Alfred Marshall’s derivation of ‘consumer surplus’ in his book ‘Principles of Economics’, was one of the first attempts by economists to measure the effect of prices on people’s welfare. It also relied on a set of unrealistic assumptions, which raised much controversy among economists back in the time.
Picture of Alfred Marshall
Marshallian consumer surplus – what is it?
When Marshall first published his book ‘Principles of Economics’ in 1890, one of his aims was to provide a general approach for measuring how much people ‘truly’ value the goods they purchase. After all, the price of a good itself often isn’t a great measure of value. I could buy a car for £15,000, for example, while I would still get it for £20,000. In this scenario, according to Marshall’s thinking, not only am I buying the car, but I also earn another £5,000 of “surplus satisfaction”, which is my ‘consumer surplus’. In other words, my consumer surplus is the extra money I saved by paying less than how much I ‘truly’ value the car.
Marshall develops his argument further by incorporating in his analysis a consumer’s demand function. Let’s assume, for example, that one chooses the number of plain T-shirts they buy according to Figure 1 below (i.e. they buy one T-shirt if it costs £15, two if they cost £12 each, three if they cost £9 each, etc.). And let’s assume a T-shirt costs £12, which means they would buy two T-shirts. To estimate the consumer’s consumer surplus in this scenario, Marshall roughly uses the following method:
We already know they would buy one T-shirt even if it cost £15, which implies they value it at £15. Given that they paid £12 for this T-shirt, this suggests that they have a ‘surplus satisfaction’ of £3 from the purchase of the first T-shirt (£15 - £12 = £3).
We also know they wouldn’t buy a second T-shirt if the price was £15, which means they value it less than £15. After all, the more T-shirts they have already, the less they value any new ones (diminishing marginal utility of consumption). And since they would buy a second T-shirt if it cost £12, then they value it at £12, which suggests they get no consumer surplus from this purchase (£12 - £12 = £0).
Consequently, their total consumer surplus from buying the two T-shirts is £3 (£3 + £0).
Figure 1: A consumer’s demand function for T-shirts
Illustration by Bonsai Economics.
The constant marginal utility of money assumption
While Marshall’s consumer surplus can initially impress with the simplicity of its logic, it relies on a variety of assumptions. One of the most contentious ones is that people’s wealth doesn’t affect the amount of goods they purchase (or, in formal terms, that the marginal utility of money is constant).
To illustrate why Marshall’s theory needs this assumption, let’s go back to the T-shirt example, and assume that the consumer doesn’t face a single price for T-shirts. Instead, the first T-shirt always costs £15, and only after they have bought it, can they get the second one for £12. At first instance, one may conclude that the person would still buy the two T-shirts. After all, as it was argued before, the consumer values the first one at £15, and the second one at £12. But in the real world, this needn’t be the case. In this second scenario, a person needs to spend more money to buy the first T-shirt (£15 instead of £12), which could make them choose against buying the second one for £12. In other words, the only reason the consumer would buy the second T-shirt with a common price of £12, was because the first one cost £12 as well. This example suggests that the consumer could actually value the second T-shirt less than £12, as they may choose not to buy it at this price.
The implication of the above scenario is that in order for Marshall’s consumer surplus to be meaningful, one needs to assume that a consumer’s wealth doesn’t affect their purchasing decisions (constant marginal utility of money assumption). In such a world, a consumer wouldn’t ever feel ‘poorer’, and they would always buy the second T-shirt for £12, even if the first one cost £15.
While Marshall defended his assumption on the grounds that his theory should only be used to analyse small purchases, for which one’s wealth shouldn’t matter much, it still attracted severe criticism at his time (see Dooley, 1983). And even if one were to agree that his theory holds for small purchases, this still limits tremendously the scope for applying his theory in real-world scenarios.
A breakthrough for Economics
Although Marshall’s theory of consumer surplus has many issues, several of which aren’t discussed in this post, it has been clearly very influential on the economics profession, as is evident from its popularity in Economics textbooks. What’s more, it has provided a fertile ground for later theories of consumer surplus, such as the Hicksian consumer surplus, which doesn’t assume a constant marginal utility of money.
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