Marshall discusses his Laws of Derived Demand in his Principles of Economics. Specifically, in Chapter VI of Book V.
Marshall listed four “conditions” that result in wage-inelastic derived demand for the corresponding factor of production:
“no good substitute being available at moderate price”
“stiff and inelastic” final demand
“small part of the expenses of production” (i.e., small factor-cost share)
Inelastic supply of other factors
Putting aside the fourth law, we can discuss the first three in the context of the Allen-Hicks formula for the own-price elasticity of derived demand, βii, in the two-factor case (see also Chicago Price Theory Chapter 11).
where si is good i’s share in factor cost, εD < 0 is the price-elasticity of demand for the final product, and σ > 0 is the elasticity of factor substitution. None of these parameters are necessarily constants; they may vary according to the factor allocation. Marshall’s first law can be understood as a comparative static with respect to σ in the direction of zero, holding constant si and εD. The second law can be understood as a comparative static with respect to εD holding constant si and σ. The debated third law is a comparative static with respect to the share parameter, with Hicks at least holding constant εD and σ.
ChatGPT confidently asserts that there are three Marshall’s Laws. Three is a fair count if we exclude the law that Hicks disputed. However, by that count, ChapGPT gets them 5/6 incorrect. Instead, it lists the definition of derived demand, followed by a statement about long versus short run. The third in its list is perhaps a combination of the disputed third law and the first law.
Mulligan: What are Marshall's Laws of Derived Demand?
ChatGPT: Marshall's Laws of Derived Demand are a set of principles that describe the relationship between the demand for a particular factor of production (such as labor) and the demand for the goods and services that factor helps produce. These laws were developed by economist Alfred Marshall in the late 19th century and are still widely studied and referenced today.
The three laws of derived demand are as follows:
The demand for a factor of production is derived from the demand for the product that the factor helps produce.
The demand for a factor of production is more elastic in the long run than in the short run.
The elasticity of demand for a factor of production depends on its importance in the production process and the availability of substitutes.
Taken together, these laws suggest that the demand for labor, for example, is ultimately determined by the demand for the goods and services that labor helps produce. In the short run, the demand for labor may be relatively inelastic because it can be difficult for firms to quickly adjust their production processes to changes in demand. However, in the long run, firms may be able to find substitutes for labor or change their production methods, making the demand for labor more elastic. The importance of labor in the production process also affects its elasticity of demand: if there are few substitutes for a particular type of labor, its demand may be relatively inelastic.
ChatGPT also confidently discusses the Hicks challenge but refers to a “law” that was not even one of the four.
Mulligan: Didn't Hicks show that Marshall was wrong about one of the laws?
ChatGPT: Yes, economist John Hicks challenged one of Marshall's laws of derived demand, specifically the second law, which states that the demand for a factor of production is more elastic in the long run than in the short run. Hicks argued that this law was not always true and that the elasticity of demand for a factor of production could depend on the specific circumstances.
Hicks pointed out that in some cases, the demand for a factor of production could be more elastic in the short run than in the long run. For example, if a firm has already made significant investments in a particular technology or capital equipment, it may be difficult for the firm to switch to a different production method or substitute other factors of production. In such cases, the demand for the factor of production may be relatively inelastic in the long run, while being more elastic in the short run as firms can adjust their inputs more easily.
Hicks’ critique of Marshall's second law suggests that the relationship between the demand for a factor of production and the goods and services it helps produce is complex and can vary depending on the specific circumstances of the market. Nonetheless, Marshall's laws of derived demand remain an important contribution to economic theory and continue to be studied and debated by economists today.
Next, I asked for sources. It got the books correct, which is pretty good for ChatGPT (famous for fabricating books and articles) but wrong chapters. It should be Marshall Book V, Chapter VI. Hicks’ second edition only has 11 chapters, although perhaps Chapter 12 can be understood as the material that follows Chapter 11 in which case “Chapter 12” is the correct part of the book.
Mulligan: Where did Marshall state the laws? Where did Hicks challenge one of the laws?
ChatGPT: Alfred Marshall first introduced his laws of derived demand in his seminal work "Principles of Economics," first published in 1890. Marshall's laws are discussed in Book V, Chapter III, where he discusses the theory of distribution and the demand for factors of production.
John Hicks challenged Marshall's second law in his 1932 book "The Theory of Wages." In the book, Hicks argues that the elasticity of demand for factors of production can depend on the specific production technology and market conditions. Hicks specifically critiques Marshall's assumption that the demand for a factor of production is always more elastic in the long run than in the short run. Hicks' critique is discussed in Chapter 12 of his book.
I disputed the citation of Chapter III, so it apologized [not shown here] and cited Chapter VI of Book IV, which purportedly discusses “Distribution of Produce” (the actual title is “Industrial Training”). More disputes produced more rounds of apology and fake references. It tended back to Book V, Chapter III (a famous chapter) but with a different fake chapter title at each iteration.
Cliff Clavin was the famous tavern know-it-all in Cheers. Perhaps Cliff is back, this time behind the curtain of AI spouting lots of jargon in grammatically correct but ignorant sentences. Is Norm somewhere back there too?
[image credit: https://television-b26f.kxcdn.com/wp-content/uploads/2020/08/Cheers-Cliff-Calvin-Screenshot-770x470.png]
