,500
in period 0 and receives the same amount with interests in addition to her income in period 1.
What will the consumption and savings be in the two periods if the National Insurance scheme
uses the same interest rate as the bank?
1. A standard model of choice under risk is Expected Utility Theory (EUT) in which
preferences over lotteries that pay monetary prizes (x₁, x2, ..., xs) with probabilities
(P1, P2, ..., Ps) with Eps = 1 are represented by the function
L
S
(a) What does it mean to say that a function represents the consumer's prefer-
ences?
Σpsu(xs)
Choice 1
8=1
(b) State and briefly comment on the axioms required for the EUT representation.
(c) Consider the following experiment of decision making under risk in which sub-
jects are asked which lottery they prefer in each of the following two choices:
Lottery B
0 with prob. 0.01
10 with prob. 0.89
50 with prob. 0.10
Lottery D
Choice 2
Lottery A
0 with prob. 0
10 with prob. 1
50 with prob. 0
Lottery C
0 with prob. 0.90
10 with prob. 0
50 with prob. 0.10
Suppose that the modal responses are Lottery A in Choice 1 and Lottery D in
Choice 2. Assume that utility of zero is equal to zero and illustrate why it is
not possible to reconcile these experimental…
Chapter 2 Solutions
Microeconomic Theory
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