The explanation I favor is that it is simply a stable equilibria: You accept dollar bills as payment because you expect that tomorrow, you will be able to spend those same dollar bills in order to get things you want. How did we get to that point? Maybe it’s because the bills were once redeemable for gold. Maybe it’s because the bills were needed to pay taxes. Maybe it’s because laws were passed that forced merchants to accept dollar bills during the Revolutionary War. It does not matter at all. Those are things that got us in the current equilibrium but they are no longer necessary to maintain us there. The network effects create a strong enough positive feedback loop.

According to what I am saying, if on Monday Congress repealed legal tender laws, started accepting tax payments in whatever form was most convenient and allowed any currency to be printed, on Tuesday, you could go to the Supermarket, give dollar bills at the cashier and walk out with a dozen eggs.

Now, there is a weakness in this reasoning which I readily admit. Eventually, dollar bills will no longer accepted as a form of payment and so we should see infinite regression to the present. Let’s say that at time T, the world ends and everyone knows that fact. That pretty clearly ensures that everyone will know at time T-1 that there is no point in accepting any dollar bills in exchange for anything. After all, there won’t be any use for said dollar bills. So really, dollar bills become worthless at time T-1. But then, at time T-2, we all know that dollars are just about to become worthless. So why accept them for payment? It goes on and on until T-infinity and nobody ever accepts dollar bills.

So there must be something wrong either in the argument I just outlined or the theory above. As it turns out, we can give and answer to the argument. There is significant uncertainty as to when dollar bills will lose value. So really, we are all engaged in what I like to call “end of the world arbitrage.” People who think dollar bills will be worthless soon will try to use dollar bills to buy things from people who think dollar bills will be worthless later. That’s why a survivalist will feel really good about blowing all his life savings on his supplies. Those dollar bills are about to become worthless anyways. It’s a steal! On the other hand, the supplies salesman expects those dollar bills to be valuable for a while. (That would suggest that people who warn you about the end of the world and wish to sell you space in a bunker might be less than honest.)

Now David argues that this is incredibly messy. (No argument from me.) And that the tidier explanation is that we have to use dollar bills to pay taxes. According to that theory, dollar bills are get-out-of-jail cards for tax day. Then, we use the vouchers largely because everyone needs them and therefore they make for a nice medium of exchange. Much tidier.

While I would be happy to accept his theory if the only difference was in messiness, his theory predicts that if the government stopped collecting taxes (or started accepting any currency) the dollar would stop being used. My story predicts that nothing would change. (Apart from a little bump in inflation, anti-IRS vouchers are useful) But more importantly, I don’t think David’s idea saves us from needing a solution to the infinite regression problem.

Think about the story that dollar bills are anti-IRS vouchers. One must then ask: Why are dollar bills effective anti-IRS vouchers? Whether you consider the government a benevolent actor or the sum of special interest groups locked in an influence battle, there are few who would disagree that the government wants dollar bills so it can spend them. But if that is the case, the government faces the same infinite regression problem as other people. Eventually, dollar bills are no longer useful which means the government stops accepting them as taxes, which means everyone stops using them.

The best way to settle this would be if Congress would oblige us and stop collecting taxes in dollars, repeal legal tender laws etc. Somehow, I think that’s an experiment that’s not very likely to happen.

Now far be it from me to challenge the obvious economies of scales that one gets from marriage. Shared housing and transportation costs are huge savings, division of labor in household chores can greatly increase utility and we haven’t even talked about the fact that the married couple might enjoy each other’s company. Also, despite Bryan linking to the Wikipedia article on marriage penalty, most tax accountants will tell you that it is at least for now no more than a myth and that marriage substantially reduces your tax bill. But that is not the story Bryan wants to tell us. He actually focuses on the correlation in the NLSY data-set between marriage and income and argues that marriage causes a higher income.

I couldn’t find where he posited a mechanism whereby this causation would be effected, but there are a number of plausible explanations. Marriage could induce one to become more responsible, sociable, better at teamwork etc… Marriage most assuredly allows a division of labor which may raise productivity. Bryan advances for evidence a study looking at marriages which occur while a baby is on the way. What this study tries to do is separate marriages that are selected into from marriages which would be “accidentally” entered into after an unexpected pregnancy. If spouses and employers just happen to look for the same thing in a spouse and employee, getting married because of an unexpected pregnancy would not increase your income. On the other hand, if marriage makes you more productive, marriage due to an unexpected pregnancy should be just as effective in raising your income as marriage for other reason. The study finds some support for Bryan’s argument.

I, however, believe there is an intermediate model that explains the results of the study but rejects Bryan’s implied conclusion that more poor people should get married: signaling. Being in a relationship with somebody requires a certain skillset: ability to work with someone else, reliability, perseverance, etc… If you have those skills and qualities, you are much more likely to end up in a long-term committed relationship, get married and stay married. Those qualities as it turns out are also highly valued by employers and so they may end up using marriage as a signal for those qualities.

The shotgun marriage example is simply an example of someone mimicking the signal. They get the same advantages as people who sent out the signal legitimately. But if Bryan successfully convinces individuals to marry as a way to increase their income, the signal to noise ratio will drop until the signal has no value.

PS: To my lovely wife. I didn’t marry you to get a better job.

Some of you may argue that many insurance plans already covered birth control pills. That can be explained by the tax-treatment of employer-provided health insurance. If you have health-insurance through your employer you might have noticed that you do not pay income or payroll taxes on your health insurance.

So consider the situation where you have a marginal tax-rate of 20% and that birth control costs $100 per month. If your employer wants to give you money for birth control, he will have to pay you $125 extra per month. You pay $125 * 20% = $25 in taxes and are left with $100 for the birth control. On the other hand, if your employer hires an insurance company, he can just pay $100 to the insurance company and you get birth control. Of course, the insurance company would actually charge something between $100 and $125 for the privilege of helping you and him avoid some taxes. The end result is that the cost of health insurance and healthcare goes up.

Of course, the poor and the unemployed do not have employer-provided health insurance and do not benefit from this subsidy. They do however pay the increased premiums and birth control costs when they buy health insurance on their own or purchase birth control out of their own pocket. So really, this policy, no matter how well-intentioned, is a subsidy by poor people and the unemployed to the middle-class.

I do want to clarify that this relates to the use of the birth control pill as a birth control system. They are also used therapeutically to treat certain hormonal issues and a variety of other medical conditions and their insurance coverage in those cases do not raise quite the same issues.

Consider anybody who exports to the US. That person is dealing with American consumers who are well-known around the world for getting paid in, holding and therefore paying in US dollars. Therefore, exporting to the United States means having an outflow of widgets and an inflow of US currency. In order to see what happens next, one must carefully consider what the exporter (or some intermediary) does with those US dollars. There are roughly 5 different things they can do: buy US goods and services, invest in US dollar-denominated assets, lend money to the US government, hoard dollar bills temporarily or participate in foreign dollar-denominated markets.

The first three can’t be that worrisome to our job-conscious policy-makers. Purchasing creates jobs, so does investment and if they didn’t think they could do something good for the US with that money they borrow as the US government, they shouldn’t be borrowing it whether from foreigners or locals. That leads me to the conclusion that their problem is with the money that leaves and never comes back. It is proper to worry, but protectionism is the wrong answer.

Let’s consider what happens when that money leaves. That means that that money is no-longer available in the US to mediate transactions. In other words, the money supply has shrunk. A glance at the equation of exchange MV=PY=NGDP tells you that when M falls and V remains the same, NGDP falls. NGDP unexpectedly falling below trend disturbs nominal contracts which implies a recession. [Update: It has been pointed out to me in the comments that I am overstating my case here especially without more argument/data. I agree. NGDP falling below its expected growth path is likely to disrupt nominal contracts which may under certain assumptions result in a recession. I will make a more cogent/thorough argument in favor of that in a later post.]

Of course, upon reading this, you could say: “See! Trade can be bad! That’s why we need protectionist policies.” No. We don’t need protectionist policies as long as the central bank is doing its job and stabilizing the NGDP growth path. If the central bank responds by printing more money to counter the drop in the money supply, NGDP remains on its predicted growth path and everything goes well.

Now I understand that printing money to solve a problem may be anathema to some of my readers. But think of it this way: Chinese exporters are sending us a clear market signal: they currently value pieces of paper with pictures of dead presidents more than widgets. That’s why they don’t send the money back in exchange for different widgets stamped made in the USA. As a producer, the central bank should respond to this market signal and send them more of that which they seem to crave until the market clears.

From an economic point of view, $1 of value created is $1 of value created whether it was by building widgets, serving food or growing potatoes. For sure, different goods and services have different characteristics, but “manufacturing” doesn’t have a set of properties which make it better or worst than services. The politicians I mentioned above are intelligent and highly educated, so why would they say something so nonsensical? What is it about manufacturing that makes politicians tick?

To put it simply: manufacturing wins wars. If you look at the history of WWII for instance, it is clear that the Axis was no less will and no lack of brilliant generals. What they had a lack of was fuel, steel, coal and all the other accouterments that are necessary to bring soldiers to a battle and kill somebody. This idea is well embodied in the correlates of war project which includes iron and steel production as some of the most important factors in winning a war.

In International Affairs 101, the first thing that was drilled in my young impressionable mind was the definition of a state: “States hold the monopoly on the legitimate use of force.” There is no purer expression of that definition than war. When statesmen and aspiring statesmen ponder issues, is it such a wonder that war would sip into their thoughts whether overtly or not. They are nevertheless making a mistake and their fears are counter-productive.

The fear in the minds of the Obamas, Newsoms and Gingrichs of this world is that they will find themselves leading the USA to war with no allies, no trading partners and no internal manufacturing base to power the war effort. Such a fear of course ignores history. During WWII, the Nazis did have a strong policy of favoring home-grown manufacturing. But that did not matter because the Allies were able to create a broader coalition and trade with more foreigner purchasing raw materials and other necessities. During the Iraq War, despite the strong objections of many European countries to the war, they did not stop trading with the United States. It is highly unlikely that the USA would ever stand alone without at least neutral trading partners.

Of course, many might respond that matters would be quite different if the war was with a major trading partner such as China. That may very well be true. If the USA was to fight with its primary source of steel for instance, it is quite likely that that source might dry up. This is where the extensive literature on interdependence comes in. Countries that have strong trading relationships only rarely go to war with each other. There are many different explanations, but they all boil down to one simple matter: trade is mutually beneficial and when the gains of trade are high enough, states are reluctant to endanger them with war.

Now it is of course possible that all the factors I mention above would not come in to play. It is possible even if highly unlikely for the USA to eventually stand alone, with no friends seeing hostile faces whichever way it turns. But perhaps if that were the case, the cause and therefore the solution might best be found in the mirror. Not manufacturing.

Let’s return to our widget market. This time however, we will have slightly more general supply and demand curves. S = Es P where S is how may widgets producers are ready to produce at a price P and Es is the elasticity of supply. D = Cd + Ed P where D is the number of widgets people are ready to buy at a price P and Ed is the elasticity of demand and C is some constant.

I’m sure by now you’re wondering what I mean by elasticity. It’s actually a simple concept. The elasticity is just the change in quantity demanded or quantity supplied given a change in price. So for instance above, if the price goes up by $1, the producers will be willing to produce an extra Es widgets but the consumers will be willing to buy (negative) Ed fewer widgets. The elasticity of demand is negative because the higher the price is, the fewer widgets customers are willing to buy.

Let’s put some numbers to understand elasticity. Let’s say Es = 0.2, Ed =  - 2 and the price of widgets goes up by $10.

S’ = 0.2 (P + 10)

S’ = 0.2(10) + 0.2P

S’ = 2 + 0.2P

Producers will be willing to produce 2 more widgets.

D’ = C – 2 (P + 10)

D’ = C – 2P – 20

Consumers will be willing to purchase 20 less widgets.

So let’s find the equilibrium for the general case. We set S = D.

Es P = C + Ed P

C = Es P – Ed P

C = (Es – Ed) P

P = C / (Es – Ed)

S = Es P

S = Es C / (Es – Ed)

In other words, the equilibrium price is equal to some constant divided by the elasticity of supply minus the elasticity of demand. It makes intuitive sense. The elasticity of supply is how responsive producers are to prices. The more responsive producers are to prices, the less consumers will be able to demand a lower price without producers scaling back production. The elasticity of demand is how responsive consumers are to prices. The more responsive consumers are to prices, the less producers will be able to raise prices without loosing customers.

So now let’s put some numbers on this and calculate the consumer and supplier surplus in two different cases. In the first case, Es = 0.5 and Ed = – 2 and C = 100. We plug this in to find the price

P = 100 / (0.5 + 2) = 40

S = 0.5 * 40 = 20

In case one 20 widgets are produced and purchased at $40 each. Now let’s look at a different case. In the second case, Es = 1, Ed = – 0.5 and C = 100.

P = 100 / (1 + 0.5) = 67

S = 1 * 67 = 67

In case two, 67 widgets are sold at $67 each.

Now let’s add a $10 tax per widget to the first case above. Suppliers are still paid P but consumers now pay P+10. Es = 0.5 and Ed = – 2 and C = 100. So let’s reflect that in the demand curve and compute the new equilibrium and surplus.

100 – 2 (P + 10) = 0.5P

P = 32 ($8 less for the producer and $2 more for the consumer)

Let’s now add the same $10 per widget tax to case two where demand is much less elastic. Es = 1 and Ed = – 0.5 and C = 100.

100 – 0.5(10 + P) = P

P = 63 ($4 less for producer and $6 more for consumers)

Comparing the two cases, you can see the effect of the relative effects of elasticity of demand and supply. In the first case where demand is much more elastic than supply, producers are only able to pass on 20% of the tax as a price increase to consumers. On the other hand, when you lower the relative elasticity of demand in the second case, producers are able to pass on 60% of the tax as price increase.

This is actually a fairly intuitive result. If a small change in price scares off many potential customers without inducing much more product, producers are reluctant to raise the price even when a tax is imposed. On the other hand, if customers don’t react much to price changes compared to producers, producers will be able to pass on the tax to the customers without fear of losing much business.

So how might this apply in the labor market? It is of course difficult to say as there are many different labor markets and estimating elasticities is no easy feat. But as a first-order approximation, you can look at the relative negotiating power of your employer and yourself. If you and your colleagues feel confident that you can get a raise when you ask for it, it is likely that your employer is bearing more of the burden than you are. On the other hand, if you feel that your employer can dictate the terms of your employment, it is likely that your employer is passing more of the burden on to you.

[Note] I accidentally published this post before I intended to. I have decided that I would rather leave it up and update it later rather than confuse readers by having people wonder where the post went. Mostly, expect some graphs to be added tonight or tomorrow.

Look at the economy right before and right after the IRS cashes the tax check. Whose pools of money have shrunk? That’s tax collection. A corporation’s income properly belongs to its shareholders and so when the corporate income gets taxed, the collection is against the shareholders.

Now, compare two economies. One in which the tax exists and the other where the tax does not exist. The difference between the two is the tax incidence. If I choose to work less because the higher tax makes it less worthwhile for me, that’s tax incidence. This is what we are looking at here. And ultimately, when making tax policy, this is what we are interested in.

So let’s look at a very simple market for “widgets”. The supply for widgets is S = 0.5P where S is how many widgets firms are ready to produce at a price P. The demand for widgets is D = 100 – 0.5P where D is the number of widgets people are ready to buy at a price P.

If the quantity of widgets people are willing to buy is greater than the quantity of widgets people are willing to sell, the buyers will bid up the price until the quantities are equal. If the quantity of widgets people are willing to sell is greater than the quantity of widgets people are willing to buy, the sellers will bid down the price until the quantities are equal. That’s the equilibrium where S=D.

So we can solve for this easily:

0.5P = 100 – 0.5P

P = 100 and S = D = 50.

50 widgets are produced and sold at $100 each. So now let’s calculate the surplus. The consumer surplus is how much the item was valued at minus how much it was purchased for. We get that from the demand curve. Consumers were willing to pay $198 for the first widget, but they paid $100 for each widget, so the surplus from the first widget is $98 and so on and so forth. (Actually, we assume continuous quantities, so we integrate the area under the demand curve and subtract the price paid times the quantity. Look at the diagrams for the consumer surplus and producer surplus triangles if the math-speak is confusing you) The total consumer surplus is $2,500. You can do the same for the producer surplus. Producers were willing to be paid $2 for the first widget, but they were paid $100 for every widget so the producer surplus on the first widget was $98. As it turns out, the total producer surplus is also of $2,500. So we have $5,000 of economic value that has been produced through these trades.

Now let’s introduce a $20 tax per widget. We will say that the tax is collected on the buyers of widgets. In other words, the quoted price is a before-tax price. So now we have to adjust the demand function. After all, buyers don’t care about the before-tax price. They care about the money that enters and leaves their wallet whether it’s because of taxes or any other reason. Consumers are now ready to pay $20 less per widget to the producer since they then pay an extra $20 to the government. So we have to adjust the demand curve.

D = 100 – 0.5(P + 20) we can simplify this D = 90 – 0.5P

[Updated Thanks Michael. The math is correct, I simply made a typo in the above-equation]

Solving for the new equilibrium

0.5P = 90 – 0.5P

P = 90 S = D = 45. In other words, now, only 45 widgets are made and the producers are paid $90 for each widget only. Of course, the consumer has to pay the $20 on top which means the consumer is now paying $110 per widget. The total tax collected is $900.

So now once again let’s calculate the surplus for consumers and producers. Well, for the first widget, the consumer was willing to pay $198, but they paid $110 including the tax, so their surplus for that first widget is of $88. The total consumer surplus is $2,025. For the first widget, the producers were willing to accept $2 but they got $90 for every widget so they got a surplus of $88 on the first widget. The total producer surplus is $2,025 for a total economic value created of $4,050. That’s $950 less than the $5,000 created without the tax.

Note that in this simple example, the seller and buyer share equally in the loss from the tax despite the consumer writing the check to the IRS. You could re-do the math having the producer send the check. The result is the same. I will follow up with another post detailing how in different markets, the burden might be shared differently between producers and consumers.

Note that this works the same way whether we are selling widgets to consumers or selling work to our employers. If you tax something, it will cost more to those who buy it, bring in less to those who produce it and less of it will be bought, sold and produced.

A lot of very interesting points were brought up and I can’t respond to all of them, but I want to respond to what I felt was a theme in the comments. It goes something like this: “Greg Mankiw and you don’t get it. We want to know whether Warren Buffett should be paying higher taxes or not.”

The problem with that argument is that tax policy is hard. It’s very hard. There are plenty of complicated questions, some of which have no clear objective answers. In other words, it’s complicated enough as it is and getting tax incidence mixed up with tax collection will just confuse the issues further. So let’s get the basics right first. If the President is proposing policy based upon a flawed understanding of the current tax system, his policy is also going to be flawed. Garbage in, garbage out.

So how should we tax Warren Buffett? I’m going to argue that raising taxes on capital gains is a bad idea. There are many ways to reach that conclusion (and ways to reach the opposite conclusion too) and I’m only going to bring up one here and I will bring up more in future posts.

Taxing capital gains discourages capital formation. Let’s imagine a very simple economy. Every day, people have 8 hours of time during which they may work. During that 8 hours of work, they have two activities available to them. They can spend 1 hour making a loaf of bread or they can spend 4 hours creating a machine. That machine every day creates 2 loaves of bread forever.

So how do you split your day? Well, you could make 8 loaves of bread, 2 machines or 4 loaves of bread and a machine. Which you choose depends upon how impatient you are. (Your time discount rate in econ-speak) If you are a very impatient person, you might choose to make 8 loaves of bread every day because having the bread right now is important to you. If you are very forward-looking, you might make 2 machines every day because you are willing to wait. If you are somewhere in between, you might make 4 loaves of bread and a machine every day.

Now obviously, we want there to be as many loaves of bread to go around as possible. That’s what growth is all about right? In the very short run, that means making 8 loaves of bread per day. But over the long-run, we’re better off the more machines there are because then we have many loaves of bread produced automatically every day.

Now the government imposes a tax on the output of the machine. Every day, when the machine creates 2 loaves, one is sent to the government and never seen again. Of course, this will shift the incentives. If you were on the edge whether to make a machine or just an extra 4 loaves, you now will decide to make the 4 loaves. In the long run, we are poorer.

[Update]

I don’t want to curb anyone’s well-deserved enthusiasm for my post, but I want to clarify something. What I am referring to here is the taxation of capital, not necessarily the income-progressivity of the tax system. Now of course, accumulating more capital does tend to lead to one being “rich”. But that’s a second-order consideration here.

Unless you have been living in under a rock for the past 3+ years, you at some point in time have heard about Warren Buffett’s claim that he pays less in taxes than his secretary. More specifically he claimed that he paid 19% of his income in taxes while his secretary paid roughly 33%, (the exact numbers change all the time) the difference being accounted for his revenue being from “capital gains” which are taxed at 15% while his secretary is paid a wage which are taxed at a much higher rate. (Even at relatively low income levels) This has since become for liberals a symbol of an unfair and inequal society while conservatives have largely been complaining about job-destroying-class-warfare. Everyone has been playing their role to perfection with the latest stunt being Michelle Obama inviting Buffett’s secretary (Debbie the Secretary? Or are we done with “[firstname] the [job]” titles?) to listen to the State of the Union with her where the “Buffett rule” came up. (look it up, it changes every five minutes)

But what about economists? Were they doing their jobs? Well, Greg Mankiw was. In a column in the New York Times, he pointed out that Buffett’s numbers are misleading because he forgot about all those taxes he paid indirectly by being a shareholder of Berkshire Hathaway which pays significant amounts in taxes. Greg Mankiw argues quite reasonably that the profits belong to the shareholders and therefore, if you tax the profits, you tax the shareholders.

This obviously did not sit well with some people. And by some people, I mean LOTS of people. An argument I have now read over and over again is that it is unfair to assume the burden of the corporate tax falls on shareholders only. After all, it also depresses salaries, prices paid to vendors, etc… That is true. That is also besides the point.

The problem is that once again people are confusing tax incidence with tax collection. The difference is simple: If you make a gasoline company pay $1 for every gallon of gas they sell, the tax collection is a burden of $1 per gallon of gas on the gasoline company. But the tax incidence is very different since the gas company will raise their prices by some amount. So if they raise their prices by 90 cents, the tax incidence is 90 cents on consumers and 10 cents on producers. However, most people will stop at who wrote the check to the IRS. This is a basic mistake that people make all the time and teaching people about tax incidence is a job that every economist takes on when they talk about taxes.

But what’s the mistake here? Isn’t it true that the burden of the corporate tax is born by both shareholders, vendors and consumers? Well of course, but we need to choose what we’re talking about and stick to it. If we talk about the incidence of the tax, we need to remember that the income tax paid by Buffett’s secretary creates a burden for both her and her employer. It’s quite obvious that Buffett and Obama are not talking about the burden of taxation. Otherwise, Mr Buffett could not get his numbers by glancing at his tax return and his secretary’s tax return. He has to perform a complicated analysis which is unlikely to be completed in his life time. So they must be talking about tax collection at which point it doesn’t make sense to talk about the burden of the corporate tax on consumers, employees and vendors.

“But wait!” I hear you say. “Mr Buffett doesn’t actually write a check to the IRS for Berkshire Hathaway’s taxes. So obviously Greg Mankiw is looking at tax incidence (and doing a poor job at that) which means we can ignore him and return to Buffett’s numbers.”  No. You can’t. Taxes are applied against people, not things. When you pay your property tax, you pay the tax. Not your house. So you have to attribute the corporate tax collection to somebody. That person should be the shareholders.

Imagine that you are self-employed. Every year, you earn $100,000, pay 35% in taxes and have $65,000 left in your pocket. Now you form a corporation. $100,000 goes into the corporation. There is a corporate tax rate of 25%, so that leaves $75,000 which you pay to yourself as a dividend which are taxed at 15% which leaves you roughly $65,000. So sure, you could say that your tax rate was 15%, but that would be nonsensical. Nothing of significance has changed. What about if you get a partner and the corporation earns $200,000 paying $65,000 to each of you? Well, what changed? Nothing.

The bottom line is that if you want to look at the effects of tax policy by looking at tax collection, Buffett pays a share of Berkshire Hathaway’s tax bill and his original numbers are wrong in the way Mankiw said. If you want to look at tax incidence, the picture is very messy and Buffett’s numbers are definitely wrong.