The Laffer Curve and Kansas

What is the matter with Kansas? After several years of budget crisis, they are finally admitting—in a dramatic fashion—that cutting taxes maybe contributed to the state budget deficit. The argument for cutting taxes in the first place hinged on an arcane bit of economic theory called the Laffer Curve. Named for Reagan’s economic adviser, the Laffer Curve asserts that under certain circumstances, lower taxes can actually allow the government to make more money.

The Laffer curve is not as crazy as reports make it sound—though it isn’t exactly the most urgent model either. The idea is that the higher the tax rate, the less people buy because it drives up the final cost; the higher the price of pizza the less you buy. Presumably, consumers don’t care very much if the price reflects tax, profit, or business expenses. That means the tax base, the amount of money that can be taxed, is shrinking. At the same time, the higher tax rate means that the amount of the tax base that becomes tax is higher.

This tug-of-war between a shrinking tax base and a growing tax rate doesn’t play out in any general way; there is no rule for when one might expect one to outweigh the other. With that said, let’s take a pretty standard supply and demand graph like you might find in an introductory textbook. You would expect to find two straight lines, one sloping up and one sloping down. The numbers* I assumed are purely fiction, chosen for their mathematical form and not based on Kansas data. Nonetheless, they illustrate the essential problem to a good approximation. Graphing the amount of revenue the government earns versus the tax rate gives you this chart:

Laffer Curve.png

Notice that until the tax rate is a whopping 200% the government makes more money for raising taxes. 200% isn’t an unusual number to get for the turnaround point on the Laffer Curve for a broad range of assumptions, though I must note it is possible to contrive models that put it near Kansas’s tax rate. Nonetheless, for a number of completely standard assumptions, the warning of the Laffer Curve is that if you lower taxes, the government will make less money.

Why did Governor Brownback fall for something freshmen getting econ degrees could have computed as wrong? I suspect it is wishful thinking. The analysis that Brownback relied on was sophisticated, and had an additional supposition that the low tax rate would draw businesses into the state. (They never came.) There is something appealing to my contrarian nature about the idea that taxes going up makes revenue go down, and I bet that would be stronger if I were conservative. It’s also possible—though I can only speculate—that Brownback just doesn’t care if revenue falls.

Trump’s budget makes the same kinds of claims, that if we cut taxes, GDP will roar. Conservatives in particular like to talk about the States as “laboratories of Democracy”; it is one of the places I agree. The experiment succeeded in Kansas; under normal circumstances, cutting taxes leads to decreased revenue, not an increase.

*I used {S: p=q} and {D: p=10-q} in case anyone is dying to verify my work.


A Venezuelan Inflation Addendum

Sometimes the news dovetails with my blog.

Yesterday, I responded a Benjamin Studebaker piece where he argued, in my view, unpersuasively that the left can organize to overcome some fundamental problems in Europe’s periphery. While much of my response dealt with inflation, for the sake of length, I emphasized the havoc a “Grexit” would cause for government programs. Regrettably, I had to give short shrift to the effect inflation has on labor.

Enter Venezuela! Yesterday, enormous protests erupted against the embattled Maduro government. Under Maduro’s predecessor, Hugo Chavez, the government began pursuing the kind of communist policies that were, frankly, a throwback in the 1970s. The effects of the price controls and crackdowns have been at turns humorous and horrific. Humorous: The country ran out of toilet paper a few times. Horrific: Caracas has the highest murder rate in the world as gangs try to secure food to sell on the black market. Driving all this is acceleration inflation, which is making everyone poorer. Even if you want to hose the investment class, rapid inflation is deeply anti-labor.


To get some idea why Venezuela’s policies are accidentally anti-labor, one must only look to their minimum wage. In 2016, the Maduro government raised the minimum wage 322%; in US terms, that would take the wage from $7.50 to $23.35. During that same time, however, the price of goods went up by 800%. That means that $7.50 in goods would then cost $58. People making the minimum wage in Venezuela could only buy 40% of what they could at the start of the year even after the wage hikes. That’s equivalent to slashing the minimum wage to $2.90 in the US.

The Maduro government has taken the position that it is because of, “economic war and mafia attacks”. Even if you are inclined to swallow these half truths uncritically, you must wonder why the Maduro government has failed so spectacularly at trade (mismanagement of public companies) and the mafia is thriving (nothing feeds a black market like price controls). And let’s not pull the punch: The government is exaggerating much of the narrative to dodge responsibility.

While my post yesterday focused on the problems inflation causes for government financing and the argument I was responding to looked exclusively at its effects on the investor class, the lesson here is that inflation erodes labor’s standing pretty dramatically. I looked at the minimum wage because that is an unambiguous statistic, but in many ways it is missing the point. Estimating real wages during dramatic inflation is difficult because it is a moving target. We can safely say those who were working above the minimum have almost certainly not seen a raise for awhile and the erosion of the value of their labor is even greater than the government’s actions on the minimum wage.

This isn’t a question of class warfare. Its a question of not cutting off you nose to spite your face.

As in Everything, Trade-Offs in Europe

Benjamin Studebaker has published a piece that is an object lessen in wishful thinking. He posits, in short, that if the left in Europe commits to strategically reforming the EU’s institutions then we can solve the problem in Greece. It lays the blame at the steps of core banks without critically engaging with the fundamental economics that drove the periphery to those banks. It is not so much that he’s wrong that those core banks played a role, but rather that his effort refuses to engage with the steep trade offs imposed by economic realities.

Too Neat a Tale

Consider first his analysis of the vicious cycle of debt Europe finds itself in:

It’s clear that the EU, as constructed, is not working for the countries in the periphery—places like Greece, Spain, Portugal, and Italy. In the 2000’s, these countries became export dumps for the core countries, particularly Germany. German companies used the periphery export markets to get rich, and German banks lent money to the periphery economies to enable them to pay for German goods. This produced a sick feedback loop in which Germany lent money to the periphery so that the periphery could continue to buy German goods so that German companies could continue to generate profit which they then put into the German banks and which the German banks then loaned to the periphery so that it could buy more goods so that German companies could make more profit and so on and so forth.


While I agree there is truth to this story, it is a little too neat. German banks did not lend money to a passive Greek government. Greece fought to enter that lending market and, lest we forget, cooked the books to get access to both the money and a lower interest rate. An account that picks up with German companies benefiting enormously from having a competitive advantage that Greek officials successfully hid from them obscures that Greece removed the safeguards that would have protected their markets. Be careful of telling too neat a tale in the core’s favor, though; the core adhered to the letter, but not the spirit, of those safeguards and I suspect wishful (though, not predatory) thinking was under that. Regardless, that the core bought their dishonest accounting is not equivalent in culpability to the original lie.

And why did Greek officials do this? Studebaker’s account and diagram elides that as well, but it was to expand government spending. I support a robust safety net, so make no mistake: this is not a morality play about how gutting services is justice for the Greek people. But a more careful accounting of the Greek crisis shows that Greek officials were the primary architects of a system they initially benefited from. It also reveals that Greece faces a fundamental tradeoff that a Grexit cannot alleviate, though we’ll see there is a surprising, political case for Grexit. But first, the obvious question:

Why The Euro?

All countries face a pretty simple tradeoff, captured by something called the Phillip’s curve. The Phillip’s curve says that the more countries try to tamp down on inflation, the more unemployment will rise. This makes an intuitive sort of sense, though there is no completely uncontroversial explanation for the finer points of the relationship. Governments which spend more will drive up prices by competing with consumers for goods, but the stimulus will employ people and vice versa. While the quality of the tradeoff is pretty much universal, the quantity tends to change over time and between countries. The difference between the Drachma era and the Euro era is striking:


Joining the Euro’s integrated market lowered the barriers to international debt finance; more people had an easier time bidding on Greek debt. More bidders means a lower price and, in turn, a lower price on debt means lower inflation. This was further compounded by the fact that core banks believed that Greek debt was safer than it was. That same lie suggested that the trade imbalance should not have ballooned the way it did, and the economic history here is that at first it didn’t. It wasn’t until it became clear that Greece cooked the books that their current account collapsed:


There are two stylized fact here:

  1. The benefit of the Drachma is that it protects against deep current account imbalances. The downside is that it makes financing the government much more expensive.
  2. The benefit of the Euro is that it offers cheap financing for government programs, but that debt often returns as GDP-sapping imports.

Again, I’m not placing government debt at the center of this story as a morality play. I’m doing so because government spending and social programs are key to understanding Greek finances and motivations as well as German exporting. The Greek government could have unilaterally reduced imports by cutting social programs; they implicitly did the opposite by entering the European market and increasing their debt load. And this deeply undercuts Studebaker’s thesis.

Before I address that, there is one other thing I need to address that does not fit neatly into this narrative.

Absolution for Whom?

There is a proposal, casually thrown out, that also needs addressed:

Federal institutions can wipe out the debt of the periphery and create new European regulations to ensure nothing like this ever happens again.

Yeah, no, they cannot. From the data here (PDF), European banking equity is about 180 Billion Euros. Greek debt alone is 350 Billion Euros. Doing this by fiat would would bankrupt the banking system and throw Europe back 800 years. It is not an option.

Buying out the debt, just writing off the enormous political undertaking that would be, would have deep, second-order problems. A quick estimate suggests peripheral debt represents about 29% of the GDP of the EU. (Spain and Italy are the bigger problem in nominal terms, but Greece has a much more beleaguered economy because GDP and population are much lower.) For perspective here, government spending in Britain is 40% of the UK’s GDP. If we allow this take 6 years and all countries make a contribution proportional to their GDP, this program would require a tax hike of 12% added to the current tax bill provided there are no negative effects from the tax. Accomplishing this in a single year would require a 75% increase in the tax rate, clearly unfeasible. To keep taxes below 5% for the UK will require at least 15 years and 2% requires more than 36.

Large scale debt forgiveness programs, be they by decree or payment are simply enormous undertakings.

Constrained Goals

With this all in mind, we turn our attention to the political coalition Studebaker proposes. It is a fairy tale as it requires both the core and periphery to shoot themselves in the foot.

Grexit would, admittedly, help Greece maintain austerity but as a pitch for the left to rally around it comes up wanting. The case for it is cynical: if the core is unlikely to reduce the austerity burden, the best way to make austerity less bitter is to dump the Euro. (Under the Drachma, 2% inflation, like we’re seeing now, corresponded to a third the unemployment rate. Some transition costs may apply.) But it requires giving up the goal of expansive services which, frankly, I do not see the left agreeing to that. Contrast Studebaker:

The European Union in its current form is much better for the core countries than for the periphery. It’s especially good for Germany, and it’s especially good for rich Germans. They need the periphery to be in the EU so that it can continue to serve as Germany’s export market. But this is not sustainable–it imposes too much suffering on the poor and working people of the periphery. These people are right to reject this exploitation, and by rejecting it they will put a tremendous amount of pressure on Germany and on the rest of the core to find a political and institutional solution which alleviates their grievances.

The flaw here is that the problem is not “exploitation” in any straightforward sense of the word. Even ignoring the considerable problem of existing debt, the fundamental trade off between financing government services and Greek employment is not, ultimately, a question of German banking. While I have demonstrated that the institution of the Euro has a profound impact on the slope of that trade off, none of the options Studebaker puts on the table overcomes it—nor could they. The periphery, by construction, can only have their cake and eat it too if the core agrees to a catastrophe. Again, Studebaker:

At the same time, by supporting federalism and integration, the left in the core can help develop and prepare the ground for the kind of solutions which can genuinely help the periphery. If the left in the core aids and abets the right, then the response to exits and exit demands from the periphery will simply be disintegration. The left must keep the core countries firmly committed to the European project so that they will not just accept the exit of the periphery and it must build support in the core for the Europe of the future. If the right in the core chooses to support exit and the left chooses to support institutional improvements, the center will have to ally with the left to prevent disintegration. The center must be forced to choose between an end to the euro and the common market and the creation of a new European economic compact in which the center makes concessions to workers and the poor in exchange for continued openness within Europe.

Here again, the economic details of his proposal are at odds with his goals. Asking the core to bear the incredible economic cost of paying down peripheral debt (I presume he would agree bankrupting Europe is not an option?), strikes me as a political non-starter. Germany has a growth rate of 1.2% per year; the steep increases in taxes I estimated above would wipe out any benefits of keeping the Common Market here. This is definitely a case where an honest accounting of the plan by the left should drive the center into the open arms of the populist right. Given the strict choice between the proposal to wipe the debt or let the EU disintegrate, you would be hard pressed to convince me to wipe the debt. We’re talking a major decrease in national wealth to pay for what was, essentially, fraud. Note, this is not an appeal to “mere politics”, but an account of how a majority of informed voters would be expected to reject this. With that in mind:

This will only work if the exit threat in the periphery is genuine. Germany called SYRIZA’s bluff–SYRIZA wasn’t really willing to ditch the Euro and leave the union. It wasn’t willing to reintroduce the drachma and expose rich Greeks to the inflation that would come along with that. The political movements in the periphery must do more than talk about exit, they must be willing to carry it out if necessary. In this way we can partner the integrationist and protectionist lefts together–by pairing a genuine threat of exit in the periphery with a strong push for federalism in the core, we can split the neoliberals off from the right nationalists in the core countries and force them into making concessions. What the left needs is a good cop, bad cop routine, where the British, French, Dutch, and German leftists are the good cops and the Greek, Italian, Spanish, and Portuguese leftists are the bad cops.

Insofar as “neoliberal” is a real thing (and it isn’t), I seem to be one. And if there is one thing I have noticed when neoliberals are invoked, it is because “we” have raised the issue that there is some sort of constraint—usually economic. But if “we” really understood the politics or facts or weren’t so blinkered by our corporate allegiances, “we” would support a truer form of progressivism. But I submit that in light of the evidence, SYRIZA let the bluff be called because they were not prepared for a post-Euro Greece. The status quo is not good, but giving up the Euro means giving up on any chance to finance social services for a generation. I would have advised that ship has sailed, but holding out for a better deal with more services as debt stabilizes in Greece is a defensible course for the left.

The Power of Wishful Thinking

This is a mode I see regrettably often on the left. Studebaker has a very clear set of goals here: the ascendance of the left, expansive social services, and an integrated core in Europe. There is nothing wrong with having a set of goals unmoored from what is possible; incidentally, I share this trinity. Despite being a curmudgeon about proof, I support left wing policy goals and economic integration. But too often, I see a set of goals proposed and the argument that a suitable political coalition can erase the trade offs. But, that is profoundly out of touch with reality.

What I find wanting in Studebaker’s analysis, both here and elsewhere, is the gratuitous hand-waving. Even without my detailing of the Phillip’s curve above, his proposal is, at its heart, to create government agencies that get what he wants. (“We need stronger European institutions that can step in and prevent any European state from exploiting any other”.) I understand quite intimately the challenge of blogging is that fleshing out those ideas to a high standard is difficult, but there is a galling hubris in presuming one can make debt equal to nearly a third of the EU’s GDP disappear by giving more power to the EU Parliament. Is the EU going to abolish double entry accounting? The proposal to just waive all that debt is, without hyperbole, not wholly different. The idea that the government might be able to change the Phillip’s curve dramatically is less of a sin only by comparison. Changes at the Central Banks are among the few that can, and even then within a pretty narrow range of options.

The basic lesson of economics is that in everything are trade offs. Government financing only works if interest rates are low; inflating away debt is a terrible way to ensure continuity of government services in a country that is struggling to make ends meet. But, with low interest rates, comes high unemployment precisely because you have to hack back at services to achieve it. This isn’t a failure by SYRZIA and core parties to organize. It’s basic opportunity cost.

And so long as the left is unwilling to admit they have to give things up to reach some of their goals, they will struggle to build potent coalitions with those who take governance seriously.

A Lot of Words to Explain that Protectionism Is a Bad Idea and You Shouldn’t Do It

Our President, in his wisdom, has proposed a 20% tariff on imported goods. Or goods from Mexico? Or maybe that was just an example?  Like most things the White House does now, it was a bit confusing.

At any rate, it inspired a fair few of you to ask about tariffs. Who actually pays for them? What effect do they have on the economy? I am happy to oblige. If you are not here for econ lesson, but just want my opinion or juicy quotes, skim until you see the “Conclusion” header. It’s about 1200 words south of here; sorry.

I will be showing the graphical analysis in the least technical language I can manage because I find the graphs visually intuitive. Further, I will be giving some hypothetical numbers to go with it. This is not an actually economic prediction as the graphs I’ve put up or extremely stylized. It is just to give a sense of the magnitudes at work.


Let’s use the example of tomatoes as imports. (Lindsay Graham humorously defended the virtue of Mexican spirits, but I worry that we are losing sight of how much food, cars, and appliances account for our trade relationship.) If America were to simply close her borders, tomato production might well look like this next graph. Again, these numbers are simply for illustration; this is not meant to be a literal model of the tomato market.


The idea behind this representation is pretty simple. Starting with the red line, Demand, it shows the more expensive something is, the less you will buy. Likewise, the green line, Supply, shows that the more expensive something is, the more that will be sold. The tenuous point where they are equal is where they cross. Easy enough.

How much better off are we for being able to trade? Think about someone who would pay 10 dollars for tomatoes. They are paying 4 dollars less for the same amount of tomatoes. You can figure out exactly how much that is worth by finding the area of the triangle A, which in our example is $18. the same idea applies to Supply, but we want to look above the curve. If you would produce at 2 dollars, you make 4 dollars more by selling your tomatoes in this market. I have labeled that “B+C+D” for reasons that will become clear as we go along. Because of the arbitrary shapes I chose, it is also worth $18.

Let’s allow Mexico ship us tomatoes. Mexico has a warmer climate and it is easier to grow tomatoes there. As a result, the market price is going to be lower. I set it at $3 on this graph:


The mustard colored line is the price of goods now that we trade. It changes things quite a bit. First, it drives out anyone in the US not willing to sell as cheap as Mexico can. It pushes the area that producers benefit from all the way down to “D”, which is $4.50, a quarter of before. (It would be hasty to say that there would be a quarter as many jobs for tomato growers, but as a first approximation, that would make sense.) I presume this what Trump means when he says we are “losing” to Mexico. But we’re not finished. Consumer benefit is now everything above the mustard line and below the red line. That’s “A+B+C+E+F+G+H”. Here our numbers come out to be $40.5 dollars.  It is a matter of simple arithmetic to figure out if we are collectively better off. We subtract closed economy numbers from the open economy numbers.


What we find is that Americans are better off for allowing trade by the size of the triangle “E+F+G+H”, which you can also see by comparing the areas on the graphs. This is an area of $9. That means that the tomato market makes us 25% better off if we open the economy to trade.

Now, let’s imagine that we elected a furious basketball to the White House and he decided to demand a 20% tariff on tomatoes imported to the US from Mexico. That graph would like this:


This is where things get complicated. To start, you can see that producers are a bit better off, now benefiting in the area “C+D” Consumers are pushed back to the area “A+B+F”. Its the rest of the areas we have to grapple with. Each of “E”, “G”, and “H” has different meaning.

“E” is the increase in costs that domestic producers pay because of they are less efficient. (This is not an increase in price, but rather how much they pay to grow tomatoes.) “G” is how much goes to the government, presumably to pay for the wall. “H” is how much less consumers get because Mexican producers leave the country. It is standard to presume that tax money counts towards societal benefit, and despite how doubtful I am the wall counts, I will follow suit. Because E and H alone count as waste, it is “only” $0.36 of waste over the open economy case, or .8%. If you can justify the spending, you can probably justify the tariff. Except…


We benefit enormously from our trade with Mexico. We send a good deal of corn south of the border—enough that we actually upended the entire farming sector after NAFTA was signed. Following our earlier analysis, we can see how a trade war might begin. The above analysis, in order to keep things simple, implicitly assumed that Mexico had exactly benefit from trading with us. Obviously, this is not realistic, but insofar as we don’t care about what our trade policy does to Mexico, there is no reason to make it more complicated. Now, though, we care about how a tariff impacts American businesses. this is a graph that could represent a tariff on corn, levied in retaliation.


Before the tariff is levied, the United States benefits at “G+I+J+M+N”. After, it is reduced to “I+G”.While it also reduces Mexican welfare (by “F+L”), the greater burden falls on the country receiving the tariff. That is why countries get into trade wars when tariffs start going up. They can retaliate with less damage to themselves than to the other. It can quickly spiral out of control.

The best way to avoid this is trade deals—NAFTA and TPP, populist boogeymen both. Unilaterally breaking those trade deals is a good way to reduce producer welfare in your country.

Some Overreach

Bearing in mind that I literally just made up the numbers above, it nonetheless might help to put some numbers on this. Assuming that Mexico levied the tariff against the US:

Cost of Mexican Tariff to Mexico: 7 cents.

Cost of Mexican Tariff to America: $2.43.

The damage of this tariff is 35 times higher for the people it is leveled against. Of course we get into trade wars. Standard theory advises against them, but once our furious basketball has started one, retaliation makes a certain amount of sense. Other countries watching do not want in on that action. There is no world where a tariff makes sense, except when someone has raised a tariff against you.


Here is the part you came for. The part you can lob into comment sections. The following things are basically agreed upon by economists, with pretty little mainstream dissent:

  • Tariffs always decreases the general welfare in both countries.
  • The benefit business interests for the countries that raise them.
  • They hurt consumers in country where the tariffs were levied.
  • Consumers effectively pay 100% of tariffs EVEN IF the tariff is legally raised against foreign companies.
  • Tariffs do, broadly but not absolutely, hurt the country they are raised against more than the country that raises them. (Both cases appear in this article.) That makes retaliation politically attractive and a real threat.
  • Finally, the benefit of the tariff assumes you don’t spend it on something worthless—not a forgone conclusion, it turns out.

Protectionism is cutting off your nose to spite your face. Don’t do it.

Presidential Party is a Bad Predictor of Economic Success

There is, you might have heard, a meek debate happening around the 2016 election. Some people think we should put more emphasis on economic policies. Others think we should stay the course. Before I offer my take on that, I would like to submit that economic policy is not an especially obvious source of economic growth.

The graph below shows the per capita GDP growth of all the quarters since July 1948. I start presidential terms in the third quarter of their term, the idea being that is the first full annual budget they administer. The horizontal axis is the percent of quarters that are below the quarter in question. The vertical axis is the percent growth.


The graph is a surprisingly good test of your willingness to read a graph in a partisan way. It shows that there is not a large differences, on whole, between Democrats and Republicans. It also shows there is a measurable advantage on average to voting democratic, especially around a recession. If you, for example, so a chasm between them, you might want to consider the ways you twist information to support a Democratic worldview. Likewise, if you cannot see the clear advantage of voting Democratic, you should consider that you are very partisan.

To grasp the data here, imagine that electing a president in 2016 was merely having the new president draw, at random, a quarter from a previous president in their party to have that growth again. This is obviously a gross misrepresentation of Presidential power, but it gives a sense of what this kind of backwards-looking analysis says. For virtually every draw our Republican president would make, the Democrat would have a better chance of doing at least as well. (There are some exceptions around the 95th percentile.)

So, if the Democrats drew their 50th percentile quarter, the GOP would only have a 37% chance of beating them on a draw, which makes them the superior choice on average. If the GOP drew there 50th percentile as well, growth would only be fifth of a percent lower. So while the Democrats do nominally better, the difference over most of the distribution is quite small, averaging to a third of percent. For the median earner, this is about $8.25 a month

One place that this simple exercise suggests a stronger Democratic advantage is around recessions—the very left of the graph. The Democrats have fewer quarters with very deep decreases in per capita GDP. At the widest gap, there is nearly a percent difference in income contraction. This is approximately $25 a month difference. Still not an incredible sum, but more noticeable. This seems to validate expansionist policies, a Keynesian glut of spending, in a recession. I suspect that this accounts for a fairly large part of the finding that Democrats do better than republicans. Make of that what you will.

This is not an unexpected finding for a few minutes with Excel. Let’s take a widely cited 2004 study by Achen and Bartels (PDF). (Bartels is the author of Unequal Democracy, which makes use of these findings.) Their study implies* a higher difference between Republicans and Democrats, at about half a percent. For the median earner, that is $11.75 a month.

Tomorrow’s post will make use of this observation that the difference in growth between parties is small, but for now let us draw a simple conclusion. The Republicans and Democrats have surprisingly little effect on overall growth on average. One way to explain this difference by pointing out that treating Reagan and Bush or Clinton and Carter as cut from the same cloth is a bit silly; I am inclined to agree. I think it is reasonable to say that if all you care about is average income growth, you can detect a slight advantage to voting Democratic. But it is easily overwhelmed by policy details and simple economic luck.

*Table 5 gives values for election and non election year income growth. (This is a slightly different metric than the one I chose, but comparable enough.) Using a weighted average, it appears there is just shy of half of a percent difference between democrats and republicans. The authors do not report this number in their study. You might note that they draw the conclusion that voters are very bad at factoring this small difference and credits the ways both parties tend to have higher growth in election years. I am inclined to say that voters are very bad about caring about 12 dollars a month when it arrives so abstractly, but at any rate, I’m not really here to disagree with the original study.