12-2 Overview I. The Mean and the Variance II. Uncertainty and Consumer Behavior III. Uncertainty and the Firm IV.Uncertainty and the Market V. Auctions
12-3 Perfect Information Up to this point we have made the assumption of perfect information. Most decisions are made under uncertainty. Most managers attempt to maximize profits while mitigating risk.
12-4 The Mean The expected value or average of a random variable. Computed as the sum of the probabilities that different outcomes will occur multiplied by the resulting payoffs: E[x] = q 1 x 1 + q 2 x 2 +…+q n x n, where x i is payoff i, q i is the probability that payoff i occurs, and q 1 + q 2 +…+q n = 1. The mean provides information about the average value of a random variable but yields no information about the degree of risk associated with the random variable.
12-5 The Variance & Standard Deviation Variance –A measure of risk. –The sum of the probabilities that different outcomes will occur multiplied by the squared deviations from the mean of the random variable: s 2 = q 1 (x 1 - E[x]) 2 + q 2 (x 2 - E[x]) 2 +…+q n (x n - E[x]) 2 Standard Deviation –The square root of the variance. High variances (standard deviations) are associated with higher degrees of risk
12-6 Uncertainty and Consumer Behavior Risk Aversion –Risk Averse: An individual who prefers a sure amount of $M to a risky prospect with an expected value, E[x] of $M. –Risk Loving: An individual who prefers a risky prospect with an expected value, E[x] of $M to a sure amount of $M. –Risk Neutral: An individual who is indifferent between a risky prospect where E[x] = $M and a sure amount of $M.
12-7 Diminishing Marginal Utility of Income Most individuals are risk averse and have diminishing marginal utility of income. $100 added to income provides less satisfaction then $100 subtracted from income. Some people are risk-loving and exhibit increasing marginal utility of income.
12-8 Managerial Decision-Making in a Risk Averse Environment Product quality – consumer prefers a sure thing rather than taking a chance on a new product. Manager can lower the price of the new product to compensate for the risk in buying the new product (free samples). Manager can develop comparison advertising campaign to demonstrate better quality of the new product compared with current good. Money back guarantees.
12-9 How Risk Aversion Influences Decisions Chain stores – becoming part of a chain sends a message of uniform quality to the consumer. Applies to many types of retailers. Insurance – small insurance premium to offset the possibility of a catastrophic loss. The consumer is purchasing a “sure thing”; the protection from loss.
12-10 Price Uncertainty and Consumer Search Suppose again imperfect information Suppose consumers face numerous stores selling identical products, but charge different prices. The consumer wants to purchase the product at the lowest possible price, but also incurs a cost, c, to acquire price information. There is free recall and replacement. –Free recall means a consumer can return to any previously visited store. –Replacement means that the distribution of prices does not change just because the consumer learns of a price being charged by a particular store.
12-11 Price Uncertainty and Consumer Search The consumer’s reservation price, the price at which the consumer is indifferent between purchasing and continue to search, is R. When should a consumer cease searching for price information?
12-12 Consumer Search Rule Consumer will search until Therefore, a consumer will continue to search for a lower price when the observed price is greater than R and stop searching when the observed price is less than R.
12-13 Example 25% of retailers sell a fine damask tablecloth for $200. 75% sell the same tablecloth for $300 meaning the consumer will find a price of $300 in 75% of the stores she enters. What is the expected benefit of searching for a lower price? EB =.25( ) +.75(0) = $25.
12-14 Example If the consumer continues to search for the lower priced store, 25% of the time she will save $100, and 75% of the time she will save zero. E(B) = $25 Consumer should continue her search if the cost of the search < E(B)
12-15 Consumer Search The Optimal Search Strategy. cc EB Reservation Price AcceptRejectR $ P 0
12-16 Consumer Search: Rising Search Costs cc EB R $ P 0 An increase in search costs raises the reservation price. R*R* c*
12-17 Uncertainty and the Firm Risk Aversion –Are managers risk averse or risk neutral? –Risk-neutral manager is interested in maximizing E(profits). Variance of returns does not affect her decisions. –Risk-averse manager will prefer a risky project if it offers higher expected returns than a “safe” project. –How much higher depends on the risk preferences of the manager.
12-18 Uncertainty and the Firm Diversification –“Don’t put all your eggs in one basket.” –Investing in multiple projects decreases risk exposure. –While most managers are risk-averse most owners are risk-neutral. –Manager is expected to maximize the expected Present Value of the firm. –Shareholders can diversify away from firm-specific risk.
12-19 Uncertainty and the Firm Profit Maximization –When demand is uncertain, MR is uncertain and expected profits are maximized at the point where expected marginal revenue equals marginal cost: E[MR] = MC.
12-20 Example: Profit-Maximization in Uncertain Environments Suppose that economists predict that there is a 20 percent chance that the price in a competitive wheat market will be $5.62 per bushel and an 80 percent chance that the competitive price of wheat will be $2.98 per bushel. If a farmer can produce wheat at cost C(Q) = Q 2, how many bushels of wheat should he produce? What are his expected profits?
12-21 Profit-Maximization in Uncertain Environments Answer: –E[Price] = 0.2 x $ x $2.98 = $3.508 –In a competitive market firms produce where E[P] = MC. –3.508 = 0.02Q. Thus, Q = bushels. –Expect profits = TR=(3.508 x 175.4)= $ –TC = [ (175.4)] = $ –Expected[Profits] = $287.65
12-22 Uncertainty and the Market Uncertainty can profoundly impact market’s abilities to efficiently allocate resources.
12-23 Asymmetric Information Situation that exists when some people have better information than others. People with the least information can rationally refuse to participate in the market. Insider trading Job applicants Issuing credit
12-24 Two Types of Asymmetric Information Hidden characteristics –lead to adverse selection –Things one party to a transaction knows about itself, but which are unknown by the other party. Hidden actions – lead to moral hazard –Actions taken by one party in a relationship that cannot be observed by the other party.
12-25 Adverse Selection Situation where individuals have hidden characteristics and in which a selection process results in a pool of individuals with undesirable characteristics. Examples –Choice of medical plans. –High-interest loans. –Auto insurance for drivers with bad records.
12-26 Moral Hazard Situation where one party to a contract takes a hidden action that benefits him or her at the expense of another party. Examples –The principal-agent problem – effort of the manager is not observable so fixed salary poses a moral hazard problem. –Contract with financial incentives addresses this problem. –Care taken with rental cars – when people are fully insured they are less likely to take precautions against loss. –Deductibles
12-27 Possible Solutions 1. Signaling –Attempt by an informed party to send an observable indicator of his or her hidden characteristics to an uninformed party. –To work, the signal must not be easily mimicked by other types. –In product markets firms use free trial periods, money back guarantees, packaging indicating quality. –In labor markets: Education.
12-28 Possible Solutions 2. Screening –Attempt by an uninformed party to sort individuals according to their characteristics. –Often accomplished through a self-selection device A mechanism in which informed parties are presented with a set of options, and the options they choose reveal their hidden characteristics to an uninformed party. –Price discrimination –airline pricing example pg 454
12-29 Auctions Importance – firms participate in auctions either as the auctioneer or as a bidder. Uses –Art –Treasury bills –Spectrum rights –Consumer goods (eBay and other Internet auction sites) –Oil leases Major types of Auction –English –First-price, sealed-bid –Second-price, sealed-bid –Dutch
12-30 English Auction An ascending sequential bid auction. Bidders observe the bids of others and decide whether or not to increase the bid. The item is sold to the highest bidder.
12-31 First-Price, Sealed-bid An auction whereby bidders simultaneously submit bids on pieces of paper. The item goes to the highest bidder. Bidders do not know the bids of other players.
12-32 Second-Price, Sealed-bid The same bidding process as a first-price, sealed-bid auction. However, the high bidder pays the amount bid by the 2nd highest bidder.
12-33 Dutch Auction A descending price auction. The auctioneer begins with a high asking price. The bid decreases until one bidder is willing to pay the quoted price. Strategically equivalent to a first-price, sealed- bid auction.
12-34 Information Structures The type of auctions differ according to the information the bidders possess. Perfect information - Each bidder knows exactly the items worth and knows how the item is valued by each other bidder. Perfect information is rare in an auction. There usually exists asymmetric information.
12-35 Information Structures Independent private values –Bidders know their own valuation of the item, but not other bidders’ valuations. Again asymmetric information. –Bidders’ valuations do not depend on those of other bidders. An item’s worth to a bidder is determined by individual tastes that are known only to the bidder. These values are independent because they do not depend on the valuation of others.
12-36 Information Structures Affiliated (or correlated) value estimates –Bidders do not know their own valuation of the item or the valuations of others. –Bidders use their own information to form a value estimate (art). –Value estimates are affiliated: the higher a bidder’s estimate, the more likely it is that other bidders also have high value estimates. –Common values is the special case in which the true (but unknown) value of the item is the same for all bidders. (Govt use of auctions to sell mineral rights). – True value is unknown but the value is the same for each bidder.
12-37 Optimal Bidding Strategy in an English Auction Independent private valuations Bidders learn nothing useful to them about their own valuation during the bidding process. The optimal strategy is to remain active until the price exceeds your own valuation of the object.
12-38 Optimal Bidding Strategy in a Second-Price Sealed-Bid Auction With independent private valuations, the optimal strategy is to bid your own valuation of the item. This is a dominant strategy. –You don’t pay your own bid, so bidding less than your value only increases the chance that you don’t win. –If you bid more than your valuation, you risk buying the item for more than it is worth to you.
12-39 Optimal Bidding Strategy in a First-Price, Sealed-Bid Auction If there are n bidders who all perceive independent and private valuations to be evenly (or uniformly) distributed between a lowest possible valuation of L and a highest possible valuation of H, then the optimal bid for a risk- neutral player whose own valuation is v is
12-40 Example Two bidders with independent private valuations (n = 2). Lowest perceived valuation is unity (L = 1). Optimal bid for a player whose valuation is two (v = 2) is given by
12-41 Optimal Bidding Strategies with Correlated Value Estimates Difficult to describe because –Bidders do not know their own valuations of the item, let alone the valuations others. –The auction process itself may reveal information about how much the other bidders value the object. Optimal bidding requires that players use any information gained during the auction to update their own value estimates.
12-42 The Winner’s Curse In a common-values auction, the winner is the bidder who is the most optimistic about the true value of the item (oil, gas, mineral lease e.g.). Chance that the other bidders are wrong and the winner is right are slim. To avoid the winner's curse, a bidder should revise downward his or her private estimate of the value to account for this fact. The winner’s curse is most pronounced in sealed-bid auctions.
12-43 Expected Revenues in Auctions with Risk Neutral Bidders Which is the best type of auction from the auctioneer’s perspective? Independent Private Values – players already know their valuations and learn nothing about the item’s worth from the auction process English = Second Price = First Price = Dutch.
12-44 Expected Revenues in Auctions with Risk Neutral Bidders Affiliated Value Estimates –English > Second Price > First Price = Dutch. –Bidders offers are smaller than they would be based on their private value estimate in order to avoid winner’s curse. –Bids are more closely linked to other players information, which mitigates players’ concerns about the winner’s curse. –English is largest because players gain the most information during the auction.
12-45 Conclusion Information plays an important role in how economic agents make decisions. –When information is costly to acquire, consumers will continue to search for price information as long as the observed price is greater than the consumer’s reservation price. –When there is uncertainty surrounding the price a firm can charge, a firm maximizes profit at the point where the expected marginal revenue equals marginal cost. Many items are sold via auctions –English auction –First-price, sealed bid auction –Second-price, sealed bid auction –Dutch auction