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Lecture 18

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Western University
Economics 2150A/B
Kristin Denniston

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
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