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.