This document discusses concepts related to risk and decision-making under uncertainty in microeconomics. It defines key terms like probability, expected value, expected utility, and certainty equivalent. It then provides examples to illustrate risk aversion versus risk neutrality versus risk loving preferences. Specifically, it analyzes a lottery versus a certain cash prize to determine the certainty equivalent and risk premium. The document also discusses strategies for reducing risk, such as diversification and insurance.

1. Microeconomics
Session 18-19

2. DESCRIBING RISK
probability Likelihood that a given outcome will occur.
expected value Probability-weighted average of the payoffs associated
with all possible outcomes.
payoff Value associated with a possible outcome.
expected utility Sum of the utilities associated with all possible
outcomes, weighted by the probability that each outcome will occur.

3. MAKE A CHOICE
• 1> Rupees 10,000 (Ten Thousand)
• 2> A lottery ticket to fetch Rupees
1,000,000 (Ten Lakh) with probability
1/100.
• Do you prefer
– 1 over 2
– 2 over 1
– Indifferent between 1 and 2

4. Expected Value of a Lottery
• This lottery has two outcomes
– Rs 0 with probability 0.99
– Rs 10,00,000 with probability 0.01
• Expected value = x1 ·P(x1) + x2 ·P(x2)
= 0 × 0.99 + 10,00,000 × 0.01
= Rs 10,000

6. Think about it!
• Those who prefer 1 over 2 may prefer Rs.
8,000 as much as the lottery 2.
• Then the certainty equivalent of gamble 2
is Rs. 8,000 lakh.
• The risk premium is expected value of the
gamble – certainty equivalent = Rs. 10,000
– Rs. 8,000 = Rs. 2,000.

7. EXPECTED UTILITY OF MONEY
Utility
Prize
U(High)
U(low)
EU (lottery)
Low HighE(lottery)CE
Risk premium

8. RISK AVERSION
• The certainty equivalent of a monetary gamble g is an
amount CE(g) such that the consumer is indifferent
between accepting the gamble or accepting CE(g) with
certainty.
• If E(g) is the expected payoff from a gamble the
risk premium associated with that gamble is:
E(g) − CE(g)
• risk premium Maximum amount of money that a risk-
averse person will pay to avoid taking a risk.
• A consumer is
Risk averse: if CE(g) < E(g)
Risk neutral: if CE(g) = E(g)
Risk lover: if CE(g) > E(g)

9. PREFERENCES TOWARD RISK
Risk Averse, Risk Loving, and
Risk Neutral (continued)
In (b), the consumer is risk
loving:
She would prefer the
gamble to the certain
income.
Finally, the consumer in (c)
is risk neutral,
and indifferent between
certain and uncertain
events with the same
expected income.
Figure 5.3

10. Problem
• Find certainty equivalent and risk premium
for these utility functions:
–U(x) = x2
–U(x) = √x
–U(x) = x

11. REDUCING RISK
● diversification Practice of reducing risk by allocating resources to a
variety of activities whose outcomes are not closely related.
TABLE 5.5 Income from Sales of Appliances ($)
Hot Weather Cold Weather
Air conditioner sales
Heater sales
30,000
12,000
12,000
30,000
● negatively correlated variables Variables having a tendency to move in
opposite directions.
● mutual fund Organization that pools funds of individual investors to buy a
large number of different stocks or other financial assets.
● positively correlated variables Variables having a tendency to move in
the same direction. For example, a recession will cause stock prices to
move in the same direction.

12. REDUCING RISK
Insurance
The ability to avoid risk by operating on a large scale is based on the law of large
numbers, which tells us that although single events may be random and largely
unpredictable, the average outcome of many similar events can be predicted.
● actuarially fair Characterizing a situation in which an insurance premium
is equal to the expected payout.
Actuarial Fairness
TABLE 5.6 The Decision to Insure ($)
Insurance
Burglary
(Pr = .1)
No Burglary
(Pr = .9)
Expected
Wealth
Standard
Deviation
No
Yes
40,000
49,000
50,000
49,000
49,000
49,000
3000
0
The Law of Large Numbers

13. Homework
• Page 628, Chapter 18, Exercise 3
• Page 628, Chapter 18, Exercise 5
• Page 628, Chapter 18, Exercise 6
• Page 628, Chapter 18, Exercise 7