WHAT is economics concerned with? A layman taking in the raging debates over financial stability, inflation, economic growth, and budget deficits, would say it’s about money. That, of course, is not right. Money matters only insofar as it is a proxy for welfare. Money is a handy way of denominating prices and economists love prices because they are so efficient at allocating supply and demand so as to maximise welfare. Yet markets do not have to have money or prices to serve that welfare-maximising function. That distinction lies at the heart of the work that won this year’s Nobel Prize in economics, the subject of this week’s Free Exchange column.

Lloyd Shapley of UCLA and Alvin Roth of Stanford University got the prize for studying the barriers to welfare maximisation in markets without prices: examples including matching college applicants to colleges, kidney donors to recipients, and even husbands to wives. Mr Shapley and David Gale (now deceased) devised an algorithm 50 years ago that would maximise the satisfaction of such multi-sided matching games. Read the column to learn more about how the theory works and its applications. I want to focus here on a more philosophical implication of their work.

Mr Gale’s and Mr Shapley’s seminal 1962 paper was somewhat whimsical. Imagine a man, John, in love with a woman, Mary, but Mary is married to someone else. So John marries someone else as well. What if a year later he discovers Mary really does love him? Odds are they will find a way to be together, but it may involve infidelity, divorce and scandal (Prince Charles and Camilla can relate). On the other hand, if Mary really loves her husband more than John, both marriages will endure. Mr Gale and Mr Shapley devised an algorithm that would match partners in a way to minimise the number of unstable marriages and maximise the number of stable ones.

Mr Gale and Mr Shapley acknowledged that their marriage-matching algorithm had “entered the world of mathematical make believe.” But they went on to make a larger point:

Our result provides a handy counterexample to some of the stereotypes which nonmathematicians believe mathematics to be concerned with. Most mathematicians at one time or another have probably found themselves in the position of trying to refute the notion that they are people with ‘a head for figures’ or that they ‘know a lot of formulas’. At such times it may be convenient to have an illustration at hand to show that mathematics need not be concerned with figures … [our theorem] is carried out not in mathematical symbols but in ordinary English; there are no obscure or technical terms. Knowledge of calculus is not presupposed. In fact, one hardly needs to know how to count. Yet any mathematician will immediately recognize the argument as mathematical, while people without mathematical training will probably find difficulty in following the argument, though not because of unfamiliarity with the subject matter. What, then to raise the old question, is mathematics? The answer, it appears, is that any argument which is carried out with sufficient precision is mathematical, and the reason that your friends and ours cannot understand mathematics is not because they have no head for figures, but because they are unable to achieve the degree of concentration required to follow a moderately involved sequence of inferences.

In a similar way, Mr Shapley’s and Mr Roth’s Nobel prize illustrates a larger point about economics. Undergraduates often study “utility functions” to learn how people choose alternative consumption baskets in a way that makes them better off. Once they go on to graduate school and then a job, they deal almost exclusively with priced transactions: for wheat, autos or equities.

Yet in countless private and public policy questions, welfare can be improved in ways that do not show up in the price. Mr Roth’s work on public school admissions and kidney donations are an obvious example, but there are countless others. I recall reading that Starbucks had a plan that would let an employee in one store trade jobs with an employee in another so that both could work closer to home. The result would not change either employee’s output or wages, or Starbucks’ profits. Conceivably GDP would fall because the employees would spend less on petrol or bus fare. But provided the swap was voluntary, the welfare of both would without question rise.

During election season, presidential candidates invariably defend their policies in terms of dollars or jobs: Barack Obama’s health care plan will save a family so much on insurance; his green energy investments will create so many jobs. Mitt Romney’s voucher plan will reduce Medicare’s costs. Yet some of the greatest welfare impacts of these policies can’t be priced. Obamacare eliminates much of the anxiety that hangs over every uninsured worker who worries about a financially crippling disease or injury. That surely must raise welfare. The energy efficiency standards imposed on makers of automobiles, appliances, toilets and light bulbs may save consumers’ money, but deprive them of choice: if you want a faster but less efficient dishwasher, you can’t buy one anymore. That is a loss of welfare that is not incorporated in regulators’ cost-benefit analysis. Nick Rowe once beautifully illustrated the flaw in the theory that public works projects, no matter how useless (such as digging holes and filling them in) were an effective form of stimulus in a liqudity trap. Truly useless projects may raise GDP, he noted, but they did not raise welfare, so the government may as well just hand the cash over to the workers.

WHAT is economics concerned with? A layman taking in the raging debates over financial stability, inflation, economic growth, and budget deficits, would say it’s about money. That, of course, is not right. Money matters only insofar as it is a proxy for welfare. Money is a handy way of denominating prices and economists love prices because they are so efficient at allocating supply and demand so as to maximise welfare. Yet markets do not have to have money or prices to serve that welfare-maximising function. That distinction lies at the heart of the work that won this year’s Nobel Prize in economics, the subject of this week’s Free Exchange column.

Lloyd Shapley of UCLA and Alvin Roth of Stanford University got the prize for studying the barriers to welfare maximisation in markets without prices: examples including matching college applicants to colleges, kidney donors to recipients, and even husbands to wives. Mr Shapley and David Gale (now deceased) devised an algorithm 50 years ago that would maximise the satisfaction of such multi-sided matching games. Read the column to learn more about how the theory works and its applications. I want to focus here on a more philosophical implication of their work.

Mr Gale’s and Mr Shapley’s seminal 1962 paper was somewhat whimsical. Imagine a man, John, in love with a woman, Mary, but Mary is married to someone else. So John marries someone else as well. What if a year later he discovers Mary really does love him? Odds are they will find a way to be together, but it may involve infidelity, divorce and scandal (Prince Charles and Camilla can relate). On the other hand, if Mary really loves her husband more than John, both marriages will endure. Mr Gale and Mr Shapley devised an algorithm that would match partners in a way to minimise the number of unstable marriages and maximise the number of stable ones.

Mr Gale and Mr Shapley acknowledged that their marriage-matching algorithm had “entered the world of mathematical make believe.” But they went on to make a larger point:

Our result provides a handy counterexample to some of the stereotypes which nonmathematicians believe mathematics to be concerned with. Most mathematicians at one time or another have probably found themselves in the position of trying to refute the notion that they are people with ‘a head for figures’ or that they ‘know a lot of formulas’. At such times it may be convenient to have an illustration at hand to show that mathematics need not be concerned with figures … [our theorem] is carried out not in mathematical symbols but in ordinary English; there are no obscure or technical terms. Knowledge of calculus is not presupposed. In fact, one hardly needs to know how to count. Yet any mathematician will immediately recognize the argument as mathematical, while people without mathematical training will probably find difficulty in following the argument, though not because of unfamiliarity with the subject matter. What, then to raise the old question, is mathematics? The answer, it appears, is that any argument which is carried out with sufficient precision is mathematical, and the reason that your friends and ours cannot understand mathematics is not because they have no head for figures, but because they are unable to achieve the degree of concentration required to follow a moderately involved sequence of inferences.

In a similar way, Mr Shapley’s and Mr Roth’s Nobel prize illustrates a larger point about economics. Undergraduates often study “utility functions” to learn how people choose alternative consumption baskets in a way that makes them better off. Once they go on to graduate school and then a job, they deal almost exclusively with priced transactions: for wheat, autos or equities.

Yet in countless private and public policy questions, welfare can be improved in ways that do not show up in the price. Mr Roth’s work on public school admissions and kidney donations are an obvious example, but there are countless others. I recall reading that Starbucks had a plan that would let an employee in one store trade jobs with an employee in another so that both could work closer to home. The result would not change either employee’s output or wages, or Starbucks’ profits. Conceivably GDP would fall because the employees would spend less on petrol or bus fare. But provided the swap was voluntary, the welfare of both would without question rise.

During election season, presidential candidates invariably defend their policies in terms of dollars or jobs: Barack Obama’s health care plan will save a family so much on insurance; his green energy investments will create so many jobs. Mitt Romney’s voucher plan will reduce Medicare’s costs. Yet some of the greatest welfare impacts of these policies can’t be priced. Obamacare eliminates much of the anxiety that hangs over every uninsured worker who worries about a financially crippling disease or injury. That surely must raise welfare. The energy efficiency standards imposed on makers of automobiles, appliances, toilets and light bulbs may save consumers’ money, but deprive them of choice: if you want a faster but less efficient dishwasher, you can’t buy one anymore. That is a loss of welfare that is not incorporated in regulators’ cost-benefit analysis. Nick Rowe once beautifully illustrated the flaw in the theory that public works projects, no matter how useless (such as digging holes and filling them in) were an effective form of stimulus in a liqudity trap. Truly useless projects may raise GDP, he noted, but they did not raise welfare, so the government may as well just hand the cash over to the workers.

Contrary to the claims of Mr Romney and Paul Ryan, vouchers won’t solve Medicare’s long-term cost problem. Experience suggests the introduction of competition has only a transitory impact on health cost growth. Yet vouchers offer Medicare beneficiaries something they don’t have now: choice. By letting them allocate their Medicare dollars to an insurance plan that better suits their idiosyncratic preferences, they can achieve a higher welfare than if the same money were spent on the same plan everyone gets. (Note that proviso: the *same* money. If the voucher is worth less than the money they would have otherwise spent, the impact on welfare is ambiguous.) The value of that choice is not easily quantified, but it is real. It may not be obvious to presidential candidates, but that’s why we have economists.

Contrary to the claims of Mr Romney and Paul Ryan, vouchers won’t solve Medicare’s long-term cost problem. Experience suggests the introduction of competition has only a transitory impact on health cost growth. Yet vouchers offer Medicare beneficiaries something they don’t have now: choice. By letting them allocate their Medicare dollars to an insurance plan that better suits their idiosyncratic preferences, they can achieve a higher welfare than if the same money were spent on the same plan everyone gets. (Note that proviso: the *same* money. If the voucher is worth less than the money they would have otherwise spent, the impact on welfare is ambiguous.) The value of that choice is not easily quantified, but it is real. It may not be obvious to presidential candidates, but that’s why we have economists.