,, The two options have the same expected value, but Option 2 is more risky

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1 ECON14 (Fall 010) (Tutorial 11) Chapter 1 The Economics of Information Mean (Expected value): whe e Variance: Example: Option 1: Flip a coin. If it comes up heads, you receive$1: if it comes up tails, you pay $1 Option : Flip a coin. If it comes up heads, you receive$10: if it comes up tails, you pay $10,, The two options have the same expected value, but Option is more risky Uncertainty and consumer behavior Attitude/ preferences toward risk Utility U(100 ) U(50) U() U(100 ) Utility U() Utilit y U(100 ) U() EU EU = U(50) EU U(50) U(0) U(0) U(0) Risk Aversion Risk Neutrality Risk Loving (1) Risk averse Preferring a sure amount of to a risky prospect with an expected value of Diminishing marginal utility in () Risk neutral Indifferent between a risky prospect with an expected value of and a sure amount of Constant marginal utility in (3) Risk loving Preferring a risky prospect with an expected value of to sure amount of Increasing marginal utility in Implications of risk-averse consumers for optimal managerial decisions Examples: product quality, chain stores, insurance 1

2 Consumer search Reservation price: the price at which a consumer is indifferent between purchasing at that price and searching for a lower price, i.e., when The consumer rejects prices above the reservation price (R) and accepts prices below the reservation price The optimal search strategy is to search for a better price when the price charged by a firm is above the reservation price and stop searching when a price below the reservation price is found Uncertainty and producer behavior Unce tainty affects the manage s input and output decision Managers who are given incentive to maximize expected profits are in general risk neutral, while owners of the firms are risk averse Example: Demonstration problem 1. (P.444) Project Boom Recession (90%) (10%) Mean SD A B A+B T-bill The manager should not invest in T-bill as the A+B offers higher profit regardless of what happens to the economic. Neither a risk averse/ risk neutral manager will never choose project A as the mean (expected profit) is negative The manager would choose project B or joint project of A+B depending on his preferences for risk Producer search: for low prices of inputs Profit maximization Demand, so as the revenues and profits are uncertain Managers maximizes expected profits y equating expected marginal revenue and marginal cost when setting output, i.e., Example: Demonstration problem 1.4 (P.447) How much apple juice should Appleway Industries produce in a competitive market? Fi m s cost function: C = Q Market price: $ for 30% chance and $1 for 70% chance Appleway s p ofit: Expected price: Marginal cost: Equating Expected profit:

3 Uncertainty and the market Asymmetric information: a situation at exists when some people have better information than others The problem of adverse selection and moral hazard arises with the presence of asymmetric information Examples: between consumers and sellers, employers and employees, insurance companies and policy buyers, etc. (1) Adverse selection A situation where individuals have hidden characteristics and in which a selection process results in a pool of individuals with undesirable characteristics Example: The market for used car: the market for lemon (DD-SS diagram) In the used car market, there are high-quality cars and low-quality cars Sellers know more about the qualities of their cars than potential buyers The buyers who do not have much information on the qualities of cars will be willing to pay only the price with is compatible with the average quality The sellers of good used cars will leave the market and he average quality of cars drops The buyers will find that the average quality of cards sold is worse than expected, they will offer a lower prices The quality of cars further drops, only cars with the lowest quality will be transacted in the market This is an example of market failure due to asymmetric information Other examples: Car/health insurance, the credit market, labor market () Moral hazard A situation when one party to a contract takes a hidden action that benefits him or her at the expense of another party Examples: Principal-agent problem The owners can overcome the problem by monitoring the managers or by making the manage s wage contingent on fi m s p ofit Car/ Health insurance: when individuals are fully insured, they have less incentive to avoid a loss Insurance companies try to reduce moral hazard by requiring a deductible on all insurance claims (what is deductible?) (3) Signaling an attempt by an informed party to send an observable indicator of his or her hidden characteristics to an uninformed party The better informed party plays an active role to send signals to the other party In order to make the information transmitted credible, the agent concerned may have to make the signaling costly Examples: free trial periods, money back guarantees of products, academic credentials (4) Screening an attempt by an uninformed party to sort individuals according to their characteristics The less informed party tries to extract as much as information as they can Example: Self-selection device in labor market 3

4 Problems and Examples Question 4 (Baye, P.467) You are a manager of a firm that sells a commodity in a market that resembles prefect competition, and your cost function is C(Q) = Q + Q. Unfortunately, due to production lags, your must make your output decision prior to knowing for certain the price that will prevail in the market. You believe that there is a 60% change the market price will be $100 and a 40% chance it will be $00. (a) Calculate the expected market price (b) What output should you produce in order to maximize expected profits? (c) What are your expected profits (a) Expected market price: Ep.6 $100.4 $00 $140 (b) Set Ep = MC to get 140 = 1 + 4Q. Solve for Q to find your profit-maximizing output, Q = units. (c) Your expected profits are (Ep)Q C(Q) = $140(34.75) ( (34.75) )=$, Question 1 (Baye, P.469) As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 50% change of low demand and a 50% change of high demand. The corresponding demand functions for these two scenarios are P = Q and P = Q, respectively. Your cost function is C(Q) = Q. How many new homes should you build, and what profits can you expect? Your expected inverse demand is E(P) =.5(00,000 50Q) +.5(400,000 50Q) = 300,000 50Q. Therefore, your expected marginal revenue is E(MR) = 300, Q. Your marginal cost is MC = $00,000. Setting E(MR) = MC yields 300, Q 00,000. Solving, Q = 00. The price you expect is thus E(P) = 300,000 50(00) = $50,000. Your profits are thus ($50,000 -$00,000)(00) - $110,000 = $9,890,000. Question 13 (Baye, P.469) Life insurance companies require applicants to submit to a physical examination as proof of insurability prior to issuing standard life insurance policies. In contrast, credit card companies offe thei custome s a type of insu ance called c edit life insu ance which pays off the credit card balance if the cardholder dies. Would you expect insurance premiums to be higher (per dollar of death benefits) on standard life policies? Explain One would expect higher premiums on credit life, and the problem of adverse selection arises. People who cannot pass physicals will select toward this type of insurance, resulting in higher premiums. Furthermore, people who are healthy and can pass a physical will be unwilling to pay the higher premiums, thus exacerbating this effect. 4

5 Question 17 (Baye, P.470) The past year, Used Imported Autos sold very few cars and lost over $ As a consequence, its manager is contemplating two strategies to increase its sales volume. The low cost strategy involves change the dealership name to Quality Used Imported Autos to signal to customers that the company sells high quality cars. The high cost strategy involves issuing a 10-point auto inspection on all used cars on the lot and offering consumers a 30-day warranty on every used card sold. Which of these two strategies do you think would have the greatest impact on sales volume? Explain The 30-day warranty and 10-point inspection would have the greatest impact. This not only reduces buyer risk from being duped by a used car dealer, but provides a costly signal about the quality of the used cars sold. An unscrupulous dealer would find it costly to mimic this strategy. Recognizing both of these facts, rational buyers will be more willing to purchase cars from the dealer. Question 18 (Baye, P.470) Pelican Point Financial G oup s clientele consists of two types of investo s. The fi st type of investor makes many transactions in a given year and has a net worth of over $1 million. These investors seek unlimited access to investment consultants and are willing to pay up to $10000 annually for no fee based transactions, or alternatively $5 per trade. The other type of investor also has a net worth of over $1 million but makes few transactions each year and therefore is willing to pay $100 per trade. As the manager of Pelican Point Financial Group, you are unable to determine whether any given individual is a high or low volume transaction investor. Design a self-selection mechanism that permits you to identify each type of investor Offer two plans for customers with more than $1 million in assets. One plan (perhaps called the F ee T ade Account) has an annual maintenance fee of $ good fo up to 400 f ee transactions (computed as $10,000/$5) per year (each additional transaction is priced at $5 each). The othe plan (pe haps called the F ee Se vice Account) has no annual maintenance fee but charges $100 per transaction. Given these two options, investors will sort themselves into the plans based on their individual characteristics. 5

6 Question 1 (Baye, P.471) You are considering a $ investment in fast-food industry and have narrowed your choice to eithe a McDonald s o a Station East Coast Subs f anchise. McDonald s indicates that, based on the location where you are proposing to open a new restaurant, there is a 5% probability that aggregate 10 year profits (net of initial investment) will be $10 million, a 50% change probability that profits will be $5 million, and a 5% chance that profits will be -$1 million. The aggregate 10-year profit projections (net of initial investment) for a Station East Coast Subs franchise is $30 million with a.5 % probability, $5 million with a 95% probability and -30 million with a.5% probability. Consider both the risk and expected profitability of these two investment opportunities, which is a better investment? Explain. The expected value of aggregate ten-yea p ofits of a McDonald s f anchise is. 5 $10.50 $5.5 $1 $4. 75 million. Simila ly the expected value of a Station East Coast Subs f anchise is. 05 $30.95 $5.05( $30) $4. million. 75 The va iance and standa d deviation of owning a McDonald s f anchise is and McDonalds ' McDonald' s 1875 McDonald' s , respectively. Simila ly the va iance and standa d deviation fo Station East Coast Subs is and , respectively. Since the expected values are the same we can compare the standard deviations to determine the most risky investment. Since McDonald' s there is more risk associated with a Station East Coast Subs f anchise. 6