In brief: when wages are pushed up in ‘essential’ sectors, the cost of those sectors goes up as a share of people’s income. This can be difficult. Baumol identified one ‘cost disease’ which can drive this effect. Could increasing prevalence and share of income from investments (often alongside labour) have a similar cost-inflating effect?
Disclaimer: I am not an economist.
Baumol’s original cost disease
Baumol’s ‘cost disease’ is a tricky phenomenon in advanced economies. As we improve the efficiency of formerly labour-intensive processes (like agriculture), they diminish as a share of overall activity (no need to employ all those peasants any more)… but they push up wages in other sectors which have not been so automated (like healthcare), making those other sectors more expensive as a share of incomes.
Why does the wage push up happen? The efficient industries, where workers’ activities are highly productive, must pay far more than previously (consider a modern farmer vs a downtrodden serf), and this new level represents a higher ‘best alternative’ for workers in the less productive sectors (why be a poorly-paid doctor when you could be a well-paid farmer?). Thus the less productive sectors can find workers only at higher wage costs than previously — even if the work and output are essentially identical.
This would be mostly fine (after all, everyone is getting paid more, so they can afford more) except when the less productive sectors are closer to the ‘necessity’ end of the commodity-necessity spectrum, and difficult to substitute with other goods. (If I can’t afford healthcare, it’s little consolation that I could buy mountains of bread.) [1] This tension is a driver of much policy challenge in developed economies.
A ‘cost of capitalists’ disease?
One way of looking at Baumol is to note that it arises because it’s harder (more expensive) to incentivise people to do the important scarce work. Are there (or could there be) other forces in this direction?
In the early days of capitalism and the later industrial revolution, there was a fairly clean role distinction between capitalists, those whose main income came from return on investment (or rent), and workers, those whose main income came from wages paid for work.
Today, gradually, many who work for wages also have passive income from interest and investments as well as the expected lifetime income from (state and private) pensions. For most workers in developed economies, these are an appreciable, though not yet remotely dominant, source of lifetime income. Looking forward, barring radical upsets or increased concentration of income [2] , we might expect a trend where eventually most or all people are capitalists in this sense, deriving income from ownership of (shares in) automated production (or perhaps in some cases from de-facto shares via political rights to a universal minimal income of some kind).
It’s widely known that with a higher baseline income, we’re marginally less incentivised by further offers of income: $1000 extra looks a lot when your current income is $500, and less when it’s $500k. [3] Could an increasing prevalence and share of income from investments similarly make it difficult to animate labour across tasks where it’s important?
I haven’t thought through where the overall equilibrium might land here: perhaps this effect is matched or beaten by rising incomes or by increased productivity from automation. (Another reason to not care might be that the trajectory toward the ‘fully automated luxury communism’ of widespread investment income seems too far fetched — a valid rebuttal, even if empirically we’ve moved some small part of the way in that direction.)
I’d love economically-minded people to weigh in here.
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For better or worse, some things which are more substitutable, but which haven’t seen labour productivity increases, such as live classical music, are simply consumed less (at much greater expense): we often choose more scaled alternatives like TV, streaming, or cinema instead.
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I don’t consider these at all out of the question, but for this discussion I bracket them out.
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I’m unclear how strong this effect is: some evidence shows that windfalls decrease propensity for work (a short term, localised effect), but clearly over the decades as societies get enormously richer we still mostly work many hours weekly for many decades of life (demonstrating a relatively weak longer term or generalised effect). This might be explained by relative wealth and positional goods.
Interesting question! As @harsimony alluded to, there are opposing effects here: increasing returns to capital may reduce labor supplied as people shift toward leisure, but increasingly scarce labor pushes wages up and pushes interest rates down, causing people to shift away from leisure toward labor. Let’s see how these competing effects play out in a simple macroeconomic model. The TLDR is that, in the simple model below, the two effects exactly cancel.
Suppose there is a competitive economy with production function F(K,L)=AKαL1−α, and a representative agent with utility function U(C,L)=Cβ(Lmax−L)1−β where C is consumption, L is labor, K is capital, w is the wage, and r is the rental rate of capital (a.k.a. the interest rate). Note that the representative agent values both consumption and leisure (where leisure is Lmax−L). Labor supplied is the function L(w,r) that maximizes U under the constraint C=wL+rK (this just says that the agent consumes all income, and we’ll neglect savings for simplicity). The labor supply that solves this maximization problem is
L(w,r)=βLmax−(1−β)rKw
Exactly as you suggested in your question, Oly, L is decreasing in returns to capital rK. In other words, if wage is held fixed, people work less when they have more passive income rK. However, L is increasing in w (as long as people have at least some passive income, otherwise L is independent of w). Now let’s ask, as K increases through capital accumulation, will workers work more or less?
In equilibrium, w=∂LF(K,L)=(1−α)A(K/L)α and r=∂KF(K,L)=αA(L/K)1−α. Now we have a system of three equations (these two equations and the labor supply above) and, for fixed K, three unknowns (w,r,L). The equilibrium labor, L∗, that solves this system is
L∗=(1−α)β1−αβLmax
The equilibrium labor is independent of capital stock K! Hence, in this simple model, the two opposing effects exactly cancel: workers work a constant amount as their passive income from capital increases.
It’s certainly also true that one could write down a different model where these two effects don’t exactly cancel, and it’s possible you could cook up a model where something really pathological happens (perhaps where workers work so much less as their passive income increases that total output goes down?). But I think the simple model above is a good baseline for what to expect.
This is great! A good concrete operationalisation.
I think this is tacitly assuming that capital ownership/income is already uniformly distributed across all workers, so the only exogenous variable is the capital accumulation. That’s addressing part of the question quite nicely—though I was also wondering about the changing distribution (and prevalence) of capital ownership. I don’t think this single representative agent is what cashes out if we imagine that distribution changing...? But it’s a nice illustration of some kind of ‘universal ownership’ endpoint.
I’m also not sure of the Cobb-Douglasness of utility on consumption and leisure inputs! This seems to imply that, for a given leisure allowance, utility grows faster in consumption than I’m given to believe it does in practice. It’s super interesting that things cancel out in this case, though. That said, it’s an equivalent maximisation to treating utility as logarithmic in consumption plus logarithmic in leisure, which is not crazy.
This gives me some great inspiration if I want to come back to this and look at more modelling variations. Thanks,
You’re right that the result could change if there were heterogeneous agents with an uneven distribution of capital. However, the model above can be reformulated to include an uneven distribution of capital, and the result remains mostly the same. Specifically, suppose that instead of the representative agent, there were N agents with identical preferences (the same utility function as above) but different capital allocations Ki. Then, total labor supply (the sum of all agents’ labor supplies) would be
L(w,r)=βNLmax−(1−β)r∑iKiw
This leads to an equivalent result for total labor supplied: L∗=(1−α)β1−αβNLmax. So the model still predicts that total labor supplied is independent of the capital stock, regardless of how capital is distributed. But, how much each agent contributes to that total labor supply does depend on the distribution of capital. If the distribution of capital changes, agents who gain a larger share of total capital will work less than before, and those whose share of total capital falls will work more than before.
You’re totally right, the representative agent actually was representative! So (unsurprisingly) this directs attention to how capital ownership might be distributed between (workers over different) sectors.
I noticed something funny about the optimal L: it’s negative if wages are sufficiently dwarfed by capital interest. But this makes sense: if they could, these workers would buy more time in the day for leisure by sacrificing some income.
I’d guess (haven’t mathed it through though) that general CES utility and production functions don’t produce this independence of total labour on total capital, and that this is a special Cobb-Douglass case. But it’s also not totally implausible. (After all, indeed humans have tended to work a lot on the whole throughout the last century or two of unprecedented capital accumulation, despite Keynes’ predictions.)
Good point about workers preferring negative L when they have a high passive income!
I think you’re right about using a CES utility function. My guess would be that for an elasticity of substitution (between consumption and leisure) less than 1, the equilibrium L∗ would go down as rK goes up (and vice versa for an elasticity greater than 1). I actually can’t decide whether I’d predict most people’s elasticity to be more or less than 1. A complicating factor, which you mentioned in your footnote 3, is that people’s preferences for wealth are highly influenced by the people around them (both by the wealth of those around them, and by the culture). I’ve always wanted to explore the economic consequences of this—my intuition is that it messes up all the classic “welfare theorems” in economics.
Right, I think positional goods and the like are among several distortions of the basic premises of the welfare theorems (and indeed empirically many people are sad, lonely, etc. in our modern world of abundance) - I sometimes think those theorems imply a sort of normative ‘well, just don’t worry about other people’s stuff!’ (i.e. non-envy, which is, after all, a deadly sin). cf Paretotopia, which makes exactly this normative case in the AI futurism frame.
Definitely agree! The “don’t worry about other people’s stuff” argument gets thrown around a lot, and is often assumed to be equivalent to “don’t be envious”, but I think that argument actually contains a logical mistake. Suppose person A doesn’t care directly about their relative wealth (i.e. their utility function is independent of their relative wealth), but their utility function depends on their interactions with other people (such as friendships, job interviews, etc) and those other people interact with person A in a way that depends on person A’s relative wealth. Then, it can be instrumentally useful for person A to increase their relative wealth despite their utility function being independent of relative wealth! So person A has no envy, but their utility is (indirectly) affected by their relative wealth.
Well, why do we envy? Evopsych just-so story says that, of course, others having much impinges on me whether I want it to or not (my security/precarity, liberty, relative success in interactive situations, …).
I think you can express that in a ‘goods’ framing by glossing it as the consumption of ‘status and interactive goods’ or something like that (but noting that these are positional and contingent on the wider playing field, which the bog standard welfare theorem utility functions aren’t).
I think this is a real phenomenon, although I don’t think the best point of comparison is the Baumol effect. The Baumol effect is all about the differential impact on different sectors, wheras this would be a kind of universal effect where it’s harder to use money to motivate people to work, once they already have a lot of money.
I think a closer point of comparison is simply the high labor costs in rich first-world nations, compared to low labor costs in third-world nations. You can get a haircut or eat a nice meal in India for a tiny fraction of what it costs to buy a similar service in the USA. Partly you could say this is due to a Baumol effect of a sort, where the people in the USA have more productive alternative jobs they could be working, because they’re living in a rich country with lots of capital, educated workers, well-run firms, etc. But maybe another part of the equation is that even barbers and cooks in the USA are pretty rich by global standards?
As a person becomes richer, it’s perfectly sensible IMO for them to become less willing to do various menial tasks for low pay. But of course there are still some menial tasks that must get done! Imagine a society much richer than ours—everyone is the equivalent of today’s multimillionares (in the sense that they can easily afford lots of high-quality mass-manufactured goods—they own a big home, plus a few vacation homes, a couple of cars, they can afford to fly all over the world by jet, etc), and many people are the equivalent of billionaires / trillionaires. This society would be awesome, but it would’t really be quite as rich as it seems at first glance, because people would still have to perform a bunch of service tasks; we couldn’t ALL be retired all the time. I suppose you could just go full-Baumol and pay people exorbitant CEO-wages just to flip burgers at mcdonalds. But in real life society would probably settle on a mix of strategies:
Making jobs more enjoyable, so people /want/ to do them more, and you don’t have to pay them so much to incentivize them. Things like providing a comfortable work environment, trying to have a positive social vibe in the workplace, finding ways to make the work more fun or satisfying than it would normally be (even if this comes at some cost to efficiency).
Trying to “pay people” in appreciation and (ever-scarce) social status instead of (abundant, ineffective) cash where possible, et cetera. But of course, overall, social-status is somewhat of a zero-sum game, so idk how much juice you could squeeze there...
Trying to simply minimize the amount of unnecessary service work—lots more automation wherever it’s feasible, even in situations where this creates a slightly downgraded experience for the consumer.
And then, indeed, just paying people a ton more.
I think strategies like these are already at work when you look at the difference between poor vs rich nations—jobs in rich countries not only pay more but are also generally more automated, have better working conditions, etc. It’s funny to imagine how the future might be WAY further in the rich-world direction than even today’s rich world, since it seems so unbalanced to us (just like how paying 30% of GDP for healthcare would’ve seemed absurd to preindustrial / pre-Baumol-effect societies). But it’ll probably happen!
It sounds like a real phenomenon, but I have trouble imagining a scenario where it’s important. I expect demand for human labor to decline faster than the number of people with investment income rises. That probably means declining wages for the median person, although maybe rising wages for a small number of people with unusual skills.