[h/t to Mike Schibly for pointing out that I switched millions to billions in the section titled “A Generalization to Medical Devices.” That has been corrected as of February 4, 2014, 4:15 pm Pacific standard time.]

[An alert reader pointed me to a serious error in the first version of this article. My dollar tax per CT scanner was about eight times too high. That makes deadweight losses and most other calculations considerably smaller. This is the corrected version of the article. And thanks for bringing this problem to my attention.]

In this blog entry, I’ll discuss the impact of the ACA medical device tax. The Patient Affordable Care Act (ACA) includes a 2.3 percent sales tax on these devices. The impact of this particular tax has not been discussed much. But it’s important. In this blog entry, I’ll describe the tax, discuss its likely impacts, and look at the incidence of the tax.

## Background on the ACA Medical Device Tax

I decided to write this after hearing a statement made on NPR’s Morning Edition on July 2, 2012. In a discussion of the medical device tax, the following exchange took place. The speakers are:

- Paul Van de Water, an economist with the “left-leaning Center on Budget and Policy Priorities.”[1] Dr. Van de Walter got his Ph.D. in economics from MIT in 1975. Speaking as an MIT alumnus, this embarrasses me.
- Chris Arnold, NPR reporter.

“…

ARNOLD: Okay. So here’s how this new tax works. When a medical device gets sold, there will be a 2.3 percent sales or excise tax. Now, people who support this tax say that the medical device makers are exaggerating about the impact. Paul Van de Water is an economist with the left-leaning Center on Budget and Policy Priorities. He says that this tax is basically the same as a sales tax that you pay at the grocery store.

PAUL VAN DE WATER: The grocery store is collecting the tax. The grocery store is the institution that sends the tax to the state government, just the way the medical device manufacturer is going to write the check to the Treasury.

…

ARNOLD: Still, economist Paul Van de Water is skeptical. He says it’s not like a hospital will decide to do fewer hip replacement surgeries just because of a two percent tax on replacement hips. So he says the device makers should be able to pass along the cost. The industry, though, is lobbying hard. Last month the House of Representatives voted to repeal the tax, but there’s likely to be a bigger hurdle in the Senate. Chris Arnold, NPR News, Boston.”[2]

Economists study this sort of thing all the time. The topic falls under the general heading of the incidence of a tax. And the only way that 100 percent of a tax is passed along to buyers is if the demand curve is vertical. In the real world, there are no vertical demand curves. Ergo, Dr. Van de Water’s statement is false.

But there’s still an interesting question remaining. What short and long run impacts on the industry will this tax create? This is likely to get a bit tedious, so bear with me.

## The Medical Device Tax

The Patient Affordable Care Act (PACA) includes a 2.3 percent tax on sales of medical devices. The tax would apply to any medical device sold in the U.S. regardless of where it was manufactured. Here’s an excerpt from a September, 2011 study published in the journal Health Affairs.

“… the final incidence of the fees imposed on medical device manufacturers, pharmaceutical companies, and insurers is more complicated. To the extent that these fees are passed on to the end consumers in the form of higher medical prices and thus premiums, they will probably be borne proportional to the burden of premiums, which, as noted, are regressive.

On the other hand, if these fees function more like corporate income taxes, current economic theory would suggest at least some of the burden would be financed through corporate capital. Some of the burden would also fall on labor through reductions in productivity and hence, wages as the incremental burden is shared by capital and labor. Similarly, at least some of the incidence of penalties on employers for not providing coverage could fall on wages.”[3]

Before analyzing the incidence of this tax, let’s understand one important point. This tax is on sales, not profit. Even a start-up company with massively negative profits will still have any sales subjected to this tax. That fact alone will dampen innovation.[4]

What this boils down to is the relative price elasticities of supply and demand. Arguments presented so far focus on short-run impacts. Later I’ll also consider the long-run impacts.

## What is a Taxable Medical Device?

Like so many aspects of the PACA, the rules for which devices are subject to the tax are being created by the IRS and FDA. The IRS has issued a proposed set of rules which are still open for comment. Here’s what the IRS says (from the previously linked page):

” Section 4191(b)(1) provides that, in general, a “taxable medical device” is any device, as defined in section 201(h) of the Federal Food, Drug & Cosmetic Act (FFDCA),(codified as amended at 21 U.S.C. 301 et seq. (2006)), that is intended for humans. Section 201(h) of the FFDCA provides generally that the term “device” means an instrument, apparatus, implement, machine, contrivance, implant, in vitro reagent, or other similar or related article, including any component, part, or accessory, that is recognized in the official National Formulary, or the United States Pharmacopeia, or any supplement to them; intended for use in the diagnosis of disease or other conditions, or in the cure, mitigation, treatment, or prevention of disease; or intended to affect the structure or any function of the body, and that does not achieve its primary intended purposes through chemical action within or on the body and that is not dependent upon being metabolized for the achievement of its primary intended purposes.

Section 4191(b)(2) provides that the term “taxable medical device” does not include eyeglasses, contact lenses, hearing aids, and any other medical device determined by the Secretary to be of a type that is generally purchased by the general public at retail for individual use.”

As is customary with sales taxes, devices purchased for resale or as intermediate goods (parts) are not subject to the tax.

Before we get into the theory, we need some data. Luckily, the Census Bureau does periodic detailed surveys of industries. Their 2010 report is available, conveniently as an Excel table. I have included Table 1 in my Excel workbook. (If you download that Excel workbook, beware of a couple of things. First, it’s an Excel 2007 macro-enabled (,xlsm) workbook. Second, the worksheets are highly interconnected. Check dependencies before you make any changes. Of course, if you screw something up you can always download another copy here.)

In 2010, the total spent on medical devices including ionizing radiation equipment was $26,796.9 million. The average from 2006 through 2010 is $26,202.7 million. Eyeballing the data, the total has fluctuated with a standard deviation of $1,396.1 million. Importantly, there is no obvious trend in the data:

A quick linear regression reveals no statistically significant trend. So let’s assume the average will be the actual in 2013. The tax will raise about $602.7 million dollars during that year. (Yes, I’ll discuss the likely long-run impacts later.)

Let’s look at one specific market: CT scanners. Since 2006 there has been a slight, but statistically significant downward trend in sales. A simply trend forecast indicates sales of about $1,078.1 million in 2013. That will raise about $24.8 million in tax revenue.

Now we’re ready to look at who will bear the burden of these taxes. The real question is how much will be paid by buyers and how much by sellers. Dr. Van de Water believes 100 percent of the tax will be paid by buyers. Let’s learn some economics, then consider the implications for the medical devices market.

## The Incidence of a Tax: Who Pays?

Economists divide the world of sales taxes into two types. A *specific tax* is a tax per unit purchased. The example people in most countries understand is taxes on gasoline. Many of those taxes are per gallon or per liter. (Note that sales taxes are also levied on gasoline sales in many places. That means gasoline taxes are both specific and *ad valorem*.)

The second tax is an *ad valorem* tax, a percentage of the money amount of the transaction. Sales taxes generally fall into this category. The medical device tax also falls into this category.

For analytical purposes, it really doesn’t matter much which form the tax takes. To make this article somewhat more comprehensible I’ll convert the *ad valorem* tax into its specific tax equivalent..

A specific tax drives a wedge between the price buyers pay and the price sellers receive. The difference, the amount of the tax per unit, goes to the government. An easy way to understand such a tax is with a simple supply – demand diagram. I’ll consider CT scanners with a price of $150,000.[5] Our forecast sales revenue of $1,078.1 million in 2013 implies sales of 7,187 units. The remaining question is the price elasticities of supply and demand.

### A Digression on Elasticity

(If you’re familiar with elasticity, feel free to skip to the next section.)

Price elasticity is the ratio of the percentage change in quantity demanded or supplied divided by the percentage change in price. For example, consider the following calculation of the price elasticity of demand:

The interpretation is simple. A one percent increase in price will cause quantity demanded to fall by 0.1364 percent. At a price of $20, demand is *inelastic* because the absolute value of the elasticity is less than 1.0.

Now consider the same demand curve at a different price:

At the higher price, demand has become *elastic* because the absolute value of elasticity is greater than 1.0. At this price, quantity demanded is very responsive to price changes. A one percent increase in price will cause quantity demanded to fall by 1.5 percent.

Note that the sign of the coefficient of price in the demand curve is negative. This is consistent with the first law of demand: holding everything else constant, at a higher price, buyers will purchase less of any product. In other words, demand curves slope downward. And the slope of any demand curve is negative.[6]

Similar calculations apply to the price elasticity of supply. Since supply curves slope upward, supply elasticity will be a positive number.

Naturally, economists calculate elasticity a bit differently. We like to use the point elasticity of demand. That means we need calculus:

You may have noticed something about the two previous examples. Even though the demand curve is a straight line (linear) the elasticity changes as the price and quantity change. Elasticity is not the same as the slope of the demand curve. For that reason, economists often use a constant elasticity demand curve formulation:

## Elasticity and Medical Devices

So let’s use the constant elasticity formulation for convenience. Assume a price elasticity of demand of -0.5 and a price elasticity of supply of +1.[7] Given P = $150,000 and Q = 7,187, we can figure out the constant terms in the demand and supply curves, giving us:

Be patient: we’ll use these equations in just a minute. But it will be easier to start with linear equations:

The linear demand and supply curves are carefully constructed so that at the equilibrium price and quantity (P = $150,000 and Q = 7,289.85) the price elasticity of demand is -0.5 and the supply elasticity is +1.0. (The accompanying Excel workbook calculates both elasticities at each point on the linear demand and supply curves.)

### Simple Supply – Demand Models

Using historical data and some assumptions, I’ve guesstimated supply and demand models using both linear and constant-elasticity formulations. The linear model is constructed to guarantee that, at the market equilibrium, demand and supply elasticities will be -0.5 and +1.0 respectively.

The linear and nonlinear models looks like this:

With the tax, the implied quantity is 7,131.90. Here’s what it looks like for both models. (The nonlinear model appears to be linear because the horizontal and vertical axes have been zoomed.)

### Welfare Loss

The welfare loss is the area of the triangle bounded by the supply curve, the demand curve, and the vertical line that shows the quantity with the tax. Economists call this the *deadweight loss* created by the tax. It’s a widely-used measure of the inefficiency created by taxes, subsidies, and externalities. Using the linear model, the deadweight loss is $95,060.90. With the constant-elasticity model the deadweight loss is $781,431.81. (I used a somewhat non-standard method of numerical integration to calculate this number. The Excel workbook also shows the result using the more common formulation. The deadweight loss is about $5,000 greater using that method.)

## The Incidence of the Medical Device Tax

So who pays the tax? Let’s begin with a simple example using the linear supply and demand curves developed above. We’ll also begin by treating the tax as if it was a specific tax, equal to 2.3 percent of $150,000 or $3,450.23 per CT scanner. The idea is to find the quantity at which the difference between the demand price and the supply price is equal to the size of the tax. The graphs above illustrate this for our CT scanners.

Using a little algebra, we can determine that the quantity will be 7,131.90 units (the horizontal intercept of the green vertical line in the above graphs). Using the linear model, the demand price will be $152,300.16 and the supply price $148,849.92. Given the equilibrium price of $150,000, the amount of the tax paid by buyers will be $152,300.16 − $150,000 = $2,300.16. Sellers will pay $150,000 − $148,849.92 = $1,150.08. And the total payment will equal the amount of the tax. The deadweight loss will cost consumers $63,373.93 and the cost to sellers will be $31,686.97.

You may have noticed something about this example. Buyers will pay 2/3 of the tax and sellers will pay the other 1/3. The incidence of the tax that falls on consumers is equal to

where η is the price elasticity of supply and ε is the price elasticity of demand. The remaining 1/3 is, of course, paid by the seller.

This leads us to a very important result of economic analysis: it does not matter whether the tax is actually paid by buyers or sellers. The incidence only depends on elasticities, not who actually makes the payment.

“But,” the reader wonders, “can it really be that simple? What about the nonlinear constant elasticity forms of the demand and supply curves?”

It turns out it does not matter. The only things that determine the incidence of a tax are the elasticities of supply and demand. Below is a graph that may be persuasive. Note that the demand and supply prices are the same as in the linear case.

### A Generalization to Medical Devices

Now that we’ve seen that elasticities are the only things that matter, we can extend this to the entire category of medical devices covered by PACA. We will continue to assume the price elasticity of demand is -0.5 and the supply elasticity is +1.0.

As noted earlier, the average spending on covered medical devices from 2006 to 2010 was $26,202.7 million. Further, while this amount fluctuates from year to year, there is no statistical trend over those five years. Let’s assume this amount is 2013 spending. With a tax rate of 2.3%, the total tax collected will be $602.7 million. We can predict that 2/3 of that amount ($401.8 million) and sellers will pay the other 1/3 ($200.9 million). The statement that “the tax will just be passed along to buyers” is patently false.

## A Quick Look at the Long Run

Present and past members of Congress and the Executive branch have succeeded in pretty much destroying the U.S. candy manufacturing industry. Restrictions on U.S. sugar imports keep the U.S. price of sugar about twice the world price. The candy industry uses a lot of sugar. Therefore, since under NAFTA they cannot trans-ship sugar through Mexico or Canada, they are moving production and jobs to those two countries. Buy the sugar at world prices, transform it into candy and export the candy to the U.S. Simple, huh?

The point of that example is simple: people and businesses respond to incentives. I predict a surge in hospitals and clinics just south of the U.S. – Mexico border. These places will house very expensive medical devices. Medical tourism will expand a great deal, at least among those who can afford it. (This won’t happen in Canada because in that country it’s illegal for individuals to pay for healthcare.)

“But,” you ask, “a 2.3 percent tax isn’t all that much.”

You should get a job in Washington, D.C. if you believe that. Remember, the tax on a single CT scanner is almost $25,000. A positron emission tomography (PET) scanner runs upwards of $8 million,[8] generating a tax of nearly $200,000.

And, of course, as the clinics move the jobs will go with them. And wealthy people will be able to get their high-end treatments immediately in Mexico while those not so well off will be treated under ObamaCare.

## References

Arnold, C. (2012), National Public Radio, Morning Edition, July 2, 2012. Transcript and audio available at http://www.npr.org/2012/07/02/156096945/sales-tax-in-health-law-targets-medical-devices accessed July 3, 2012.

CT scanner prices from

http://www.absolutemed.com/Medical-Equipment/CT-Scanners-Systems. Accessed July 3, 2012.

Ketsche, P.E., E.K. Adams, S. Wallace, V. D. Kannan, and H. Kannan (2011). “Lower-Income Families Pay A Higher Share Of Income Toward National Health Care Spending Than Higher-Income Families Do.” Health Affairs, September 2011 30:1637-1646; doi: 10.1377/hlthaff.2010.0712.

Pertile, P., E. Torri, L. Flor, and S. Tardivo (2009). “The timing of adoption of positron emission tomography: a real options approach.” Health Care Management Science 12:217-227 DO I 10.1 007/s 1 072(HJ08-9085-4

U.S. Bureau of the Census:

“MA334S – Electromedical and Irradiation Equipment” (2005, available at http://www.census.gov/cir/www/334/ma334s.html. Accessed July 4, 2012.)

“MA334A – Electromedical Equipment and Analytical Instruments” (2009 and 2010, available at http://www.census.gov/manufacturing/cir/historical_data/ma334a/index.html, Accessed July 6, 2012.)

U.S. Internal Revenue Service (2012). REG-113770-10, “Notice of Proposed Rulemaking and Notice of Public Hearing Taxable Medical Devices.” Available at http://www.irs.gov/irb/2012-13_IRB/ar12.html. Accessed July 7, 2102.

[1] Statement by NPR reporter Chris Arnold. National Public Radio, Morning Edition, July 2, 2012. Transcript and audio available at http://www.npr.org/2012/07/02/156096945/sales-tax-in-health-law-targets-medical-devices

accessed July 3, 2012.

[2] *Ibid*.

[3] “Lower-Income Families Pay A Higher Share Of Income Toward National Health Care Spending Than Higher-Income Families Do.” Patricia Ketsche, E. Kathleen Adams, Sally Wallace, Viji Diane Kannan, and Harini Kannan. Health Affairs, September 2011 30:1637-1646; doi: 10.1377/hlthaff.2010.0712.

[4] If you’re thinking that 2.3 percent isn’t all that much, it can be the difference between life and death for a startup company. Especially when entrepreneurial mobility is available. There is no law stating that medical entrepreneurs must develop their ideas in the U.S.

[5] http://www.absolutemed.com/Medical-Equipment/CT-Scanners-Systems accessed July 3, 2012.

[6] People often believe the first law of demand is derived from pure mathematics. In fact, using nothing but math and the standard assumptions about consumer behavior, you cannot prove demand curves slope downward. The first law of demand is based on the millions of demand curves estimated statistically from real world data. This is the empirical part of economics called econometrics. It is a good part of what economists do in practice.

[7] If you don’t like my elasticity assumptions, download the Excel workbook and fiddle with them yourself.

[8] The price of a PET scanner is incredibly difficult to find. I used the figure in Pertile, P., E. Torri, L. Flor, and S. Tardivo (2009), Table 1. This data is the last worksheet in the Excel workbook. If you can find a better number, use it — and be sure to let me know what it is and where the heck you found it.

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Phil AtioLooking at this calculation…

2.3 percent of $150,000 or $24,796.82 per CT scanner

Are you sure this is correct?