Class Notes
(808,753)

Canada
(493,377)

Western University
(47,698)

Economics
(934)

Economics 2150A/B
(80)

Kristin Denniston
(23)

Lecture 18

# Economics 2151B - Lecture 18.docx

Unlock Document

Western University

Economics

Economics 2150A/B

Kristin Denniston

Winter

Description

Economics 2151B
Monday March 12
Lecture 17
Chapter 15 – Uncertainty and Imperfect Information
Homework 4
• Due Monday March 24
• Chapters 14 and 15
• Under ‘Tests and Quizzes’ on OWL
Describing Risky Outcomes
Random Event: An event that has several possible outcomes, each of which is
uncertain
• Each outcome occurs with some probability
• eg. rolling a die (there are 6 possible outcomes, each with a 1/6 chance of being
rolled)
• If you have listed all of the possible outcomes, their occurrence will sum to 1
o 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1
We can create a Probability Distribution for the random event.
• A probability distribution tells us all of the possible outcomes that could occur,
and their associated probabilities of occurrence.
Example: A stock price is currently $100. There is a 30% chance that the stock price
increases to $120, a 40% chance that the stock price stays the same, and a 30%
chance that the stock price decreases to $80.
• We can create a probability distribution from this information.
o There are only 3 possible outcomes, and they all have their own
probability of occurrence (which will sum to 1)
• You can view the graph in Figure 15.2 (page 1 of your notes)
We describe a random event using:
1. Expected Value
• E(x) = ∑ xP(x)
2. Variance
• Describes the spread in outcomes
• Variance represents riskiness – the higher the variance, the higher the
uncertainty of your outcomes
∑ .
• x [x – E(s)] P(x)
• Example from above stock price: v(x) = (80-100) (.3) + (100 – 100) (.4) +
2
(120 – 100) (.3) = 240
3. Standard Deviation = √ variance • the higher the standard deviation or variance, the greater the uncertainty
of risk
Utility Curves for different decision-makers:
1) Risk Averse
• Prefer a certain income to an uncertain income
• Most decision-makers are risk averse
• Has a concave indifference curve
• Diminishing marginal utility with respect to income
dU
o MU = dI
o Incremental increase in income will increase utility more at low
incomes than high incomes
2) Risk Neutral
• The expected value (utility) from a gamble is equal to their actual utility
• They are indifferent between certain income and uncertain income
o eg. whether we have $55,000 in our hand or whether we won it in
the lottery
• Their indifference curve is a straight line (constant at every point on the
line)
3) Risk Loving
• Convex indifference curve
• Increasing marginal utility
• This person likes a gamble (they get more utility from the gamble than with
the same amount of money handed to them)
Example 15.5
50I
Suppose that you have a utility function, U = √ . The lottery provides a payoff of
$0 with a probability of .75, and a payoff of $200 with a probability of .25. Verify that the
expected value of the lottery is $50.
• Because the utility function is a square root, the individual is likely risk averse
• EV = .75(0) + .25(200) = 50
• *Make sure that you use income to find your expected value, not utility.
What is the expected utility?
• EU = .75 √ 50(0) + .25 √ 50(200) = 25
Risk Premium
• The risk premium tells us how much a risk averse individual would pay to avoid a
gamble
• pU(I1)+1-p)(U(I2) = U(EV-RP) Example 15.18 (page 8)
• U = I – 3200I2
• I = 100
o There is an 80% chance we don’t have a loss, and a 20% chance that we
do.
• Accident I = 100-20
• What is the highest premium that you are willing to pay for an insurance policy
that fully indemnifies you against the loss?
• .2[I-3200(80) ] + .8[1-3200(100) ] = .644 = U(100-Premium) = 1-3200(100-P) 2
• P = 5.19 $5190 (the price you are willing to pay to guarantee you will make
$100,000 even if a bad event happens)
Fairly Priced Insurance
• The premium cost of the insurance is equal to the probabili

More
Less
Related notes for Economics 2150A/B