Two Economists and $200 of GDP
What a joke about economists dumping trash gets right and wrong about GDP
The joke goes like this:
Two economists are out for a walk when Alice offers Bob $100 to let her tip a bucket of household rubbish over him. Bob agrees. A little later, Bob offers Alice $100 to return the favor. Now both are covered in trash, and the same bill has changed hands twice.
Alice looks at the soggy mess and says, “We have the same hundred dollars between us as before, plus two ruined outfits. That hardly seems like progress.”
Bob grins: “Two paid services. GDP is up by $200.”
The situation is told as a demonstration that GDP can rise while nobody appears better off, but in my opinion it is misleading.
A deal both sides agreed to
Consider the initial proposal Alice makes to Bob. Specifically, Alice offers $100 in exchange for Bob letting her pour the garbage over him. Assuming Alice to be rational, this implies that she believes she would get at least $100 of utility from the comedic sight. From here, Bob accepts the deal. Assuming Bob to be rational this time, we have that the displeasure from being covered in garbage cannot exceed $100 since Bob participates voluntarily for that amount. So after this moment, Alice loses $100 but gains over $100 in utility from Bob's humiliation. Bob on the other hand gains $100 and the humiliation he faces is not worth more than $100 to him. This means that the transaction genuinely did increase utility overall!
The same argument follows in the reverse direction. By the end of both exchanges, it genuinely does make sense to say the GDP increased by $200 because of the two transactions of $100 each and both individuals are better off than they were before since their entertainment from seeing the other outweighs their own humiliation.
GDP != utility
Even still, this example highlights some of the problems with using GDP as a measure. GDP records market production at prices but fails to measure how much satisfaction, or utility, people get from it.
Let's give labels to the utility (as measured in dollars) that Alice gains from watching Bob as \(A_p\) and the utility lost by Bob from wearing the trash as \(B_n\). For the inverse transaction, we similarly have \(B_p\) and \(A_n\). By virtue of the transaction size being $100, we have that \(A_p, B_p \ge 100\) and that \(A_n, B_n \le 100\). The total utility of society changes by \(A_p + B_p - A_n - B_n\). Moreover since \(A_n \le 100 \le A_p\) and \(B_n \le 100 \le B_p\), the societal utility increases. But importantly, the amount it increases may not be $200, it could be less or more depending on these exact values.
So the economists may or may not have received more than $100 of value apiece from each deal. Watching your friend put on garbage could be priceless or worth exactly $100. We cannot infer the precise amount from the transaction price, only that $100 is a lower bound. Ultimately, while utility is in some sense the end game that we want to optimize for, we must resort to measures like GDP as proxies since it is not observable in absolute terms (note that GDP does have other uses apart from being a proxy of consumer utility).
Consumer surplus
Internalizing this distinction becomes quite illustrative in common economic scenarios. For instance, GDP per person is helpful for comparing the scale of market production between two economies, but prices and incomes do not tell us exactly how much people value what they consume. GDP adjusted for purchasing-power parity (GDP at PPP) accounts for differences in the prices of comparable goods and services across countries (i.e. cost of living). This is better way to compare consumer wellbeing between countries, with the high-level idea being that a person buying a e.g. banana for $2 in one country and $0.3 in another should roughly get the same amount of utility.
If you just look at the nominal GDP of a banana transaction ($2 vs $0.3), then it would seem that the first country is doing a lot better despite the same physical goods being transacted. The fundamental flaw is that GDP fails to capture consumer surplus, defined as the consumer utility gained from a transaction minus the cost they paid for it, so it may reward higher cost goods with lower consumer surplus. GDP at PPP doens't capture consumer surplus either, but it helps normalizes the scale between different economies so that we can better compare them.
What if they just swapped cash?
Let's change the structure of the original deal slightly. Alice and Bob now agree to each dump a bucket of household rubbish over themselves, and to pass the same $100 back and forth as part of the arrangement. The point is that we have one atomic transaction instead of the two before, although the GDP still increases by $200.
Here, we cannot conclude any relationship between the utility Alice receives and the $100 she pays because the entertainment value she receives is _conflated_ with the raw $100 she is being paid. However, we can still conclude that for both participants, the entertainment is still greater than the embarrassment because they agree, but we just cannot compare it to being above or below $100.
In this scenario, the GDP can increase by an amount fully independent of the increase in utility; it genuinely is as if the monetary transaction never happened and more akin to the net-zero balance transfer the original joke attempts to portray.
Generalizations
There are other irregularities with GDP (e.g. how a worker marrying his cleaner decreases GDP despite everyone being better off), but I think this perspective of relating GDP, voluntary atomic transactions, and utility gives a general framework on being able to identify those discrepancies and fundamentally why they are occurring.