Marshall's Second Law of Demand

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Economists love “laws.” We've got laws of demand, laws of supply, laws of diminishing marginal utility, Say’s Law, Gresham's Law, Law of Comparative Advantage, and more. None of them are actually laws, but that’s beside the point.

Did you know there is a Second Law of Demand?

Actually, there are many second laws of demand. Economists aren’t great at keeping consistent terms…. I usually use Alchian and Allen’s definition: "In the long run, demand is more elastic for any given good as substitutes for that good become more readily apparent and available." I like that because it gives us a natural way to think of demand curves changing through time, allowing us to make predictions, say about inflation, since we know more about the slopes than just their direction.

But that’s not the second law I want to focus on today.

Alfred Marshall—pretty important for the development of the First Law of Demand—also suggested that demand curves have more structure than just being downward sloping. In particular, Marshall wrote, “The elasticity of demand is great for high prices, and great, or at least considerable, for medium prices; but it declines as the price falls; and gradually fades away if the fall goes so far that satiety level is reached.”1

Recently, people in the trade literature started to call this Marshall's Second Law of Demand. I don’t know why. It’s definitely not the first law. And it is not to be confused with any of the four laws Bronfenbrenner pulls out of Marshall. They call it the Marshall’s Second Law of Demand. Don’t blame me.

What’s the idea? Imagine the price of a good rises. Marshall's First Law says the quantity will drop. Duh. Marshall’s Second Law says the quantity demanded will drop more drastically at higher prices—consumers are more prone to substitute as prices rise.

Or we can think of it in the opposite direction. Flipped around, the claim is that “the price elasticity of demand falls with quantity consumed.” Be careful, though. This can be tricky to visualize since elasticity is not slope, so I won’t draw any graphs.

The reason international trade has picked up on Marshall's old theory is that it has modern relevance for patterns of trade and competition. First, let’s think about one of my favorite topics: markups. In the Econ 101 “monopoly” model, markups depend on the elasticity of demand facing a firm. With perfectly elastic residual demand, there is no markup. As elasticity declines, markups rise. Many models in trade/macro/IO start from each firm having a residual demand curves with a constant elasticity. Unfortunately, that implies that all firms charge the same markup, since everywhere on the demand has the same elasticity.

If we break out of constant elasticity and bring back Marshall’s Second Law into trade models, it generates two empirically consistent predictions:

First, more productive, lower-cost firms will charge higher markups. Here, Marshall’s Second Law suggests low-cost firms charge higher markups because they are further down the demand curve to the less elastic portion. Their greater efficiency allows them to profitably undercut rivals, even with the higher markups. Rather than strictly market power, these markups likely reflect unobserved performance differences that benefit consumers through lower prices. This is why I’ve argued we should not presume higher markups automatically imply worse outcomes, especially if they stem from unobserved productivity advantages. Do we want firms to be to the left on the demand curve with less production and lower output? Obviously not!

Second, as I've argued before, tougher competition can actually increase concentration by redistributing sales to the most efficient firms. This insight from the trade literature that opening markets reallocates shares to more productive exporters provides a specific example.

Marshall’s Second Law of Demand captures this feature too. Lower trade barriers make markets more contestable, acting as greater competition. Increased competition reduces profits for all firms by lowering markups in an industry. However, Marshall’s Second Law predicts that more efficient, lower-cost producers will maintain higher markups and profits than less efficient rivals. When competitive pressures force markups down, efficient firms’ margins remain higher than inefficient firms’ already lower markups. So while industry profits decline overall, productive firms can better withstand competition with their markup advantage.

This explains the productivity-enhancing reallocations under tougher competition predicted by Marshall’s Second Law. Competition squeezes less efficient firms who cannot stay profitable with lower markups, while productive firms gain share as their still-higher margins allow them to endure competitive pressures. The path to growth under greater competition is to become more efficient.

Both patterns (higher markups for higher productivity firms and competition reallocating production toward more efficient firms) show up in real-world data.

So incorporating Marshall's Second Law into trade theory helps explain observed facts: (1) variable markups tied to productivity, (2) productivity-enhancing reallocations after opening up trade. The simplest models with constant markups cannot generate these predictions - they fix sales shares regardless of trade integration.

What does this have to do with Marshall, besides one quote? I don’t know. Not much?

But I’ll always argue that there are old ideas that remain relevant. Marshall gave us more than just a downward-sloping demand curve, and those ideas provide insights into how opening up trade shapes prices, markups, and firm/industry performance - often in ways that enhance productivity. Again, markups may be residuals indicating unobserved factors, not inherently bad!