Economics of Uncertainty and Information

• If you are going to take the exam at DSS you should contact Alex Whalley (whalley@econ.umd.edu) immediately

• I have posted Problem Set 6.• It is due the first discussion session on or

after Wednesday, May 3.• You can select ANY three questions on the

problem set to complete.

• The Department of Economics policy on grading requires me to use the grading system I announce at the beginning of the semester in all cases.

• I cannot make any exceptions to that rule.

Introduction

• In this lecture, we will discuss briefly some of the issues that have been at the “frontiers” of economics.

• They concern decisions when there is uncertainty and also issues that arise when some agents are better informed than others.

• Some of this material is in Mankiw, Chapter 22, but most will be in this set of slides.

Information and Uncertainty• Two topics

– Risk– Asymmetric information

• Hidden characteristics• Hidden actions

• Risk– Expected value– Insurance

• Fair insurance • Unfair insurance

Some Concepts to Learn• Probabilities• Expected Value• Risk aversion• Risk neutrality• “Fair” insurance• Diversification• Asymmetric Information• Hidden information or adverse selection• Hidden actions or moral hazard.

Outcomes and Probabilities

• When events are uncertain or random, it is helpful to establish, first, a set of all possible outcomes.

• An outcome is the actual realization of an uncertainty:– Source of Randomness Outcomes– Flipping coin – Heads or Tails– Sales after a price – high or low sales– Writing an exam – A, B, C or D– Drilling an oilwell --finding oil or a dry well.

Outcomes and Probabilities

• A probability of an outcome is a measure of the likelihood or frequency of that outcome.

• Examples: Fair coin – probability of heads or tails is one-half.

• Probability of rolling two sixes – 1/36 (=1/6 times 1/6)

• Probability of rain tomorrow – 20%.

An expected value is the expected average outcome. Expected value is calculated by weighting each outcome by the probability it will occur, and then summing the weighted outcomes.

A Gamble and a Choice

• How would you choose between these two options?

• What is the expected value of either choice?– Alternative A

• I give you $500,000– Alternative B

• We flip a fair coin• Heads – I give you $1 million• Tails – I give you $0

Another Gamble

• What is the expected value of a craps game that paid the square of the number when it is odd and forces you to pay the square of the number when the number is even?

1 1 1/6 1/62 -4 1/6 -4/63 9 1/6 9/64 -16 1/6 -16/65 25 1/6 25/66 -36 1/6 -36/6

-21/6

A Gamble Or a Risky Situation• Suppose that you are driving a brand new $40,000

BMW 300 series car.• Despite your best possible driving habits, you

know that there is a 10% chance of getting in an accident in any year.

• An accident can be expected to cost (in terms of lost value of the car, repair expenses, and rental car costs) $3,000.

• How do you assess the “gamble” or risk of driving the car?

Expected value = .9(40,000) + .1(40,000 - 30,000) = 37,000

Fair insuranceExpected value of claims = .9(0) + .1(30,000)

= 3,000 = premium

A person is risk averse if he prefers a less risky income, holding fixed its expected value.

• Alternative A– I give you $500,000

• Alternative B– We flip a fair coin– Heads – I give you $1 million– Tails – I give you $0

• Which would you choose?• Which would MOST people choose?

A risk neutral person does not care about risk. Such a person would always choose only on the basis of expected value.

“Ashley Revell, a 32-year-old man from London, England, sold everything he owned, even his clothes, to try his luck Sunday on one spin of a roulette wheel in Las Vegas, Nevada.He put $135,300 on red, and with friends and family watching, the ball hit the mark, giving Revell $270,600.”

Monday, April 12, 2004

http://www.cnn.com/2004/SHOWBIZ/TV/04/12/roulette.win/

Diversification refers to spreading risks across many different investments. This practice can reduce risk.

Company X and Company Y

• Today’s price: $10• 20 percent probability price will fall to $2• 80 percent probability price will rise to $20• Suppose you are considering buying 10

shares in total.• What are the consequences of buying all X

or diversifying and buying some Y also?

Buy 10 shares of company X

.2 20

.8 200

EXPECTED VALUE .2 x 20 +.8 x 200 = 164

• Probability that both will fall = 4 percent

• Probability that X will rise and that Y will fall = 16 percent• Probability that X will fall and that Y will rise = 16 percent• Probability that both will rise = 64 percent

Buy 10 shares of company XX↓ .2 20 X↑.8 200

EXPECTED VALUE .2 x 20 +.8 x 200 = 164

Buy 5 shares of Company X and 5 shares of Company Y

X↓ Y↓.04 20 X↓ Y↑.16 110 Y↓ X↑.16 110 X↑ Y↑.64 200

EXPECTED VALUE

.04 x 20 +.16 x 110 + .16 x 110 + .64 x 200 =

164

The Value of Diversification

• Notice that either strategy would yield the same expected payoff.

• However, the example demonstrates a general principle:– When independent risks are collected to

together, the riskiness of the overall investment is lower.

– Diversification lowers risk. (“Do not put all your eggs in one basket!”)

FINAL EXAM

• The FINAL EXAM is to be held in two rooms: Tydings 0130 and ARM 0126. It is Thursday, May 18, 1:30-3:30. It will be ALL multiple choice and will cover material from the entire course.

• Those students who are in Alex Whalley's discussion sessions (2203, 2209) and Robin Banerjee's discussion sessions (2201, 2206, 2207) are to go to ARM. (I believe this is Reckord Armory). All other students will take the exam in Tydings.

Asymmetric information is a situation in which one side of an economic relationship has better information than the other.

Hidden characteristics are things that one side of a transaction knows about itself that the other side would like to know but does not.

Hidden actions are actions taken by one side of an economic relationship that the other side of the relationship cannot observe.

Hidden Characteristics in Labor Markets

• High ability workers• Worth $400 to the

firm• One-half

• Low ability workers• Worth $200 to the

firm• One-half

Adverse Selection

Adverse selection occurs when the uninformed side of a deal gets exactly the wrong people trading with it (i.e., it gets an adverse selection of the informed parties).

• 2000 Acura Integra GS• 21 year old male driver• Annual premium depends on deductibles

for collision and comprehensive– $100: $1,952.60– $500: $1,559.00– $1,000: $1,333.00

The Lemons Problem

• Winners• Valued at $6,000• One-half

• Lemons• Valued at $2,000• One-half

Adverse Selection in Insurance

• Loss of $10,000• High risk -- 40%• Low risk -- 20%

Moral Hazard

Moral hazard refers to hidden actions because, in such cases, the informed side may take the ‘wrong’ action.

• Hidden actions and moral hazard– Medical care– Employment -- shirking

A Special Segment: Game Theory, Asymmetric Information and

Auctions• Auctions have emerged as one of the most

important contributions of game theory to market design.

A Special Segment: Game Theory, Asymmetric Information and

Auctions• Many items, some important, some minor are sold

at auction:– Government:

• FCC Spectrum licenses, Energy supply contracts, Oil drilling rights, road construction, school milk.

– Private Sector:• Wine, antiques, tobacco, art, used cars, firms. • eBay.

Two Main Auction Formats

• First Price Sealed Bid Auction– All bidders submit a ‘bid’ or a number in a sealed

envelope.– Highest bidder gains object and pays price bid.

• Ascending bid, clock or English Auction– Price starts low on a clock or from an auctioneer.– Bidders indicate willingness to pay at that price.– If they say no, they are out of the auction.– Auctioneer or clock raises price until only one bidder

left.

One other format

• Second Price Sealed Bid Auction:– All bidders submit bids in a sealed envelope.– Highest bidder obtains object.– Pays SECOND highest bid submitted.

Game Theory

• Game Theorists have played an important role in describing how these auction games are played.

• They also analyze benefits and drawbacks of these auctions.

• They were a major voice in the process by which the FCC adopted its spectrum auctions:

• See • http://wireless.fcc.gov/auctions/default.htm?job=auction_summary&id=66

An Example: Uncertainty and NO Asymmetric Information

• Suppose you are bidding for a used car.• With probability 20% it is a lemon and

worth $500 to you• Otherwise it is worth $1000.• Assume you are risk neutral.• What is the expected value of the car to

you?

Expected Value

• The expected value is• .2×500+.8×1000=100+800=$900.

English Auction

• Suppose that everyone believes, like you, that the car is a lemon with probability 20%.

• How should you bid in an English Auction?

English Auction

• Use backward induction:• If the current price is p, you can either say

‘no’, and leave the auction, or say ‘yes’ and stay.

• Suppose p>900. What should you do?• Suppose p<900, What should you do?• When should you drop out?

Example: Auction with Asymmetric Information – The Lemons Problem

• Suppose you know there is one bidder who knows if the car is a lemon but you do not know who it is.

• That bidder has almost the same VALUE as you do for good and bad cars (1001 and 500).

• What would this bidder do if the car was bad? If it was good?

• When should you drop out?

Example: Auction with Asymmetric Information – The Lemons Problem

• You should drop out as soon as the price reaches $500.

• If you bid higher and beat the informed bidder, you would only win if the car was a lemon and you would end up paying more than it is worth.

• This is an example of what is called `the winner’s curse’ in auctions.

• Made famous by Nobel Prize winner George Akerlof in his `Market for Lemons’.

Information and Uncertainty• Two topics

– Risk– Asymmetric information

• Hidden characteristics• Hidden actions

• Risk– Expected value– Insurance

• Fair insurance • Unfair insurance

– Risk averse – Risk neutral– Investments and diversification

• Asymmetric information– Hidden characteristics– Hidden actions

• Hidden characteristics and adverse selection– Employment -- education as a signal– Market for lemons