The Rational Objection

The Power of the Soup Nazi

2006-12-13T12:17:00.000-05:00

Welcome back loyal readers. Having spent much of the last month sending out job applications, it’s time I took a break. That means taking the time to notice economic quirks in my daily life and writing about them.

While flipping through channels over Thanksgiving break, I came across an episode of Seinfeld that caught my attention: the Soup Nazi. For those unfamiliar with the episode, the Soup Nazi is the owner and operator of the most popular soup counter on the upper-west side of Manhattan. His nickname comes from the draconian code of conduct he requires his clientele to follow. Customers are required to wait single-file in line, are forbidden to speak while in line, and must place their order using formal language with as few words spoken as possible. Any deviation from the protocol results in that customer being informed rather emphatically that they will not be receiving soup and depending on the severity of the offense, be instructed on the required duration before their next allowed visit.

The episode begins with Jerry and George explaining the Soup Nazi phenomenon to Elaine. Doubting the strictness of the hyperbolically monikered soup genius, Elaine openly flaunts the rules, resulting in an abrupt “No soup for you! Come back, one year!” from the Soup Nazi. This exchange sets up the two strong-willed characters as adversaries for the remainder of the episode.

Elaine gets her chance to settle the score when an armoire given by the Soup Nazi to his favorite customer Kramer ends up in Elaine’s apartment. The Soup Nazi had apparently left handwritten copies of his recipes in the bottom drawer. Upon discovering the recipes, Elaine becomes increasingly excited at her opportunity for revenge, telling Jerry “I could give these to every restaurant in town. I could have 'em published! I could…I could drop fliers from a plane above the city.”

It is at this point that the episode takes a most disappointing turn as Jerry tries to dissuade Elaine from bringing down her nemesis saying “I don't want you causing any trouble down at that soup stand. I happen to love that soup.” But if all he cares about is the soup, why would he care who makes it? If anything, letting the recipes out would improve the situation for Jerry as a consumer. You see, the Soup Nazi, by virtue of having the best soup around, enjoys a certain monopoly power. Economists recognize monopoly power as a means for certain retailers to raise prices, reduce access to the product, and skimp on services, all to the detriment of the consumer. In this case, the Soup Nazi wields his monopoly power with long lines and by enforcing an authoritarian code of conduct. But if the soup recipes were made widely available, lines would be reduced and codes of conduct relaxed as other retailers compete for customers. The soup Nazi could then change his ways and compete for customers with the rest or resist such changes and be put out of business. He loses something either way while Jerry and the rest of the soup fanatics gain.

The writers of Seinfeld show a complete lack of economic insight regarding the demise of the Soup Nazi. Even at the episode’s end, as the Soup Nazi rations the last of his stock before going out of business, Newman laments the last of the soup. But why should this be the last of the soup? As I just explained, availability of the soup should be expected to increase as other retailers duplicate the recipes of the Soup Nazi.

This simple bit of economic logic was not lost on the writers of the Simpsons who consider an analogous situation in the episode “Flaming Moe’s.” In this episode, Homer shares his secret recipe for a cocktail called the Flaming Homer with Moe, owner of the local bar. Moe’s business takes off when he begins serving the irresistible cocktail under the name Flaming Moe. Soon Aerosmith is playing there every night and Homer can’t even find a seat at the bar. Homer becomes consumed with jealousy and eventually reveals the secret ingredient to everyone in the bar.

Can you guess what happens next? The scene that follows shows every other storefront along the main strip advertising the Flaming Moe. This is good for consumers as Moe, exercising monopoly power, had been successful charging high prices and restricting access to his product. Once the secret got out, anyone could produce it and so his power as a monopolist was lost. This is precisely what should have happened at the end of the Soup Nazi episode. Realizing the inevitability of this outcome, it makes no sense for Jerry to try and prevent Elaine from making the recipes public. This is not to say that revealing another party’s proprietary information is in any way ethical. Enforcement of property rights is a necessary component of the legal system in any society that hopes to reward technical innovations and artistic creativity by its citizens. (Editor’s note: The irony of having said this while also providing links to youtube clips has not been lost on the author.) But anyone familiar with the show should know that Jerry and his friends are guided only by self interest. And in this case, self interest dictates that Jerry allow the recipes to be made public.

As an addendum, I just saw the movie Mean Girls and noticed a mistake in the math. In the Mathletes competition toward the end, the competitors were asked to solve the following equation: lim x->0 [ln(1-x)*sin(x)/(1-cos^2(x))]. That is the limit of a fraction as x goes to zero in both the numerator and the denominator. The girl from the other school said the answer was 1 and was ruled incorrect. Notice that both the numerator, ln(1-x)*sin(x), and the denominator, (1-cos^2(x)), are equal to zero when evaluated at x=0. So what is zero divided by zero? Recall what your high school teacher taught you: "any number divided by zero is 'undefined.'" Applying that very lesson, Lindsay Lohan's character responds, "the limit does not exist," and wins the competition. While her answer was consistent with what most of us were taught, it is in fact wrong.

When adults use calculus to solve problems, it is not enough to say that 0/0 is 'undefined.' 'Undefined' didn't put a man on the moon. 'Undefined' is just another way of saying, "I don't know." To know what 0/0 is, you have to know the speed at which both the numerator and the denominator go to zero. Think about this problem: lim x-> [c/x], where c is an arbitrary non-negative constant. As x goes to zero, the ratio c/x goes to infinity. Since zero is a non-negative constant, we might reasonably conclude that 0/0 is infinity. Now think about this problem: lim x-> [x/c], for any c as before. As x goes to zero, the ratio x/c goes to zero, so we can reasonably conclude that 0/0 is zero. Last, consider this problem: lim x-> [x/x]. Since the ratio is equal to 1 for every value of x, we can reasonably conclude that 0/0 is 1. The point is, 0/0 can be zero, infinity, or some constant (1 being an example), all depending upon which gets to zero faster, the numerator or the denomenator.

l'Hospital's rule formalizes this argument and shows that for any N(x) and D(x) such that lim x->0 N(x) = 0 and lim x->0 D(x) = 0, lim x->0 [N(x)/D(x)] = lim x->0 [N'(x)/D'(x)]. In the Mean Girls problem, N(x) = ln(1-x)*sin(x) and D(x) = 1- cos^2(x). Taking derivatives of both numerator and denominator, we have that lim x->0 [N'(x)/D'(x)]= 0/0, so we're back where we started! Not to worry, we can simply apply l'Hospital's rule to again so that lim x->0 [N'(x)/D'(x)] = lim x->0 [N''(x)/D''(x)], which is equal to -2/2, or -1. So both girls were in fact wrong.

The Dilemma of a Postmodern King Solomon

2006-06-27T21:31:00.000-04:00

Divinely intelligent people don’t need to study economics. King Solomon, of biblical fame, solved a timeless economic problem having no training at all. The problem is described in the famous account from 1 Kings 3:5-14, and is often told to illustrate Solomon’s great wisdom. As the story goes, two women appear before Solomon with a baby boy, both claiming to be his true mother. To resolve the dispute, Solomon calls for a sword to be brought before him and decrees that the child be cut in half with one half going to each woman. Upon hearing the brutal verdict, the true mother shrieks and insists that the child be given to the other woman rather than have him meet such a cruel fate. Solomon immediately awards the baby to the distraught woman, as only the child’s true mother would rather he be raised by another woman than have any harm inflicted upon him.

The brilliance of Solomon’s tactic is evident in its ability to identify the woman who values the child most who in this case is also the child’s true mother. The economic task of assigning an indivisible object to the party that values it most remains a necessity to this day. Examples include the assignment of equipment among employees, the granting of exclusivity over an article of intellectual property, or the allocation of a marital asset of sentimental value during divorce proceedings. In such settings, it is often the case that the involved parties know the identity of the one who values the disputed object most, but the arbiter or decision maker does not.

For this exercise, let’s consider the allocation of a family heirloom whose ownership is disputed amongst two siblings, a brother and a sister. Solomon’s tactic is useless to us since anyone familiar with the story will know how best to respond, and we’re left with the dispute still intact. It is true that Newman did successfully employ Solomon’s tactic to resolve a dispute over a bike in an episode of Seinfeld, but his success relied on the ignorance of Elaine. For this reason, we need improve upon Solomon’s tactic and devise a mechanism to allocate efficiently (read “to the party who values it most”) the heirloom even when the parties to the dispute anticipate that the mechanism will be used.

Invoking the Nobel-Prize-worthy theory of Ronald Coase, proponents of the Chicago School of economics would argue that this dilemma is no dilemma at all as we can simply grant ownership at random. The efficient allocation will then be arrived at through mutually-beneficial trade. To see this, suppose that by the flip of a coin, the heirloom is awarded to the un-deserving heir. Since the deserving heir values the heirloom more than her sibling, she can offer her brother enough to make trade worthwhile so the object ultimately ends up in her hands. In the event the coin flip favors the deserving heir, the un-deserving heir will be unable to sufficiently compensate his sister for giving up the heirloom and it will stay in the hands of his more deserving sister. Either way, the heirloom ends up in the hands of the deserving sister and our objective has been met.

The problem is, when bargaining is required to achieve the efficient allocation, both sides have an incentive to misrepresent their willingness to pay and willingness to accept respectively. Agreement may only be reached after significant delay and at a greater expense to all involved. Since it requires agreement between two sides already prone to disagreement, random assignment is really no solution at all.

A better approach would assign the heirloom without any additional interaction between the disputing parties. We might try asking each side, in private, how much the heirloom is worth to them, but how would we know if we are getting an honest answer? In an artful use of game theory, William Vickrey devised a mechanism called a second-price auction that provides the correct incentive for both parties to truthfully reveal their valuation. The second-price auction works like the familiar sealed-bid auction except that instead of paying the proposed bid, the winning bidder pays an amount equal to the next highest bid. Vickrey showed that each party, when required to participate in a second-price auction, can do no better than to bid their respective valuation regardless of what they think the other will bid. To see this, consider the bidding decision of either sibling, say the sister. Since the price she pays upon winning is independent of her bid, her bid serves as the maximum price at which she can still win the auction. At any price above her valuation, she prefers to lose the auction since her payment would exceed here valuation. At any price below her valuation she prefers to win since her valuation would exceed her payment. By bidding her valuation, she is guaranteed to always win when doing so makes her better off and always lose when winning would have made her worse off.

By having the siblings participate in a second-price auction, the party with the greatest value for the heirloom will place the highest bid and be awarded the heirloom. This is efficient except when the deserving party is constrained to bid no more than her income allows and she loses to her less-deserving brother. To bypass this problem, we need an allocation rule that does not involve any form of payment. The trick is to screen out the un-deserving party by having the disputing parties play a game designed in such a way so as to be unprofitable only for the un-deserving party. If the un-deserving party, who knows he is un-deserving, refuses to participate in such a game, then the deserving party identifies herself as such by indicating her willingness to participate. And with one side to the disagreement dropping his case, the game is never actually played, so nary a payment is ever made.

In a paper to be presented next month at the International Conference on Game Theory, professors Cheng-Zhong Qin & Chun-Lei Yang of UC Santa Barbara and Academia Sinica in Taipei respectively design such a game. Their mechanism, dubbed “bid and guess,” is a variant on the celebrated second-price auction. In this game, both parties are asked to submit sealed bids along with a guess of the other party’s bid. When the envelopes are opened by the arbiter, the rules of the game determine who gets the item, how much they pay, and the size of the entry fee paid by each participant. As in the second-price auction, the high bidder gets the item and pays an amount equal the next-highest bid. The size of the entry fee is calculated to be some fraction of the difference between the bidder’s guess and his opponents actual bid. To insure that income does not constrain the bidders, the arbiter can offer either party a loan at no interest.

Qin & Yang show that within the bid-and-guess game, both parties can do no better than to bid their respective valuations and make a guess that has them paying a positive entry fee. Since the less deserving party necessarily loses the auction while still incurring an entry fee, he finds it unprofitable to participate at all. Thus, if he knows the bid and guess mechanism will be employed by the arbiter, he will drop the dispute before it ever gets to that point. The deserving party will nonetheless agree to participate since her total payment including the entry fee can never exceed her valuation. Using this mechanism, a hypothetical Solomon can resolve all property disputes efficiently without any divine knowledge of human nature.

Now I know you’re saying, “No one will ever use anything as ridiculous as bid and guess to resolve a property dispute,” and you’re right. But that’s not the point. The point is, by understanding the incentives created by various mechanisms, you can understand the logic behind the institutional arrangements that we see in the real world. A good example of this way of thinking is in the allocation of spectrum licenses by the FCC to wireless service providers. From the standpoint of efficiency, licenses should be awarded to those companies capable of providing the best service at the lowest cost. Since these companies are likely to earn the greatest profits, they should also place the greatest value on owning a license. Thus, the problem facing the FCC is similar to that of the arbiter in the dispute over the heirloom. Initially, administrative hearings were convened to identify the companies most deserving of the licenses. When this process became too cumbersome, lotteries were instituted. Since entry was free and open to the public, these lotteries attracted many non-serious applicants giving rise the type of problems already discussed with respect to random assignment. The economically sensible solution came in 1994 with the implementation of an auction mechanism that awarded each license to the highest bidder with the added feature of permitting companies to bid on multiple licenses simultaneously. By allowing companies to bid on several licenses at once, the simultaneous ascending auction made it possible for companies to take advantage of cost savings incurred when providing cellular service to Tacoma is cheaper for someone also providing service to Seattle. These auctions have allocated licenses faster than ever before while raising millions for the federal government. And who did the FCC consult to design such auctions? Why mathematical economists of course.

Migrant-Induced Migraines

2006-04-25T01:08:00.000-04:00

As if the issue of immigration weren't complicated enough, emotionally-charged appeals of politicians and pundits make the prospect of sensible discussion all the more grim. One of the more inane appeals--espoused by the political far-right--argues that anyone who has entered the country without going through the prescribed channels has broken the law and should thus be deported. But as a democratic society, we write the law and in doing so we define what is legal and what is not. So if we the people determine that the 11 million or so illegal immigrants should be here inasmuch as their presence benefits society, it does us no good to deport them for breaking a law that had not served our interest as citizens. This rational proposition harkens back to the lessons of the Greek tragedy Antigone. Sure Antigone had broken the law in burying her treasonous brother, but is one not obligated to confront a law one deems unjust? Before answering that question, one must first establish what makes a law "just." As an economist, my criterion of choice is efficiency. Applying efficiency to the issue of immigration requires us to structure the law in such a way so as to do the most good for the most people, where the people at issue are the current population of American citizens.

Defining the Policy Problem

U.S. immigration policy can be thought of as a mechanism, comprised of various organizations, serving simultaneously to identify who should be permitted to enter the country and to establish an incentive/deterrence system that insures only those people do enter. The U.S. Citizenship and Immigration Services (USCIS, formerly Immigration and Nationalization Services) processes petitions for various forms of residence, while Border Patrol guards do what their title suggests. It is crucial to realize that neither role can be thought of in isolation. For instance, suppose it were agreed upon that the U.S. would be better off without Mexican immigrants. If preventing all Mexicans from crossing the border illegally required a wall costing $70 billion to construct, we would be better served by allowing a few to come across as long as the cost to American citizens of them doing so did not exceed $70 billion. This simple example illustrates the need--from the standpoint of efficiency--to consider the feasibility of deterring those deemed less worthy of immigrating.

Those most worthy of immigrating--from the standpoint of efficiency--are those who contribute the most to society whether viewed from an economic, cultural, intellectual, or technological standpoint. Existing immigration laws have generally succeeded in granting entry to those with exceptional skills for work-related purposes. Examples include professional athletes, world-class artists and musicians, academics, and researchers in high-tech fields. In these cases, the prospective resident or her employer must demonstrate a unique skill possessed by the foreign person not found within the domestic workforce. Demonstrating value is much more difficult in the case of low-skilled workers, typically from Mexico and central America, whose productive ability is easier to substitute from within. But ease of substitution does not make the work done by migrants any less valuable. A reliable supply of food, for instance, is more vital to the country than professional sports, but a well-known athlete like Maria Sharapova can much more easily gain resident status than a tomato grower from Guatemala.

Some Pros and Cons of Migrant Workers

It is generally agreed amongst economists that migrant workers contribute positively to the economic well-being of the United States. This would be the case whether or not they are willing to work for lower wages than domestic workers. The reason is, an employer will never pay a worker more than the price he can get for the worker's output. And the price a consumer is willing to pay for that output will never be more than the value to her of consuming it. Thus the employment of additional workers necessarily creates value for consumers. Labor leaders, seeking to limit immigration, counter that the willingness of immigrants to work for lower wages hurts employment prospects and suppresses wages for domestic workers. But to the extent that domestic labor is hurt, the gains to society, to be discussed, necessarily outweigh the losses of those hurt by foreign competition. Following the argument of the labor leaders to its logical conclusion, if an influx of foreign labor drives down domestic wages, it will reduce the cost of producing goods affected by the wage decrease. If output levels remain constant after the wage decrease, the losses to domestic labor will exactly be offset by gains to consumers in the form of lower prices and to business owners in the form of greater profits. But lower production costs allow firms to expand output and serve a broader market, creating gains in excess of the losses incurred by domestic laborers. In addition, income earned by migrant workers increases demand for products and services--some domestic--thus creating employment opportunities for those displaced. These are all benefits we would expect from an increased supply of any resource, low-skilled labor being one such resource. Given that the economic gains from immigration exceed the losses, our goal should be the distribution of gains to those hurt by it, not--as labor leaders would argue--preventing such gains from accruing by restricting immigration.

Of course the effects of immigration extend beyond the labor market and beyond markets for goods and services. Critics argue that migrant workers place additional strain on the provision of publicly provided goods and services such as schools, hospitals, roads, and the police force while they fail to contribute their fair share. Though such arguments are not without merit, it should be noted that immigrants who avoid paying income taxes must still pay sales tax on products they purchase and property tax either directly as owners or indirectly as renters. They are also less likely, ceteris paribus, to commit crimes as getting caught results in immediate deportation. And while they may exacerbate urban congestion, immigrants add to diversity and culture within their community.

Evaluating Immigration Policy

These issues are not easily reconciled. Some, like the effect of immigration on crime, job creation, and the provision of public goods, are amenable to empirical analysis at least to some extent. Others, like urban congestion and diversity, are more amorphous and largely a matter of taste. But they all must be taken into account when devising the efficient policy.

If our only concern were the economic impact, I would say the current laws have allowed for too little immigration. Since every immigrant at work creates value for the consumer of the final product, maximizing gains--to the extent it is our aim--would require granting entry to anyone coming here to work. Opening the borders would eliminate the incentive to enter the country illegally and reduce the cost of border patrol. It would presumably also solve the problem of undocumented residents as those residents currently without legal documentation could more easily obtain it without fear of deportation. Immigrants seeking work would continue to cross the border as long as the gain, in terms of increased pay, outweighed the cost--both financial and psychological--of the move. Eventually, competition for jobs will force wages down in the U.S. while a lack of competition will bid wages up in Mexico to the point where it is no longer beneficial to immigrate.

Such a neoliberal solution addresses the economic need for low-skilled labor and solves the problem of border patrol. Nevertheless, it ignores those effects external to the labor market, resulting in either too much or too little immigration. For someone concerned with the provision of public goods and/or urban congestion, the free-market approach induces too much immigration. The solution would then require continued involvement of the USCIS to limit legal immigration and Border Patrol to prevent the illegal form. Since the cost of staffing these agencies is hardly negligible, it would have to be the case that the level of immigration under the free-market approach was sufficiently costly for a more intrusive policy to be worthwhile. Conversely, for those valuing cultural diversity or believing immigration leads to a net gain in domestic jobs, the free-market approach results in too little immigration. Immigration policy would then have to concern itself with providing additional incentives to potential immigrants or employers of immigrants. Examples may include subsidies to employers or the granting of residency to the families of working immigrants. Those current seeking to extend additional rights/privileges to immigrants should be warned, however, that any privilege which reduces the incentive of an immigrant to continue working once in the U.S. may run counter to efficiency by reducing his or her economic value to society.

The article began by asking the question, "Is the current immigration policy just?" As the preceding discussion demonstrates, determining the appropriate level of immigration is a difficult task. It may be that 11 million represents too many or too few immigrants. But regardless of the number, the fact that they are here illegally represents a failure of either the USCIS to determine those worthy of entry or of Border Patrol to deter those who are not. For this reason, it is appropriate that our elected representatives address the issue. Whether or not they make immigration more or less difficult or more or less fair is a decision to be made through thoughtful discussion and deliberation, and not as is often the case, through hard-line grandstanding.

French Fried Attempt at Labor Reform

2006-03-30T11:20:00.000-05:00

One seldom encounters a movement so asinine and misguided as the recent protests in France. Over the last two weeks, somewhere between 500,000 to 1.6 million (depending on the source) students, union members, and rioters-at-large took to the streets of Paris and other cities throughout France to protest a proposed change to the laws governing labor contracts. Protests and sit-ins led to the closing of the Sorbonne, the halting of several routes of public transportation, and a few car burnings and melees. As impassioned as these idealistic responses are, they flagrantly miss the pragmatic intent of the reforms.

Employment contracts in France are currently governed by labor laws designed with the protection of employees in mind. As such, employers are constrained by guidelines that dictate when and under what conditions an employee may be terminated. Specifically, termination must be preceded by advance notification and formal justification, and be accompanied by severance pay that would be considered downright extravagant by American standards. At the same time, France has one of the highest unemployment rates in Europe at roughly 10% nationwide and over 20% for those under the age of twenty-six.

With a view toward reducing unemployment, French prime minister Dominique de Villepin has proposed a new set of labor guidelines governing the younger segment of the population. Villepin’s proposal would overhaul the existing law and allow those under the age of twenty-six to be fired from their job within the first two years of employ without formal justification and with shorter notice and reduced severance. The goal is that giving firms more autonomy over their termination policy will induce them to offer more jobs in the first place.

It is not hard to see why a French firm operating under the existing regime would hire fewer workers than a comparable American firm operating under a more flexible arrangement.* The French firm will face higher production costs as they must continue to employ someone they might otherwise have fired and by having to pay an exorbitant severance package once the firing takes place. Since the cost the employer incurs is in the number of employees and not in the number of hours worked, the French firm will carry fewer employees and work them longer hours than the American firm for a given level of output. At the same time, higher production costs translate to lower output levels as consumers demand less of the firm’s product at a higher price. Lower output requires fewer inputs, labor included.

To the extent that restrictive employment rules are to blame for the high rate of unemployment in France, easing employment rules should serve to increase hiring by firms and reduce unemployment among those covered. Of course workers under the age of twenty-six will face a more uncertain tenure, but it is not clear this is such a bad thing. If they get fired, they are back where they started, unemployed in a country with generous social insurance. This win-no-lose (as opposed to a win-win) situation cannot be considered to be any worse than the status-quo. And to the extent that someone might perceive such an environment to be worse, one always has the option of turning down any job offer.

With the economic analysis so unambiguously in favor of the new law, it is puzzling that the opposition to it has been so fervent. Of the three major parties participating in the protests--students, union members, and rioters-at-large--only the unions have something to lose when the current guidelines are relaxed. While unionized jobs are secure in the short term, firms may eventually prefer to hire younger workers subject to more flexible employment terms. Plus, unions characteristically oppose any change in employment terms decided outside of collective bargaining. With this in mind, it is likely that union leaders planted the seed of injustice in the minds of students whose festival-spirited protests attracted the more violent rioters-at-large.

The irony is, French students have little vested interest in the issue. Many university students in France will not enter the job market before the age of twenty-six. When they do, they are likely to take employment in a position with an expected tenure well in advance of two years. The new guidelines are intended to help the low-skilled suburban youth who, feeling excluded from the benefits of French citizenship, are exceedingly prone to becoming the heretofore-called “rioters-at-large.”

* I am indebted to Bob Smith for this argument.

The Ethics of Incentives

2006-03-07T01:23:00.000-05:00

Picture this: It’s a snowy December night and your flight into Syracuse just arrived over an hour late. The last shuttle to Ithaca has left and the next one won’t be along until morning. Spending the night in Syracuse is not an option due to an early morning meeting. Rather than shell out $140 for a cab ride, you call your friend Karen to ask if she can pick you up. She agrees and you offer to return the favor by taking her to dinner later in the week. You figure a dinner plus a few dollars for gas should make the trip worth her while and still cost you less than a $140 cab fare.

It’s late when Karen finally makes it to the airport. She’s groggy. To stay alert on the ride back, she cranks up a mix tape of 80s hits. The two of you rock out until the blare of a police siren jolts you back to reality. Cruising down the hill a quarter of a mile back, Karen had unwittingly exceeded the speed limit by 15 mph and is now being issued a ticket for $200. You feel terrible. After all, Karen came all this way for you; she shouldn’t pay $200 on top of it. Then again, it wasn’t your lead foot that aroused the attention of the state trooper. What to do? Should you help pay for Karen’s speeding ticket or not?

Like an episode of Dragnet, the story I have just described in true; the names have been changed to protect the innocent. The innocent are actually two friends of mine and I don’t want either of them mad at me. But the situation does bring to light an interesting dilemma; one I feel especially qualified to address. I should also mention that the involved parties did resolve the issue amicably and without dispute. So this essay is not a critique of their behavior, but merely a theoretical exercise to demonstrate what I would have done had I been in the shoes of Pamela, the passenger.

To determine who should pay the ticket, the criteria you want to account for are compensation and incentives. Karen is your friend first and foremost. And although she picked you up out of the kindness of her heart, failing to adequately compensate her could lead to ill-will. At the same time, compensating her for her speeding ticket rewards bad behavior. But was it bad behavior that led to her speeding? It was after all late--past her normal bedtime--and she likely lost focus on the speedometer due to fatigue and the distraction of the music. In her situation, you may have done the same.

The thing to recognize is, there is a proper level of care in driving such that even a driver exercising proper care may still get pulled over with some small probability. The proper level of care balances the desire to minimize the probability of getting pulled over against the desire to get home as fast as possible. If we think of care simply in terms of speed (or lack thereof), driving too slow satisfies the former desire at the expense of the latter, while driving too fast satisfies the latter at the expense of the former. The point being, you have no way of knowing whether or not Karen was exercising proper care simply by the fact that she was pulled over. All you can hope to do is provide the incentive for her to take proper care and leave the driving to her.

The compensation criteria is straightforward enough but it becomes tricky when coupled with incentives. To see this, suppose you decide to split the cost of the ticket and pay her $100. Actually, with the ticket already issued it’s too late to affect Karen’s incentives. Instead, suppose you made a deal with her ahead of time telling her that you will pay half of all tickets incurred on the trip. Under this deal, Karen is compensated for half of the penal expense of the trip. However, since she internalizes only half the cost, Karen’s incentive to exercise proper care is reduced. In this way, a tension exists between compensation and incentives. The greater is the share of the ticket you pay, the weaker is Karen’s incentive to drive the speed you would have her choose and the greater is the likelihood that you will pay out.

It should be clear that any agreement in which you give Karen more when she gets a ticket than when she doesn’t creates a perverse incentive for her to drive too fast. The solution then is to offer a fixed payment (which could involve non-pecuniary forms of compensation) independent of whether or not she gets a ticket. This way, if Karen gets a ticket and can’t expect another dime from you, she bears the full brunt of her actions. When this happens, she will take what she deems to be the proper level of care in driving.

With incentives accounted for, the payment must be large enough to compensate Karen for her time and for gas, but also for the probability and subsequent penalty of being ticketed while exercising proper care. If a dinner out and a few dollars in gas are enough cover these costs, you can feel content knowing you have done your part. If not, think about substituting something more valued like opera tickets in place of the dinner. But if the cost of fully compensating Karen exceeds $140, I would advise you to take the cab.

Lest you think this incentive-based approach too calculating to be used with those we care for, think about parenting. Parenting is rife with tradeoffs between indulging your child’s wishes and teaching them to be a good person. In “Life’s Little Instruction Book,” (Rutledge Hill Press, 1991) instruction number 88 reads, “Even if you’re financially well-to-do, have your children pay for all their automobile insurance.” Why should a child pay for her own auto insurance? Paying for auto insurance forces the child to internalize the cost of reckless driving, thus providing an additional incentive to drive carefully. The well-to-do parents are then better served to spend their money on a good car, loaded to the gills in safety features.

What Can Roman Generals Teach us About the Anti-Sweatshop Movement?

2006-02-20T19:42:00.000-05:00

We have all heard the expression, “don’t burn your bridges,” a caveat against rash behavior that can make reconciliation impossible. But to the Roman army, burning bridges or burning one’s boats was actually an effective military strategy. Though detailed historical accounts are elusive, Julius Caesar and Roman generals of the time were said to set fire to their boats during an invasion or to a bridge that could be used for retreat. By making retreat impossible, the generals intended to stiffen the resolve of their troops to conquer or be killed. This effect was not likely lost on their adversary, who fearing the must-win attitude of the mighty Roman army, would then be more likely to retreat.

To be sure, burning bridges or boats was a costly maneuver for the Roman army. Besides eliminating a critical tactical option, it made efforts of re-supplying troops a logistical nightmare. But if it led to the opposing army laying down their arms in surrender or retreating sooner than they otherwise would, such concerns would be negated.

The strategy of burning one’s bridges is one example of a commitment in the parlance of game theory. Game theory is the study of strategic interaction, using mathematical models to approximate real-world environments and predict real-world outcomes. Thomas Schelling, currently of the University of Maryland, was the first to apply the logic of game theory to the understanding of international conflict. In his 1960 book “The Strategy of Conflict,” Schelling discusses ways in which a strategic commitment—a binding promise to follow a specific course of action—can benefit the party making the commitment. With respect to the Romans, eliminating any means of retreat forced a difficult decision on the adversary: retreat or face a bloody battle. If the battle appeared unwinable for the adversary, their best response would be retreat and avoid a pointless battle. In that case, the commitment to battle by the Romans obviated the need for such a battle, much to their benefit.

Schelling was honored with the Nobel Prize for his work on “The Strategy of Conflict” due in large part to the applicability of his ideas to other economic settings, like boycotts. A movement is currently underway at Cornell University, my academic home, to convince the administration to join the Designated Suppliers Program (DSP), a consortium of universities advocating fair labor standards. The program, devised by Worker Rights Consortium (WRC), will require producers of all officially licensed apparel of member schools to demonstrate compliance with internationally recognized labor standards, allow workers to be represented by a union, and pay a living wage.

The global anti-sweatshop movement, of which the WRC is one component, is predicated on the notion that working conditions in sweatshops are inhumane. Having spent a summer in college painting houses outdoors, I can honestly say there is nothing inhumane about sweating on the job. The trouble with sweatshops is low pay and working conditions that are unhealthy and often unsafe. My earlier piece on coal mine safety argued that working conditions and pay are really two sides of the same coin, since workers in unpleasant jobs are paid more than comparable workers in more pleasant jobs. For this reason, we can boil down the demands of the anti-sweatshop movement to a call for higher wages, whether in the form of higher pay, better working conditions, or some combination of the two. In an effort to have its demand met, groups of anti-sweatshop consumers typically threaten to boycott the heartless manufacturer. However, the analysis presented herein will show that unless the consumer group can commit itself in advance to undertaking the boycott, the threat alone will fail to deter the manufacturer from its calculating behavior.

To analyze the interaction between a consortium of anti-sweatshop consumers and a manufacturer, we must utilize the tools of game theory. This involves first defining possible actions for each player and the payoffs to each potential outcome. The game involves two players, the consortium and the manufacturer. The consortium can boycott or continue to do nothing at all while the manufacturer can maintain its current level of low wages or pay its workers a living wage. The consortium gains some amount L if successful in convincing the manufacturer to pay a living wage. However, by resorting to a boycott, they incur a cost B, a result of either buying from a less-preferred manufacturer or not buying the product at all. The manufacturer loses some amount R in lost revenue from the boycott. To appease the consortium, it may decide to pay a living wage, which increases its production cost by some amount C. The payoffs are represented in the game tree found by following this link: see the game tree.

Predicting the outcome of the game requires an assumption that each player in turn chooses the best strategy for itself given the strategy of its opponent. Since the manufacturer acts first, we work backward by considering the best strategy for the consortium following each of the possible strategies for the manufacturer.

Suppose the manufacturer chooses to pay a living wage. The consortium can then boycott and receive a payoff of L-B or do nothing and receive L. Since L is greater than L-B, the consortium will choose to do nothing in the event the manufacturer raises wages.

Now suppose the manufacturer chooses to keep wages low. The consortium can either boycott yielding a payoff of –R or do nothing yielding a payoff of 0—the status quo payoff. Since 0 is greater than –R, the consortium will choose to do nothing in the event the manufacturer keeps wages low.

The upshot is, regardless of what the manufacturer chooses, the consortium is better off doing nothing than boycotting. Since the manufacturer’s decision has already been made, it does the consortium no good to boycott. The threat to boycott in this setting is nothing more than cheap talk.

This result is taken into account by the manufacturer when making its decision. Since it knows the consortium will do nothing, the manufacturer can either pay a living wage which yields a payoff of –C or keep wages low which yields a payoff of 0. Since 0 is greater than –C, the manufacturer chooses to keep wages low.

From what we have seen thus far, it would seem as though the threat to boycott cannot be effective at inducing change as it will necessarily be viewed as empty. But if the consortium of concerned consumers can take a page from the Roman’s playbook and commit to the boycott in advance of the manufacturer’s decision, their threat can no longer be ignored. Such a commitment can take the form of a written agreement like the one required of DSP members. More commonly though, commitments take the form of allegiance to specific standards of human rights that an ideologically driven organization can stake its name to.

Focusing again on the game at hand, suppose the consortium commits itself to the following strategy: do nothing if the manufacturer raises wages, boycott if it doesn’t. Since the consortium’s strategy has already been determined in advance, the manufacturer chooses between keeping wages low and facing a boycott or raising wages and avoiding it. What it chooses depends on which is greater, the lost revenue from a boycott or the cost of paying its workers a living wage. Thus if the consortium makes up a sufficiently large component of the manufacturer’s customer base, it can force the manufacturer to raise wages since doing so would be less costly than a boycott. Of course if the consortium is not large enough to do so, it would be foolish to commit to such a strategy.

We have thus far used a simple mathematical model to analyze two scenarios that depend upon whether the consortium can commit itself to a boycott. But in neither case does a boycott actually take place. Since we do observe boycotts in reality, it must be that the mathematical model does not adequately describe reality, right?

Actually, the mathematical model can account for boycotts only when one player knows something that the other doesn’t. To see this, consider a consortium whose membership is so zealous that they actually enjoy boycotting if it means standing up for a righteous cause. Unlike the type of consortium considered previously, this group will choose to boycott if the manufacturer fails to raise wages, and will do so without the need to commit to the course of action. Realizing this, the manufacturer will choose to raise wages as long as the potential loss of revenue exceeds the increase in wage cost and once again the boycott is averted. But if the manufacturer doesn’t know whether the consortium it is dealing with is the type considered previously or the type that enjoys boycotting, it will keep wages low until it observes people actually boycotting. In this way, the boycott signals to the manufacturer that they are indeed the type of consumers who enjoy boycotting and will do so until their demands are met.

Development economists tend to view sweatshops as a symptom and not the cause of abject poverty in the developing world. If Nike’s workers are there by choice, what does that say about alternative employment options? They must be pretty awful. For this reason, development economists tend to prefer measures aimed at improving overall economic welfare not just the welfare of those employed by large American corporations.

Lacking the funds, know-how, or foresight necessary to solve the larger development problem, organizations like the Workers Rights Consortium target American employers in the developing world through threats of boycott. A boycott or threat of one can be effective only if the cost to the employer through lower revenue exceeds the cost of increasing wages. But that is not sufficient. Just as Roman generals committed themselves so thoroughly to conquest by eliminating the option of retreat, so too must anti-sweatshop organizations commit themselves to boycott if they are to be successful.

Landsburg's Internet-Popcorn Paradox

2006-02-03T01:13:00.000-05:00

One of my life’s greatest joys is surfing over to Slate.com and finding a new piece by Steven Landsburg. Landsburg is the Armchair Economist. His regular contributions to Slate explore the hidden economics in day-to-day activities. His latest explains why some hotels charge extra for internet access and others don’t, then leaves the reader with an unsolved puzzle. (See the link to view the article: http://www.slate.com/id/2135226/ . I assume in what follows that the reader has read the article.)

The puzzle identified by Landsburg is as follows: Some hotels charge extra for internet access while others include internet access in the price of the room. This makes sense as hotels with different types of clientele will want to charge differently for internet access. But movie theatres differ in their clientele just as much as hotels do, but seemingly all movie theatres charge separately (and exorbitantly) for popcorn. The question is, what makes hotels and movie theatres so different?

The issue Landsburg analyzes belongs to the economic literature on product bundling, where bundling refers to the practice of pricing two goods as if they were one product. Like the literature, Landsburg shows that there exists conditions under which bundling is profitable and under which it is not. One condition he doesn’t address is that of cost. According to the literature, the strategy of bundling is less likely to be profitable when the bundled good is sold to buyers whose willingness to pay for the add-on is less than the marginal cost. To see why, let’s stay with the hotel example but say the add-on is towel service rather than internet access. Suppose the hotel is charging $120 per night for the bundled good, but many of its guests stay only one night and are not willing to pay anything for towel service though they will pay $120 for the room. By charging separately for towel service, the hotel can continue to charge these people $120 for the room alone, while saving money by not hiring as many chamber maids. This is not an issue as far as internet access is concerned as the marginal cost of internet access is zero—not so for movie theatre popcorn. The lesson for the movie theatre is, if the marginal cost of popcorn is substantial enough, selling the popcorn separately is more profitable than bundling it with the movie ticket regardless of demand conditions.

This explains why bundling may be profitable for a hotel but never for a movie theatre. But why then does my local pub offer popcorn for free, implicitly bundling the popcorn with the beer? For one thing, popcorn and beer are complementary goods so the money lost on popcorn is more than made up for on additional beer sales. But there is also a cost difference between offering free popcorn in a pub and doing so in a movie theatre. Can you guess what it is? I’ll give you a hint: it involves a teenage boy and a broom. That’s right, the difference is in the cleanup cost. Movie theatre popcorn must be swept up after each showing, while pub popcorn is swept up at most once a night. Plus, the popcorn at the pub is self-serve, so you don’t bother getting it unless you plan on eating it. At the theatre, the popcorn is served to you on the way in. And any popcorn served to someone who values it little is likely to end up on the floor. The upshot is, the cost of serving free popcorn in a movie theatre may be substantial enough to preclude bundling when you take into account the clean-up cost.

I have to say I’m not completely happy with this answer. I would have preferred an explanation relying more on game theory, but that’s what I came up with and it does seem to fit. Please post a comment if you think I’ve missed something.

Backward Looking Coal Legislation Serves the Wrong Constituency

2006-01-30T23:36:00.000-05:00

Following the death of 14 coal miners in two separate incidents in West Virginia this month, on January 26^th governor Joe Manchin signed a set of new mine safety rules into law. The new rules, passed unanimously through the state legislature, call for wireless communication and tracking devices to be carried by miners. They also call for additional stores of oxygen in mines and for the establishment of a statewide 24-hour accident response team. Had they been available, these measures may have aided the rescue of the recent victims. But for those West Virginians still employed in the coal industry, the new law may pose more harm than good--hurting the very people it is intended to protect.

Though obviously an emotionally-charged topic, worker safety must be evaluated from a pragmatic standpoint. An economic model is useful here. Consider a young man in a coal mining state who can decide between a high risk job like coal mining and a (relatively) low risk job like say auto repair. Due to the higher risk of injury and death in coal mining, he will choose mining only if he is sufficiently compensated for assuming the additional risk. Economists call this increase in pay a “compensating differential.” Operating in a competitive labor market, the coal company is obligated to pay a compensating differential to attract workers to its operation. Since higher risk implies higher wages, the firm internalizes the risk faced by its employees in its attempt to minimize labor costs.

This provides the proper incentive to lower risk through various safety measures. As additional safety measures are undertaken, the compensating differential and hence the total wage bill declines. The level of risk is reduced to the point at which the additional cost of safety is exactly equal to the saving in labor costs. At this point, the added benefit to the miners of any further safety measures would be offset by an even larger increase in the cost of providing such measures. The resulting level of safety is efficient: from a purely utilitarian standpoint, the net of benefits and costs of safety provision are maximized. The efficient level of safety is the level that the employees themselves would choose if they were charged with the decision of how much safety to provide and had to bear the cost.

Compensating differentials, however, may fail to promote the efficient level of safety under certain market imperfections. An imperfection exists if the mining company does not operate in a competitive labor market. This was likely the case in decades past when geographic mobility was limited and working in the mine was the only job available. Another impediment to an efficient market is a lack of information on the part of coal minors as to the risky-ness of their job. In either case, the mining company can lower wages and reduce safety relative to the efficient level and still recruit the necessary workforce.

Though not likely established explicitly for this purpose, workers compensation (WC) insurance can correct for such inefficiencies. WC collects funds from employers and pays damages to workers injured at work and to survivors of those killed. The premium paid by the employer is “experience rated,” so its magnitude depends upon the risky-ness of the work as measured by on-the-job injuries. Thus, WC improves information as all injuries must be reported to the insurer. Furthermore, it forces the employer to once again internalize worker risk in the form of higher premiums. Under WC, compensating differentials are smaller as the risk of employment is (at least partially) offset by insurance payments for damages. But the incentive exists for the employer to provide safety closer to the efficient level even in the presense of market imperfections.

If the coal companies internalize the benefits of greater safety through lower WC premiums and smaller compensating differentials, then why hadn’t they already adopted the measures mandated by the recent legislation? Because the costs would have exceeded the gains. A record low 22 American coal minors died on the job last year. While this may seem like a large number, the fact that it was an all-time low suggests that the most cost-effective safety measures have already been adopted. According to various news reports, industry experts question whether the wireless communication mandated by the new rules is even feasible. And it is not yet clear where the funds for the 24-hour rescue service will come from. What we do know, is that these additional measures will increase costs for the coal companies and any resultant reduction in risk will be accompanied by a decline in wages.

The passage of the law by the legislature indicates its preference for lower risk and lower wages. But the victims themselves understood the risks and chose to work in the mines instead of in a lower-paying, less dangerous job. Had they known such a tragedy would befall them, they would never have gone down the mine in the first place. The fact that they did indicates their willingness to incur some risk. We will never know whether or not the new safety measures would have saved their lives. But by increasing costs for coal companies and by transfering income from coal miners to the providers of safety, the new measures are certain to save lives in the future because fewer and fewer men will find employment as miners. If the legislation is intended to help miners, it would make sense to have consulted them. Had they done so, I doubt that the endorsement of the bill would have been unanimous.

Lessons in Oil Reserves from an Ancient Greek

2006-01-24T17:52:00.000-05:00

With gas prices rising, Americans are more than ever questioning our dependence on oil. Beside rising costs, the worry is that current demand is unsustainable, oil reserves will soon be depleted, and the American standard of living will be eroded for all future generations. I am happy to put those worries to rest: the depletion our supply of oil is inevitable so long as we continue to rely on it. And I have the wisdom of over 2,000 years to back me up.

The Greek philosopher Zeno (circa 450 B.C.) formulated a famous paradox who’s solution can shed light on the situation. Zeno’s paradox can be paraphrased as follows: Suppose I want to cross a room of length D. In order to get across, I must first travel half the distance. But before reaching half the distance, I must first travel half of that distance. And before getting there, I must travel half of that distance and so on until I can’t actually go anywhere since doing so would involve an infinite number of intermediate steps. This logic calls into the question the very possibility of motion.

Since we know motion is possible, we resolve Zeno’s paradox by noticing the following. Suppose I could walk half the original distance, which would be ½D. I could then walk half the remaining distance, ¼D, again half the remaining distance, 1/8D, and so on. Continuing in this manner, how far would I eventually walk? Adding up all my individual steps gives us ½D+ ¼D + 1/8D +… or [ ½ + ¼ + 1/8 +...]D. The term inside the brackets is the well-known geometric series, the sum of which is simply: G(r)=r+r²+r³+…=r/(1-r) for any fraction r. Letting r= ½, we have G(r)=1. This is remarkable: not only is the sum of an infinite number of increments a finite number, but by taking smaller and smaller steps we can eventually get to our destination having traveled the entire distance D. Any bewilderment should be relieved by realizing that any finite distance, broken up into an infinite number of small parts, must have the small parts add up to the original distance. Zeno’s paradox is resolved by understanding that while the number of intermediate steps is infinite, they must still add up to something finite. So motion is possible—good news for commuters.

So what does this have to do with oil reserves? Suppose D is the existing supply of some natural resource, say oil. And suppose we are given the job of determining a rate of extraction so that we will always have some oil left over for future generations. Assume that the resource is non-renewable, so once we extract D, there is none left. But to extract D, we must extract half of D. And to extract half of D, we must first extract half of that and so on. From Zeno’s paradox, we know that continuing in this manner, we will eventually extract all of our oil reserves and there will be no more. Fearing this, we may want to reduce our rate of extraction. If we consume say 1/3 of our original stock, then 1/3 of the remaining stock and so forth, we can insure that there is always some amount left over, right? Wrong. As it turns out, any manner in which we extract a constant fraction of our available reserves ultimately result in the complete depletion of the resource. To see this, suppose we decide to extract some fraction r of our existing reserve in every year. In year 1, we will extract rD, leaving D-rD=(1-r)D in reserve for year 2. In year 2, we extract fraction r of our existing reserve (1-r)D for a total extraction r(1-r)D, leaving (1-r)D-r(1-r)D =(1-r)²D for year 3. Continuing in this manner, we will extract r(1-r)^t-1D in any given year t. Summing our per-year extraction over all years, we will eventually extract [1+(1-r)+(1-r)²+(1-r)³+…]rD total. The term in brackets is 1+G(1-r)=1+(1-r)/r=1/r. Thus, our total resource extraction will be [1/r]rD=D, and we use up all of our resource regardless of the rate at which we extract it! The same principle that guarantees you will eventually make it to work in rush hour traffic guarantees that someone in the future will run out of gas and never make it.

With regard to the current discussion over oil consumption, the issue is not whether oil reserves will eventually be depleted but when. The when should be determined by balancing the benefits of current consumption with such benefits in the future while taking into account the possible development of alternative energy sources. Since consumption decisions are made on the level of the individual consumer and producer, any reduction in oil consumption would require intervention by a central authority possibly through the imposition of a tax. A tax would serve to raise the price of gas and of any product produced using oil, reducing consumption of these products and indirectly of oil itself, but in doing so lower our standard of living. The development of an alternative energy source that rendered oil useless would stop the process of depletion resulting in left-over reserves without the need to cut back consumption. Of course the remaining oil would have no value by virtue of having been rendered useless.

So I went to a lot of trouble to prove something obvious. At least the math was fun.