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# The Noise-to-Signal Ratio as a Metaphor for Deadweight Loss from Taxes

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The NSR, which many people understand more intuitively from physics, sheds light on the DWL in economics. As I explain below, while the NSR does not literally meet the Mankiw challenge, it does come close: it illustrates that each tax increase hurts economic efficiency more than the previous one.
This is a key paragraph from the January Econlib Feature Article "The Noise-to-signal Ratio as a Metaphor for the Deadweight Loss of Taxes." The article is by Cyril Morong, who teaches economics at San Antonio College in San Antonio, Texas.

Another key paragraph:

A basic insight from economics is that prices are signals that reveal the value or scarcity of resources; this helps people use them efficiently. But taxes can be seen as the noise that distorts that signal. The more distorted the signal, the less efficient prices become in allocating resources. As I show in the accompanying graphs, when a per unit tax is placed on a good, the price the sellers receive (that is, the amount they get to keep after they pay the tax to the government) falls while the price the consumers pay rises. This tax "wedge" distorts the market because it causes buyers and sellers to face two different prices for the same item: the buyer pays the price gross of tax while the seller receives a price that is net of tax. The larger this tax wedge, the greater is the distortion. In my metaphor, the greater is the noise. If you are listening to the radio and start hearing noise or static, the signal starts to lose its value. Eventually, the noise overwhelms the signal, and there is no longer a reason to listen since the NSR is so high. The same thing happens with taxes: as the NSR rises, the DWL rises at a similar rate. Thus, the NSR helps illustrate how rising taxes increasingly damage economic efficiency.

Take a look at the article, especially Figures 3 and 4, to see how closely NSR tracks DWL.

CATEGORIES: Taxation

Thaomas writes:

This is true of a single tax along a single dimension if, by assumption, the optimum is zero. It does not apply to taxation of externalities. It is best applied to substituting one tax for another, say a progressive consumption tax for a capped tax on wages or for a business income tax. Nor, of course, does it address the larger issue of whether the dead weight loss (if any) is greater than the benefits of the expenditures the tax finances/deficit not incurred.

This is a good example of "economism," an Econ. 101 concept that, though valid, is of some but limited use in actual policy making.

MikeP writes:
Both DWL and NSR show a similar, exponential, pattern of how rising taxes hurt economic efficiency.

Actually, neither is exponential. DWL is quadratic, and NSR is asymptotic -- t/(11-t) -- going to infinity at 11.

Figures 3 and 4 are drawn with different x-axes. In particular, Figure 3 doesn't reach out to a tax rate of .91 like Figure 4 does. If it did, it would post a 10 on the y-axis, 5 times above the scale of the figure, and most of the curve would be squished on the bottom of the graph.

To be sure, tax rates that high are ridiculously distorting, so we needn't expect the NSR metaphor to be accurate as the ratio of tax versus net price goes to infinity.

David R. Henderson writes:

@MikeP,
Actually, neither is exponential.
Youâ€™re absolutely right. As a math major, I should have caught that. The author, it turns out, was using the term colloquially. He and I have come up with a fix that will appear in the piece tomorrow a.m. My apology.

MikeP writes:

I understand the colloquialism. The "exponential" just caught my eye because exponentials are so meaningful in economics while being generated by processes unlike the math in this article.

But even outside of economics, I am often caught yelling at the radio when I hear that something is growing exponentially when it isn't.