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Main topics. Consumption under risk Decision-making under uncertainty Gambling and avoiding risk Demand for insurance Value of information Behavioral Economics. Probability distribution. relates probability of occurrence to each possible outcome
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Main topics • Consumption under risk • Decision-making under uncertainty • Gambling and avoiding risk • Demand for insurance • Value of information • Behavioral Economics
Probability distribution • relates probability of occurrence to each possible outcome • first of two following examples is less certain fig. 1
You should know… • Calculations • Expected values • Variance • Concepts/Terms • Fair bet • Risk averse vs. risk neutral vs. risk loving • Value of information
Fair bet • wager with an expected value of zero • flip a coin for a dollar: [½ (1)] + [½ (-1)] = 0
Gambling Why would a risk-averse person gamble when the bet is unfair? • enjoys the game • makes a mistake: can’t calculate odds correctly • has Friedman-Savage utility fig. 5
Avoiding risk • just say no: don’t participate in optional risky activities • obtain information • diversify • risk pooling • diversification can eliminate risk if two events are perfectly negatively correlated
LOTTERIES • A “lottery” is the prospect with known (monetary) payoffs, each one with a known probability of occurring • Can represent a lottery by a list of payoffs and their corresponding probabilities * payoffs given by: Xn , n = 1,…,N * probabilities given by: prn , n = 1,…,N where 0 < prn < 1 such that: pr1 + … + prN = 1
A REAL LOTTERY CALIFORNIA MEGA MILLIONS LOTTERY “Match” Prize Odds / Probabilities Prob*Prize -------------------------------------------------------------------------------------------------------------------------------------------- 5+Mega Ball Grand Prize 1 in 175,711,536 (e.g., $10M) 0.0000000057 $0.0 5 $175,000 1 in 3,904,701 0.0000002561 $0.04 4+Mega Ball $5,000 1 in 689,065 0.0000014512 $0.01 • $150 1 in 15,313 0.0000653040 $0.01 3+Mega Ball $150 1 in 13,781 0.0000725637 $0.01 2+Mega Ball $10 1 in 844 0.0011848341 $0.01 3 $7 1 in 306 0.0032679739 $0.02 1+Mega Ball $3 1 in 141 0.0070921986 $0.02 Mega Ball $2 1 in 75 0.0133333333 $0.03 Nothing $0 97.5 in 100 0.9749820794 $0.00 Expected Prize $0.21 Note: payoffs are made at one time or over many years. Source: www.calottery.com Expected payoff = Expected Prize – Cost of ticket = $0.21 - $1.00 = - $0.79
Probability 1.0 .90 .80 .70 .60 .50 .40 .30 .20 .10 0 A LITTLE STATISTICS • RANDOM VARIABLE • - Takes on values Xn with probabilities prn • - Frequency distribution, e.g., bell-shaped grade distribution
RISK PREFERENCES Q. Is the decision maker willing to take a “fair bet”? Where a “fair bet” is a lottery for which the expected payoff is zero: E(X) = pr1*X1 + pr2*X2 + … + prN*XN = 0 • If no, then they are “risk averse.” A. If yes, then they are either “risk neutral” or “risk loving”
RISK PREMIUM The “risk premium” of a lottery is the amount the decision maker would give up to have certain outcome rather than the lottery. Mathematically, “risk premium” equates the expected utility to the utility of the expect value.
Insurance • risk-averse people will pay money—risk premium—to avoid risk • worldwide insurance premiums in 1998: $2.2 trillion Lloyd Building
House insurance • Scott is risk-averse • wants to insure his $80 (thousand) house • 25% chance of fire next year • if fire occurs, house worth $40
With no insurance • expected value of house is $70 = (¼ $40) + (¾ $80) • variance $300 = [¼ ($40 - $70)2] + [¾ ($80 - $70)2]
With insurance • suppose insurance company offers fair insurance • lets Scott trade $1 if no fire for $3 if fire • insurance is fair bet because expected value is $0 = (¼ [-$3]) + (¾ $1) • Scott fully insurances: eliminates all risk • pays $10 if no fire • receives $30 if fire • net wealth in both states of nature is $70
Commercial insurance • is not fair • available only for diversifiable risks • Many important sources of risk are not diversifiable • natural disasters • terrorism
No insurance for terrorism and natural disasters • major natural disasters and terrorism are nondiversifiable risks because such catastrophic events cause many insured people to suffer losses at the same time • more homes have built where damage from storms or earthquakes is likely, larger potential losses to insurers from nondiversifiable risks • insurance companies major losses in 1990s: • $12.5 billion for losses in the 1994 Los Angeles earthquake • $15.5 billion for Hurricane Andrew in 1992 (total damages were $26.5 billion) • $3.2 billion for damage from Hurricane Fran in 1995
Dropping insurance coverage • Farmers Insurance Group reported that it paid out three times as much for the Los Angeles earthquake as it collected in earthquake premiums over 30 years. • insurance companies now refuse to offer hurricane or earthquake insurance in many parts of the country for these relatively nondiversifiable risks • Nationwide Insurance Company announced in 1996 that it was sharply curtailing sales of new policies along the Gulf of Mexico and the eastern seaboard from Texas to Maine • a Nationwide official explained, “Prudence requires us to diligently manage our exposure to catastrophic losses.”
Government steps in • in some areas, state-run pools provide insurance coverage • Florida Joint Underwriting Association • California Earthquake Authority • worse deal: • these policies extend less protection • rates are often 3x more than the previously available commercial rates • require large deductibles
The Value of Information • Risk often exists because we don’t know all the information surrounding a decision • Because of this, information is valuable and people are willing to pay for it
The Value of Information • The value of complete information • The difference between the expected value of a choice with complete information and the expected value when information is incomplete
The Value of Information – Example • Per capita milk consumption has fallen over the years • The milk producers engaged in market research to develop new sales strategies to encourage the consumption of milk
The Value of Information – Example • Findings • Milk demand is seasonal with the greatest demand in the spring • Price elasticity of demand is negative and small • Income elasticity is positive and large
The Value of Information – Example • Milk advertising increases sales most in the spring • Allocating advertising based on this information in New York increased profits by 9% or $14 million • The cost of the information was relatively low, while the value was substantial (increased profits)
Behavioral Economics • Sometimes individuals’ behavior contradicts basic assumptions of consumer choice • More information about human behavior might lead to better understanding • This is the objective of behavioral economics • Improving understanding of consumer choice by incorporating more realistic and detailed assumptions regarding human behavior
Behavioral Economics • There are a number of examples of consumer choice contradictions • You take at trip and stop at a restaurant that you will most likely never stop at again. You still think it fair to leave a 15% tip rewarding the good service. • You choose to buy a lottery ticket even though the expected value is less than the price of the ticket
Behavioral Economics • Reference Points • Economists assume that consumers place a unique value on the goods/services purchased • Psychologists have found that perceived value can depend on circumstances • You are able to buy a ticket to the sold out Cher concert for the published price of $125. You find out you can sell the ticket for $500 but you choose not to, even though you would never have paid more than $250 for the ticket.
Behavioral Economics • Reference Points (cont.) • The point from which an individual makes a consumption decision • From the example, owning the Cher ticket is the reference point • Individuals dislike losing things they own • They value items more when they own them than when they do not • Losses are valued more than gains • Utility loss from selling the ticket is greater than original utility gain from purchasing it
Behavioral Economics • Experimental Economics • Students were divided into two groups • Group one was given a mug with a market value of $5.00 • Group two received nothing • Students with mugs were asked how much they would take to sell the mug back • Lowest price for mugs, on average, was $7.00
Behavioral Economics • Experimental Economics (cont.) • Group without mugs was asked minimum amount of cash they would except in lieu of the mug • On average willing to accept $3.50 instead of getting the mug • Group one had reference point of owning the mug • Group two had reference point of no mug
Behavioral Economics • The Laws of Probability • Individuals don’t always evaluate uncertain events according to the laws of probability • Individuals also don’t always maximize expected utility • Law of small numbers • Overstate probability of an event when faced with little information • Ex: overstate likelihood they will win the lottery
Behavioral Economics • Theory up to now has explained much but not all of consumer choice • Although not all of consumer decisions can be explained by the theory up to this point, it helps us understand much of it • Behavioral economics is a developing field to help explain and elaborate on situations not well explained by the basic consumer model
