文档介绍：Environment and Natural Resource Economics Course
Nanjing Agriculture University
September 4 to September 30, 2006
Lecturers: Volker Beckmann, Humboldt University Max Spoor, ISS, The Hague
Justus Wesseler, Wageningen University
Lecture 3
Environmental Cost - Benefit - Analysis
under risk and uncertainty
Lecturer: Dr. Justus Wesseler, Wageningen University
The St. Petersburg Paradox
Game:
toss a fair coin
if head falls up at the first toss, you get 2$, if not the first but at the second toss doubled to 4$, at the third toss doubled again to
8$, …
How much would you be willing to pay to participate at the game?
Answer: the expected value of the probability weighted es.
The St. Petersburg Paradox
The expected value of the probability weighted es:
w: welfare
p: probability
Would you pay an infinite amount of money to participate in the game?
The St. Petersburg Paradox
Daniel Bernoulli’s solution involved two ideas that have since revolutionized economics:
(i), that people's utility from wealth, u(w), is not linearly related to wealth (w) but rather increases at a decreasing rate - the idea of diminishing marginal utility, u’(Y) > 0 and u”(Y) < 0;
(ii) that a person's valuation of a risky venture is not the expected return of that venture, but rather the expected utility from that venture. In the St. Petersburg case, the value of the game to an agent (assuming initial wealth is zero) is:
Due to diminishing marginal utility, people would only be willing to pay a finite amount of money to participate in the game.
Basic concepts for risk analysis
Expected e:
Expected utility of e:
Example:
U(Y)
U
U(Y2)
U(E[Y])
E[U]
U(Y1)
Y1
Y*
Y**
Y2
Y
A
B
C
E
D
Figure Risk aversion and the cost of risk bearing (Perman et al.: page 447)
E[Y]=Y**
Y*: certainty equivalent
line AB: binations
p*u(Y1)+(1-p)*u(Y2)
cost of risk bearing (CORB) = Y** -Y*
(also called risk premium)
Y*: certainty equivalent (where utility of a certain payment equ