Arthur Laffer's Wedge Model
Jude Wanniski
October 17, 1997


Supply-Side University Economics Lesson #6

Memo To: Website Students of SSU
From: Jude Wanniski
Re: Arthur Laffer’s Wedge Model

Today’s lesson is meant to create in your minds some simple pictures of the way the world works, which I have found is the best way to make lessons “stick” with me. Lesson #3 was devoted to one such picture, the Laffer Curve, which I named for Art Laffer after I watched him draw it on a cocktail napkin in 1974. It is merely the law of diminishing returns applied to tax policy, which means it is an eternal verity and can not be successfully disputed. In those days, Laffer also developed what he called his “wedge model,” which gives us a picture that helps in the further understanding of Say’s Law, Lesson #4. In addition, over the years I have played with other pictures that have helped me use these concepts for analytical purposes. If you can’t simplify a concept in political economy, so ordinary people can understand what you are talking about, I don’t think you can be sure you have developed a meaningful idea. Much of what passes as macroeconomics today is “proven” by elegant mathematical models that flow from assumptions that have minor or even serious flaws. The students who are sent into the world with such learning will always be at a disadvantage, especially if they intend to work in a fast-paced segment of the financial-services industry -- where money can be made or lost very quickly. The two new Nobel Prize winners in economics, Myron Scholes and Robert Merton, actually did their work on pricing “risk” in what amounts to a supply-side model. Their colleague, the late Fischer Black, was a friend and associate of both Art Laffer and Robert Mundell, when they were at the University of Chicago. The fact that Scholes and Merton not only developed a new concept, but also used it to start a Wall Street firm that is extremely successful, assures us that their mathematics flows from a sound assumption about the way the world works.

* * * * *

The “wedge” in the wedge model should be pictured as a government wedge that is used to come between two potential transactors. As Laffer developed it, he discussed the wedge between an employer and an employee, between management and labor. The worker gets paid $12.50 per hour or $500 per week, but because the federal, state and local governments take a variety of income and payroll taxes out of the wage, the worker sees a net of only $380, or $9.50 an hour. The $120 per week difference is the wedge. The worker is doing $500 worth of work, but getting only $380 for his labors, and has a tendency to offer less labor as the wedge increases. With a progressive income tax, the worker may be offered time-and-a-half for an extra hour’s work, but because the extra hour is taxed at a higher progressive rate, the worker will get something less than time-and-a-half. The wedge became particularly onerous in the rapid inflationary years of the 1970s, as inflation drove workers into higher tax brackets with no increase in purchasing power. In 1965, a carpenter was paid $3.12 per hour or $125 per week or $6,500 per year. After all payroll taxes, including Social Security, the net was roughly $118 per week if he had a wife and two children. Each member of the family was given a $500 deduction from gross pay, which meant taxable income was $4,500 per year or $86 per week. At the time, the employer matched the worker’s Social Security contribution and also paid health and welfare benefits, which the employer could deduct from the company’s taxable income. If these combined added to 25 cents an hour, over a year the employer would be paying another $500 or $7,000 total for the worker’s work. The government’s take of $7 per week would be $364 over the year or 5.2% of the total.

After 30 years of inflation, the carpenter has been forced into ever higher tax brackets. Today, even after the Reagan tax cuts and protection of income tax against inflation, the carpenter receives a gross pay of $25 per hour -- $1,000 per week, $52,000 per year. In addition, he has negotiated higher health and welfare benefits with his employer of $3 per hour. That comes as a cost of doing business, and therefore, is not taxable on either side, and the cost of Social Security has gone up to the employer by $2 an hour. Together, that’s another $10,400 per year. The carpenter not only has moved into a higher tax bracket because of inflation, but the value of his family deductions, at $1000 each, has not kept up with inflation. He has taxable income of $48,000 after the $4,000 is deducted. After various other allowances, his net would be roughly $36,000 -- in a state with an income tax. The employer is paying $62,400 for the carpentry and the carpenter is getting $36,000, plus the health and pension benefits covered by his employer, or $46,400. The wedge is $16,000 or just above 25% of the total, compared to 5.2% thirty years ago.

One more calculation has to be made to show the dynamics at work as the 30-year inflation has worked to erode the efficiency of the national economy. In 1965, the price of gold was $35 an ounce. Over the course of the year, the carpenter had 190 ounces of gold that he could spend. Today, with gold at $325 an ounce, in a year, the carpenter has 111 ounces of gold to spend. He is getting some extra health insurance benefits as a result of shifting those costs from his household to his employer, who can deduct them from taxable income. But the difference shows why the carpenter’s wife has to work at least a part-time job to make ends meet as they did in 1965. There will be quibbles that gold is not as good a measure of purchasing power as the government statistics, which show the carpenter and his family are not as far behind as gold says they are. We have covered that point broadly in earlier lessons and will tackle it in detail in a future lesson. The observable fact, though, is that it is much harder for a breadwinner to support a family of four today than it was 30 years ago. Laffer’s wedge partly explains why.

* * * * *

In The Way the World Works, I used Smith and Jones as the transactors when the deal is domestic. When it is across international boundaries, I use Schmidt as the foreigner and Jones as the American. Smith makes bread and Jones makes wine, and they would like to trade one loaf for the one bottle. The government needs to get a piece of the transaction in order to finance itself -- some part of the bread, some part of the wine. A tax wedge is introduced. If the tax wedge is increased to a point where Smith and Jones decide the trade no longer makes sense, because the government will wind up with most of the bread and most of the wine, they leave the market and the government gets nothing. That’s the simple wedge model.

Suppose the government gets its small tax wedge in the door, and now decides to add regulations to the transaction: The bread can only be made of this and that, and so must the wine, and the people who help Smith and Jones make the bread and the wine must be treated this way and that, and paid at least so much, which will also be taxed by the government. The wedge then can also increase to the point where there is no trade and the government gets nothing, even though on the surface the government’s initial tax seems reasonable. For analytical purposes, the wedge model reminds us of the myriad burdens that government can put on a potential transaction to discourage it from happening. It also alerts us to the idea of marginal transactions, where all change occurs. Smith has a thousand loaves and Jones has a thousand bottles. As the government wedge increases, it eventually discourages some of the trades. Smith is willing to trade some of the loaves for some of the wine, because it is too much trouble to make both bread and wine himself. Jones may want to trade more wine to get more bread, which means he has to offer Smith better terms. At a given wedge, an equilibrium is reached, where 750 loaves are traded for 812 bottles. There comes a point, of course, where both Smith and Jones decide to forget the whole thing, consume as much of their own bread and wine as they can -- liquidating their inventory -- and at the same time plan to make the investments necessary to produce their own bread and wine. At this extreme point on the Laffer Curve, or at his maximum “wedge,” both producers have dropped out of the market economy. 

Note that if the government reduces the tax on Jones, while keeping it the same on Smith, Jones will be willing to trade more than his 812 bottles for more bread, and the deal might go to 800 loaves for 900 bottles. The government will get more revenues from Smith and perhaps the same, at the lower rate on Jones. Or, the government might leave the tax rates the same. Perhaps it might remove a regulation that is burdensome to the transactions. If the transaction is taking place in a money economy, not a barter economy, perhaps the government might be wiser in its production of the “money” used as a medium of exchange between Smith and Jones. If the trade has to be made over time -- 750 loaves today for 812 bottles next year -- Smith will have to worry that if the contract is translated into dollars, one dollar for one loaf, about 92 cents for each bottle, the value of the dollar might change before the delivery of the wine. If the government devalues the dollar in the meanwhile, Jones will not have to deliver as much wine. If he paid for the loaves in gold, Smith would not have such concerns. Or, if he were paid in a dollar as good as gold, he would not have such concerns. If he suspected the government is going to renege on its promise, and devalue the dollar against gold, Smith would ask Jones for more wine to compensate for the risk, and this added wedge would in itself cause the deal to be renegotiated down.

The wedge model is useful for purposes of political analysis, because we see it is in the government’s interest at all times to make sure the combined size of the tax-regulatory-money wedge does not reach a size that breaks the camel’s back (to mix a metaphor). The simple picture encourages us to see that Smith’s willingness to trade one more loaf at an equilibrium of 750 for 812 bottles can be assured if the government wedge is slightly reduced by one of many elements available to it. If the government can do so, it will be rewarded by a part of that transaction. The optimum trade, of 1000 loaves for 1000 bottles, requires a skill by the government in knowing how to manage the tools available to it. This is mostly what the study of politics is all about and why classical economics was really the study of “political economy.” The decision-making process of the political market is intertwined with that of the economic marketplace.

When the transactors are international, two governments are involved, which means there are wedges on both sides of the trade. If one bottle of Jones’ wine is to trade for one loaf of Schmidt’s bread, the domestic example we presented above of variable tax rates can be observed more easily. If the United States says it will charge a 5% tax on all bread coming in from Europe, and Europe says it will charge a 95% tax on all wine from the states, the two rates in combination will produce almost no trade. Europeans will buy their own wine, except for the very rich who are able to buy 10 bottles of American wine to indulge their tastes. In accordance with Say’s Law of Markets, we then observe that Americans only have enough “money” to buy 10 loaves of bread. It is important to notice that if the rates were switched, 95% on bread and 5% on wine, the net result would be the same. This tells us that if our rates are high, it is to our advantage to lower them, regardless of what the foreign government does. If our rates are low, it is to our advantage to persuade the foreign government to lower its high rates, even while we leave ours intact.

Indeed, one of the reasons the Value-Added-Tax is popular with enterprises that export much of their production is that it eliminates the government wedge at the border. Everyone who buys a loaf in Europe pays a VAT tax, but when bread is offered for sale abroad, it excludes the VAT. When Jones offers his wine abroad, it exchanges for bread that is cheaper than it can be bought by the citizens who buy it abroad. The terms of trade become favorable to us, because they will be willing to trade more bread for less wine, as they will wind up with the same wine after the VAT rebate. Is it an advantage to a country without a VAT to have one, in order that its export industries could sell more wine for less bread? Government has to make the decision on whether to benefit those who make wine or those who eat bread.

Currency devaluations are similar to a VAT, in that they are meant to change the terms of trade between Jones and Schmidt. If we trade one bottle for one loaf at an exchange rate of 1 dollar per 2 Deutschemark, a devaluation to the point where $1 buys only 1 DM means that one bottle will exchange for only a half a loaf. It may be a good thing for wine exporters to sell more wine at 50 cents a bottle, as they assume they will sell more. In actual practice, the devaluation does not change the terms of trade. In the combination of tax, regulatory and money elements to the wedge between Schmidt and Jones, the terms of trade remain the same, but in devaluing its money, the devaluing country increases the risk not only to its exporters and importers, but to all domestic citizens who must trade with each other in the country’s money.

It has been useful to me over the years to transpose Laffer’s wedge to a wall, which rises brick by brick, or falls brick by brick. This is because it is easier to see the effect of the government walls between transactors. A tariff wall at our border and a tariff wall around the countries of Europe or Asia forces us to think in terms of two walls between Jones and Schmidt, who are trying to exchange goods over the top of the two walls. It then enables us to see the effects at home, when we erect two walls between Smith and Jones. The government says that when Smith and Jones are equal, the tax walls between them will be the same height. If Jones sells 1000 bottles for $1000 and Smith 1000 loaves for $1000, their tax will be the same. But if Jones can make 2000 bottles and Smith and his son can together make 2000 loaves to make the trade, the government says Jones will have to pay twice the tax as each of Smith and his son.

The progressive income tax means that the better Jones becomes at producing wine, the more he must give to the government. Most academic economists are taught that an increase in productivity causes a decline in price, but this is not the way it works in practice. If Jones can get one loaf for one bottle when he is producing 1000, why would he go to the trouble of increasing his efficiency to 2000 bottles, if the price of wine were to fall in terms of bread? The baker, who made no effort to increase efficiency, would then get 2000 bottles for 1000 loaves. In practice, Jones produces 2000 bottles and Smith, whose bakery could support only his own family, can now hire his son to support his. They each make 1000 loaves. Government is rewarded with tax revenues climbing because of the doubling of trade. Jones’s efforts to produce twice as much is rewarded by a doubling of his wages.

As the government taxes the rich in order to feed the poor, it only can go so far before the tax walls between rich vintner and the poor baker prevent marginal trades of bottles for loaves. If the vintner has no incentive to increase his wage (profit, capital gain), getting twice as many loaves by producing twice as many bottles, the baker will have no need to bake more than 1000 loaves and his son will remain unemployed. Who will feed him and his family? Probably the government, with the tax revenues it believed it would get by its tax on the rich, or, by borrowing loaves and bottles produced by Smith and Jones, in order to feed the baker’s son and his family. In other words, because there are two walls between the rich and the poor, they cannot exchange their goods if one wall is high or the other is high, or if one is zero and the other 100%. By raising the wall on the side where productivity is highest and tending higher, the party hurt most is the party on the other side.

Government of course implicitly acts along these principles when it gives a tax break to an individual who threatens to move his company from New York City to Connecticut, because local government’s wall atop the state government wall atop the federal government wall threatens bankruptcy. This is generally the least efficient way to go about it. The city and its leaders should be encouraging the state and federal governments to lower tax rates, reduce regulations, and make the dollar as good as gold, which will keep the company in place and also expand the city’s revenues. At that point, the city could lower tax rates for everyone. In New York City today, public finances are becoming healthier not necessarily because of anything Mayor Giuliani did to encourage growth, but because of the better management of federal and state “wedges” in recent years.

One of the best examples of the tax wall I’ve run across in the past 25 years is Japan’s exemption of accredited medical doctors from income tax. The tax wall between the doctors and the patients then depends exclusively on the size of the tax wall of the patient. This means the rich have to exchange more of their after-tax production to get the same volume and quality of service as the low-income workers. It makes sense to do this with doctors but not all professions because the need for doctors is ultimately universal, while the need for other services is a matter of taste or status or wealth.

There are other pictures I use involving tax mechanisms, but let the walls and the wedge serve to make their points today.