FHCE Lecture Slides Exam 2
Consumer Surplus
A dollar measure of the extent to which a consumer benefits from participating in a transaction. Useful when calculating benefits associated with public projects or estimating costs of policy decisions. In a graph, it is the area between demand curve and price.
The Winner's Curse Example
A fully rational auction bidder should take into account the fact that the winning bid tends to be too high. Knowing that the winning bid will tend to be too high, he can then protect himself by adjusting his bid downward. If other bidders are fully rational, they too will adjust their bids, and the identity of the winning bidder should be the same as before. How big should the downward adjustment be?
An Engel Curve at the Market Level
A schedule that relates the quantity demanded to the average income level in the market. Caveat: a stable relationship between average income and quantity demanded is by no means certain: - We cannot construct Engel curves at the market level by simply adding individual Engel curves horizontally. - Consumers in a market face the same price, so we can add demand curves... but they have different incomes!
Factors That Determine Time Preference
Evening the income stream (life-cycle) Relative cost of goods Bequests Hedging against uncertainty (precautionary saving) Time preference - Time preference is impossible to measure empirically. Instead, economists use proxy measures, e.g., education, healthy diet, smoking and/or drinking, exercising, wearing seatbelts, etc.
When We Cheat
Everyone has likely taken advantage of information asymmetry at some point in their lifetime, e.g.,: - Job interviews - First date / online dating - Insurance markets
Costly-to-Fake Principle
For a signal to an adversary to be credible, it must be costly to fake. Application examples: Choosing a Hard-Working, Smart Employee Product Quality Assurance Choosing a Relationship (why you should avoid dating websites!) Conspicuous Consumption as Ability Signaling
Diminishing Marginal Utility
For a utility function defined in previous example, the marginal utility declines as wealth rises. In math terms, it is concave:
Forecasting Trends with Elasticities
Forecasting the composition of future purchase patterns is among the most important applications of price and income elasticities. Consider the case of coal - an economic good with low (in absolute terms) price and income elasticities.
Quality Change: Another Bias in the CPI?
Gathering data on prices of goods is not as straightforward as it seems. - Discounts, rebates, promotions, etc. - Quality changes -- The average price for a new vehicle in 1994 was $19,675, a 5.1 percent increase over 1993 and a 72.8 percent increase over 1984. -- CPI in this period rose "only" 42.6 percent. -- Does this mean that the prices of cars rose much more rapidly during that period than those of other goods and services?
When Sellers Know More than Buyers
George Akerlof and "The Market for Lemons": Quality is known by one party (seller) and not the other. Assume 50% chance of getting a lemon. Good = $20,000 Bad = $10,000 Expected value of a used car? Good is driven out of the market by bad Case of one-day-old cars
An Individual Consumer's Demand Curve
Graph in Slides
The Acceptance Wage
How large should an offer be before you should accept it? The answer to this question is called the acceptance wage, denoted 𝑤^∗. If you are risk neutral, it is the wage for which the expected monetary benefits of sampling another offer are exactly equal to the costs:
Income Elasticity of Demand
If a good exhibits a stable Engle curve, we can define its income elasticity of demand, the percentage change in the quantity of a good demanded that results from a 1 percent change in income Categories of goods: - Necessities: 0<η<1 - Luxuries: η>1 - Inferior: η<0
Permanent & Life-Cycle Income Hypotheses
Improvement: consumption as a function of income over the long-run (lifetime). Income in any period can be decomposed into permanent and transitory components. - Thus, income in the first period is Y1 = Yp + Yt1 Permanent income is constant in all periods (i.e., average income in a long-period). In Modigliani's Life-Cycle Model (with 2 periods): - R=Yp + Yp/(1+r) , thus Yp = R(1+r)/(2+r)
Application of Price Elasticity Analysis: The Marta Fare Increase
In 1987 the Metropolitan Atlanta Rapid Transit Authority (MARTA) raised its basic fare from 60 to 75 cents/ride. In the 2 months following the fare increase, total system revenues rose 18.3 percent in comparison with the same period a year earlier. What do these figures tell us about the original price elasticity of demand for rides on the MARTA system? The revenue is defined as price * quantity. Thus, the fact that total revenues went up by 18.3 percent may be expressed as follows: (75(𝑄_1+∆𝑄)−60𝑄_1)/(60𝑄_1 )=0.183 This reduces to ∆𝑄/𝑄_1 =−0.0536 Since we know that ∆𝑃/𝑃_1 =15/60=0.25, This tells us that 𝜀=−0.0536/0.25=−0.2144 The demand for MARTA rides thus turns out to be highly inelastic, this led to the substantial increase in consumer expenditures.
The Effects of Changes in Income
Income-consumption curve (ICC) for a good 𝑋 is the set of optimal bundles traced on an indifference map as income varies (holding the prices of 𝑋 and 𝑌 constant).
Changes of resources
Increase in future income from Y20 to Y21 (top figure): - Consumption (being normal good) rises in both periods - Saving in the first period decreases Increase in current income from Y10 to Y11 (bottom figure): - Consumption (being normal good) rises in both periods - Saving in the first period increases
The Full-disclosure Principle
Individuals must disclose even unfavorable qualities about themselves, lest their silence be taken to mean that they have something even worse to hide. Examples: Product Warranties - Producers know much more than consumers about how good their products are. Regulating the Employment Interviewer - Lack of evidence that something resides in a favored category will often suggest that it belongs to a less favored one Corporate Finance - Should a company with a profitable project idea raise capital by borrowing or through public offering?
Changes of prices over time
Initially consumer maximizes satisfaction at point E0, saving S10 = Y1/p - C10. Expectation of higher inflation moves the budget constraint line to A'B. Maximum affordable consumption in the second period falls to R2/(1+g)p. Consumer finds new equilibrium at point E1, consumption grows to C11 and savings decrease to S11 = Y1/p - C11. Ambiguity exists about the relative size of substitution and income effects. Thus, the total effect is analytically not clear.
Relative Income Hypothesis
James Duesenberry Reference groups influence consumption ("Keeping Up with the Joneses") Consumption patterns subject to habit, slow to change in light of income reductions
Absolute Income Hypothesis
John Maynard Keynes First formal consumption function - Proposed by Keynes in 1936. 0<Δ𝐶/Δ𝑌<1 - Δ𝐶/Δ𝑌 is the Marginal Propensity to Consume (MPC) MPC is equal to the slope (m) of the Engel curve: 𝐶1=𝑏+𝑚𝑌1 Higher income people save a higher fraction of their income: - Poor consumer (𝐸) has higher consumption to income ratio than rich consumer (𝐹). - Consumption to income ratios of consumers 𝐸 and 𝐹 are slopes of lines 0𝐸 and 0𝐹, respectively.
Budget Constraints for 2 Years
Jones spends all his income on two goods: 𝑋 and 𝑌. The prices he paid and the quantities he consumed last year are as follows: 𝑃𝑋=10, 𝑋=50, 𝑃𝑌=20, and 𝑌=25. This year 𝑃𝑋 and 𝑃𝑌 are both 10, and Jones's income is $750. Assuming his tastes do not change, in which year was Jones better off, last year or this?
The Intertemporal Choice Model
Key assumptions: - Two periods, e.g., today and tomorrow (or this year and next year, etc.). - No bequest motive (all resource is spent). Consumer maximizes satisfaction by deciding how much to consume in current and next periods: 𝐶1 and 𝐶2, respectively. What resources are available? Labor income now and in the future, 𝑀1 and 𝑀2, respectively. Time value of money calculations are necessary: - Suppose you receive $50,000 income now and $60,000 in the future. - You deposit some of your current income in a bank, you can receive your principal plus a return on deposit (e.g., 20% in the future period). - Similarly, if you wish to borrow against your future income, you may receive $1 now for every $1.20 you must repay in the future (assuming 20% annual rate of interest). The present value of a payment of 𝑋 dollars 𝑇 years from now is 𝑋/(1+ 𝑟)𝑇, where 𝑟 is the annual rate of interest. Present value of lifetime income is the horizontal intercept of the intertemporal budget constraint.
Risk Pooling
Law of large numbers - A statistical law that says that if an event happens independently with probability 𝑝 in each of 𝑁 instances, the proportion of cases in which the event occurs approaches 𝑝 as 𝑁 grows larger. - Makes it possible for people to reduce their risk exposure through pooling arrangements. When a large group of individuals pool risk together, the prediction of average incurred loss becomes more precise.
Problems Big and Small
Lehman Brothers bankruptcy Why do job applicants in big cities dress better for interviews than applicants in small cites?
The Intertemporal Choice Model Graph
Marginal rate of time preference is the number of units of consumption in the future a consumer would exchange for 1 unit of consumption in the present. It declines as one moves downward along an indifference curve.
Permanent Income Hypothesis
Milton Friedman
The Effects of Changes in Income
Normal good - one whose quantity demanded rises as income rises (e.g., tenderloin). Inferior good - one whose quantity demanded falls
Giffen Goods
One for which the quantity demanded rises as its price rises. The Giffen good must be an inferior good.
Probability And Expected Value
People choose the alternative that has the highest expected utility (not expected value). - Expected utility: the expected utility of a gamble is the expected value of utility over all possible outcomes. The expected values of the outcomes of a set of alternatives need not have the same ranking as the expected utilities of the alternatives.
The Welfare Effects of Changes in Housing Prices
Two scenarios: - You have just purchased a house for $200,000. The very next day, the prices of all houses, including the one you just bought, double. - You have just purchased a house for $200,000. The very next day, the prices of all houses, including the one you just bought, fall by half. In each case, how does the price change affect your welfare? (Are you better off before the price change or after?)
The Reservation Price for Insurance
What is the most a consumer would pay for insurance against a loss? A risk-averse consumer with an initial wealth of 700 has the utility function 𝑈(𝑀). he faces the prospect of a loss of 600 with probability 1/3. His expected utility is: (1/3)𝑈(100)+(2/3)𝑈(700)=(1/3)(18)+(2/3)(36)=30. His expected utility lies on the chord joining 𝐴 and 𝐶, at the point directly above 𝑀=500.
The Unit-Free Property of Elasticity
When weighing costs and benefits, always compare absolute dollar amounts, not proportions. When describing how quantity demanded responds to changes in price, it's generally best to speak in terms of proportions.
Application: Two-Part Pricing
Why do some tennis clubs have an annual membership charge in addition to their hourly court fees? A suburban tennis club rents its courts for $25 per person per hour. John's demand curve for court time, 𝑃=50−1/4 𝑄, where 𝑄 is measured in hours per year (figure). Assuming there were no other tennis clubs in town, what is the maximum annual membership fee John would be willing to pay for the right to buy court time for $25/hr? The consumer surplus that John receives from being able to buy as much court time as he wants at the $25/hr price defines the (hypothetical) maximum that he would be willing to pay for membership.
A Risk-Averse Person
Will Always Refuse a Fair
Signaling and Education
Will graduating form UGA really make you a more productive and thus more valuable employee to a future employer? I sure would like to believe that, but could it just ... ... be a good and costly to fake signal that you send to the future employers?
A Hypothetical Uniform Wage Distribution
Your pay is correlated with the utilization of your skills (i.e., jobs that make better use of you particular skills should pay better). At any point in your life, there likely are jobs that would pay you better than the current job. For simplicity, we abstract from all dimensions of job variation other than wage earnings. There is a distribution of possible job vacancies to examine. It costs $5 to examine a job vacancy, all of which have wages distributed uniformly between $100 and $200:
Problem 13
Your utility function is √𝑀. Your current wealth is $400,000. There is a 0.00001 probability that your legal liability in an automobile accident will reduce your wealth to $0. What is the most you would pay for insurance to cover this risk?
Example 6.2 Expected Value of Wealth
Your utility function is 𝑈=√𝑀 and your initial wealth is 36. Will you accept a gamble in which you win 13 with probability 2/3 and lose 11 with probability 1/3?
Hyperbolic Discounting
implies that the value of reward is multiplied by discount factor that diminishes over time.
Moral hazard
incentives that lead people to file fraudulent claims or to be negligent in their care of goods insured against theft or damage.
The Utility Function of a Risk-Seeking Person
is Convex in Total Wealth
Engel curve
plots the relationship between the quantity of 𝑋 consumed and income.
Adverse selection
process by which the less desirable potential trading partners volunteer to exchange.
Market Demand Curves
the horizontal sum of all individual demand curves
John von Neumann
was a Hungarian-American mathematician who developed the theory of choice between uncertain alternatives
Statistical Discrimination
Because insurance companies must cover their costs, their average premium must exceed their average claim payment. So for the average and above average customer, buying insurance is a gamble with negative expected value. To avoid this statistical discrimination, those people should self-insure for any expected losses they can absorb.
Concept Check 6.2
Consider a person with an initial wealth level of 100 who faces a chance to win 20 with probability 1/2 and to lose 20 with probability 1/2. If this person's utility function is given by 𝑈(𝑀)=𝑀^2, will she accept this gamble?
Signaling
Signaling: communication that conveys information. Two properties of signaling between potential adversaries: 1. Signals must be costly to fake. 2. If some individuals use signals that convey favorable information about themselves, others will be forced to reveal information even when it is considerably less favorable.
The Winner's Curse Example 2
Consider an auction in which the true value of the item for sale is 0.5, and in which each bidder uses an estimate that is uniformly distributed between 0 and 1. If there were only one bidder at this auction, the expected value of the highest estimate would be 0.5 (no need to make an adjustment). If there were 𝑁 bidders? - Suppose we put the 𝑁 estimates in ascending order and call them 𝑋1, 𝑋2, ...𝑋𝑁. - If they all come from a uniform distribution, the expected values 𝑋1, 𝑋2, ...𝑋𝑁 will be evenly spaced in the interval. - In general, the highest of 𝑁 estimates will have an expected value of 𝑁/(𝑁+1).
Expected Utility Example
Consider an uncertain situation to be defined uniquely by the amount of total wealth. A person with $10,000 initial wealth must chose between two gambles: 1. 50% probability of losing $1,000, and 50% probability of gaining $2,000, 2. 50% probability of losing $100, and 50% probability of gaining $200. Assume that the utility of wealth 𝑊 is given by the function 𝑈(𝑊)=√𝑊. Which gamble would be preferred?
A Bias in the Consumer Price Index
Consumer price index (CPI): - Measures changes in the "cost of living", the amount a consumer must spend to maintain a given standard of living. - Used to measure inflation or compare cost of living in different geographical areas, e.g., http://money.cnn.com/calculator/pf/cost-of-living/. - Fails to substitution into account hence overestimating the cost of living. - The bias will be larger when there are greater differences in the rates of increase of different prices.
Consumer Choice Under Uncertainty
Decisions made under uncertainty are gambles. - Imagine a coin toss, if heads comes up you receive X extra points to your total grade. If the tails comes up I subtract 10 points from your total. Expected value: - The sum of all possible outcomes, weighted by its respective probability of occurrence. In addition to the expected value of a gamble, most people also consider how they feel about each of its possible outcomes.
Expected Utility Example
Diminishing marginal utility: for a utility function defined on wealth, one in which the marginal utility declines as wealth rises. Fair gamble: a gamble whose expected value is zero.
Example 6.5 Expected Benefit
Smith, who was injured by a defective product, is weighing the decision whether to sue the manufacturer. His utility function is given by 𝑈(𝑀)=1−(1/𝑀), where 𝑀 is his total wealth. His total wealth if he does not sue is 𝑀0=7. If he sues, he would win with probability 0.5, in which case he would receive a damage award of 5. If he loses, he will receive nothing in damages. Suppose the opportunity cost of the time required for a lawyer to file a suit on Smith's behalf is 2. Will Smith file a suit if he has to pay the lawyer a fee of 2? Can a risk-neutral lawyer offer Smith a fee schedule whose expected value is sufficient to cover the lawyer's opportunity cost (that is, whose expected value is at least 2) and that simultaneously will induce Smith to sue? If so, describe such a fee schedule.
Income and Substitution Effects of a Price Change
Substitution effect - that component of the total effect of a price change that results from the associated change in the relative attractiveness of other goods. Income effect - that component of the total effect of a price change that results from the associated change in real purchasing power. Total effect: the sum of the substitution and income effects.
Determinants of Price Elasticity of Demand
Substitution possibilities: the substitution effect of a price change tends to be small for goods with no close substitutes. Budget share: the larger the share of total expenditures accounted for by the product, the more important will be the income effect of a price change. Direction of income effect: a normal good will have a higher price elasticity than an inferior good. Time: demand for a good will be more responsive to price in the long-run than in the short-run.
Example 6A.2
Suppose 50 people are bidding for an antique clock, and each has an unbiased estimate of the true value of the clock that is drawn from a uniform distribution on the interval (0,𝐶), where 𝐶 is unknown. Your own estimate of the value of the clock is $400. How much should you bid?
Risk Neutrality Example
Suppose it is known that some fraction z of all personal computers are defective. The defective ones, however, cannot be identified except by those who own them. Consumers are risk neutral and value non-defective computers at $2,000 each. Computers do not depreciate physically with use. New computers sell for $1,000, used ones for $500. What is z?
Limitations of the Neo-classical Theory
The basic econ theory can only take us so far. Extensions needed: - Incomplete information - Asymmetric information Example: advice on where to eat from a travel guide Terminology: adverse selection vs. moral hazard
The Expected Value of an Offer that is Greater than $150
The first job you examine pays $150. Should you accept it, or pay $5 and look at another (in any case, you can still take the current offer)? You must compare the cost of examining another offer with the expected benefits. If there are to be any benefits at all, the new offer must be greater than $150. The probability of that happening is 0.5: The expected gain from sampling another offer when you have $150 offer in hand is the product of these two factors: (1) the probability that the new offer exceeds the old one, and (2) the expected gain if it does: =(1/2)($25)=$12.50
Cross-Price Elasticities of Demand
The percentage change in the quantity of one good demanded that results from a 1 percent change in the price of the other good. Types of goods: - Compliments: 𝜀_𝑋𝑍<0 - Substitutes: 𝜀_𝑋𝑍>0
The Winner's Curse
The size of the winning bid in any auction depends not on the behavior of the average bidder, but on the behavior of the highest bidder. An estimate is unbiased if, on average, it is equal to the true value. Experimental studies show that average auction-winning bids are biased! This is known as winner's curse - the general principle that the winning bid for an item often exceeds its true value.
Certainty Equivalent Value
The sum of money for which an individual would be indifferent between receiving that sum and taking the gamble. Find the value of certainty equivalent - the fee structure that makes Smith (from the previous slide) indifferent between filing / not filing the lawsuit.
Seminal Theories of Consumption & Saving
Absolute Income Hypothesis Life-Cycle Models Inter-temporal Models Permanent Income Hypothesis Relative Income Hypothesis
Life-Cycle Models Intertemporal Models
Albert Ando Franco Modigliani
The Loss in Consumer Surplus from an Oil Price Increase
An individual's demand curve for gasoline is given by: 𝑃=10−𝑄, where 𝑃 is the price of gasoline ($/gal), and 𝑄 is the quantity she consumes (gal/wk). If the individual's weekly income is $1,000 and the current price of gasoline is $2/gal, by how much will her consumer surplus decline if an oil import restriction raises the price to $3/gal?
Search for Low-priced Product
Assume a price distribution that is uniform on the interval (0,𝑃). If the price of the product you have just sampled is 𝑃^∗, the probability of getting a lower price on your next try is 𝑃^∗/𝑃. If you do find a lower price, your savings, on the average, will be 𝑃^∗/2. Your expected gain from another search at 𝑃^∗ is therefore: 𝐸𝑃(𝑃^∗ )=(𝑃^∗/2)(𝑃^∗/𝑃)=〖𝑃^∗〗^2/2𝑃 If the cost of another search is 𝐶, the expression for the acceptance price will be: 𝑃^∗=√2𝑃𝐶
Policy Application: School Vouchers
Policy Proposal: each family be given a voucher that could be used toward the tuition at any school of the family's choosing. Current system: families who choose to go to private schools do not receive a refund on their school taxes. Question: what is the effect of vouchers on the level of resources devoted to education. Suppose that the quantity of education measured in terms of classroom-hours per year is fixed. By spending more on education we mean buying education of higher quality (not buying more hours of education). Current tax system: - Charges each family 𝑃𝑒 of tax for 1 unit of public education (whether or not the family uses it). - "1 unit" is defined as a year's worth of education of public school quality. - If it does not send its child to public school, the family has the option to purchase 1 or more units of education at a private school, also at price 𝑃𝑒. - Families are required by law to provide their child with at least 1 unit of education (public or private). Result from Consumer Choice Analysis: - Switching to a voucher system will increase the level of spending on education. - Parents no longer have to forfeit their school taxes when they switch from public to private schools. Other effects (unaccounted for in our analysis): - Competition could make schools more efficient (making the net effect ambiguous). - Some of the additional resources devoted to education as a result of the voucher system would come from parents directly (not government). - Should we account for possible positive externalities?
Policy Application: A Gasoline Tax And Rebate Policy
Policy proposal made during the administration of President Jimmy Carter. Goal: use gasoline taxes to help limit the quantity demanded of gasoline. - Tax revenue would then be used to reduce the payroll tax (tax rebate). Would consumers buy the same amount of gasoline as before if the tax is rebated? Despite the rebate, the consumer substantially curtails his gasoline consumption. - If gasoline is a normal good (true empirically), the effect of the rebate is to offset partially the income effect of the price increase. - It does nothing to alter the substitution effect. Carter administration's tax-and-rebate proposal was never implemented (although the federal gas tax increased to 18.4¢/gal in 1993). The current revenue from gas tax is considered insufficient to cover even the costs of bridge and highway maintenance. Why not increase the tax? - Largely because of the objections of critics who lack the economic knowledge to understand it.
Price Elasticity of Demand
Price elasticity of demand is the percentage change in the quantity of a good demanded that result from a 1 percent change in its price. Three categories of price elasticity: - Elastic: 𝜀<−1 - Inelastic: 𝜀>−1 - Unit Elastic: 𝜀=−1
The Effect of Changes in Price
Price-consumption curve (PCC) for a good 𝑋 is the set of optimal bundles traced on an indifference map as the price of 𝑋 varies (holding income and the price of 𝑌 constant).
Dual-self Consumer and Time Preference
Research on discounting - Thaler's apples: - A) $100 in a year from now - B) $110 in a year from tomorrow - A) $100 right now - B) $110 tomorrow Given two similar rewards, humans show a preference for one that arrives sooner rather than later (hyperbolic discounting). Other examples? - Save More Tomorrow - Over-commitment & procrastination - Drugs, junk food, unprotected sex, etc. - Credit cards!
Elasticity and Total Revenue
Revenue = Price * Quantity 𝑅=𝑃𝑄 A price reduction will increase total revenue if and only if the absolute value of the price elasticity of demand is greater than 1. An increase in price will increase total revenue if and only if the absolute value of the price elasticity is less than 1.
Type of Risk Preferences
Risk averse: preferences described by a utility function with diminishing marginal utility of wealth. - A risk averse person would avoid a fair gamble. - Most people display this characteristic. Risk seeking: preferences described by a utility function with increasing marginal utility of wealth. Risk neutral: preferences described by a utility function with constant marginal utility of wealth.
Value of Reducing Uncertainty
Sarah has a utility function given by 𝑈=1−1/𝑀, where M is the present value of her lifetime income. If Sarah becomes a teacher, she will make 𝑀=5 with probability 1. If she becomes an actress, she will make 𝑀=400 if she becomes a star, but only 𝑀=2 if she fails to become a star. The probability of her becoming a star is 0.01. Smith is an infallible judge of acting talent. After a brief interview, he can state with certainty whether Sarah will become a star if she chooses to pursue a career in acting. What is the most she would be willing to pay for this information?
Permanent and transitory consumption and saving
Savings in the first period : 𝑆1=𝑌1−𝐶1 High current and low future income consumers (top figure) save a positive amount Low current and high future income consumers (bottom figure) save a negative amount (borrow). In each case, the consumer saves all transitory income and the same fraction of permanent income.
