Artificial intelligence and the 'age of leisure'

My ECONS101 class covered constrained optimisation last week, and one of the models we looked at was the labour-leisure trade-off for workers. Now artificial intelligence, and in particular generative AI, is likely to have large impacts on the labour-leisure trade-off. As the Financial Times reported last year (paywalled):

The idea that technological progress can enable people to work fewer hours is not outlandish...

But in order to believe a similar trend is going to take hold again, you have to assume three things. First: that AI will deliver a substantial boost to economic productivity...

Second, you have to assume the economic gains will be widely distributed...

Third, you have to believe workers will “cash in” those proceeds in the form of extra leisure, rather than higher income. But will they? In many developed countries, there has been a slowdown in the reduction in working hours in recent decades...

Far from trading income for leisure, it is the people with the highest salaries who tend to work the longest hours.

Will workers trade off higher productivity for more leisure time? Are we about to enter an 'age of leisure'? The constrained optimisation model for the worker (see also this post) can help us clarify the possibilities. In this model, we'll assume that AI increases productivity, and that the increase in productivity is represented by higher wages for workers. [*] The model will then tell us whether workers might respond by consuming more, or less, leisure.

Our model of the worker's decision is outlined in the diagram below. The worker's decision is constrained by the amount of discretionary time available to them. Let's call this their time endowment, E. If they spent every hour of discretionary time on leisure, they would have E hours of leisure, but zero income. That is one end point of the worker's budget constraint, on the x-axis. The x-axis measures leisure time from left to right, but that means that it also measures work time (from right to left, because each one hour less leisure means one hour more of work). The difference between E and the number of leisure hours is the number of work hours. Next, if the worker spent every hour working, they would have zero leisure, but would have an income equal to W0*E (the wage, W0, multiplied by the whole time endowment, E). That is the other end point of the worker's budget constraint, on the y-axis. The worker's budget constraint joins up those two points, and has a slope that is equal to the wage (more correctly, it is equal to -W0, and it is negative because the budget constraint is downward sloping). The slope of the budget constraint represents the opportunity cost of leisure. Every hour the worker spends on leisure, they give up the wage of W0. Now, we represent the worker's preferences over leisure and consumption by indifference curves. The worker is trying to maximise their utility, which means that they are trying to get to the highest possible indifference curve that they can, while remaining within their budget constraint. The highest indifference curve they can reach on our diagram is I0. The worker's optimum is the bundle of leisure and consumption where their highest indifference curve meets the budget constraint. This is the bundle A, which contains leisure of L0 (and work hours equal to [E-L0]), and consumption of C0.

Now, let's say that the situation shown above is the situation before the advent of AI. After AI is introduced, productivity increases, and so wages increase (from W0 to W1). This causes the budget constraint to pivot outwards and become steeper (since the slope of the budget constraint is equal to the wage, the slope has increased from -W0 to -W1). The worker can now reach a higher indifference curve, and it is the position of that higher indifference curve that determines the worker's response in terms of whether they consume more leisure or not. If they move to the higher indifference curve I1, then the worker's new optimum is the bundle of leisure and consumption B, which contains leisure of L1 (and work hours equal to [E-L1]), and consumption of C1. For this worker (whose response is shown in red on the diagram), leisure hours decrease as a result of the higher wage. On the other hand, if they move to the higher indifference curve I2, then the worker's new optimum is the bundle of leisure and consumption C, which contains leisure of L2 (and work hours equal to [E-L2]), and consumption of C2. For this worker (whose response is shown in blue on the diagram), leisure hours increase as a result of the higher wage. [**]

Either of these possibilities could happen. In fact, both could happen, with some workers increasing leisure time and others decreasing leisure time. By itself, this model doesn't answer the question of what will happen, but shows that both increased leisure and decreased leisure are possible outcomes.

The key difference here comes down to the size of the income effect of the increase in wages. When wages increase, the opportunity cost of leisure increases. That makes leisure relatively more expensive, and workers should respond by consuming less leisure. That is what we call the substitution effect - workers substitute away from leisure as it becomes more expensive. However, increased wages also lead to an income effect. Leisure is a normal good, which means that as the worker's income increases, they would like to consume more leisure. Notice that the substitution effect and the income effect are working in opposite directions here. For workers who overall decrease their leisure, the substitution effect (which says they should consume less leisure) must be bigger than the income effect (which says they should consume more leisure). For workers who overall increase their leisure, the reverse is true - the substitution effect must be smaller than the income effect.

AI may lead us into an age of leisure. But only if productivity gains lead to higher wages, and the income effect of higher wages more than offsets the substitution effect.

*****

[*] The assumption that productivity gains will lead to higher wages is a strong assumption. Indeed, the FT article questions whether this assumption is valid. If productivity gains don't lead to higher wages, then this model doesn't help us evaluate whether we're about to move into an 'age of leisure', and the impacts might be more macroeconomic than microeconomic. That is, we may end up with leisure, but arising through weaker labour demand, reduced hours, or unemployment rather than through workers voluntarily choosing more leisure as wages increase.

[**] Notice that the indifference curves I1 and I2 are crossing, and indifference curves cannot cross. However, those two indifference curves are for different workers, so there is no problem. I could easily have drawn two different diagrams, one for each worker, but I've kept them both on the same diagram for efficiency.

This week in research #117

Here's what caught my eye in research over the past week:

• Zhang et al. find that Uber’s entry into a US city significantly reduces crime rates, with larger effects in areas facing greater liquidity constraints (less bank credit supply, fewer local job opportunities, higher personal bankruptcy risk, and greater household financial stress)
• Sandorf and Navrud (open access) establish convergent validity between a contingent valuation survey and a discrete choice experiment (meaning that both measures are highly correlated), with the example they use being willingness-to-pay to reduce the spread of invasive crabs in Norway
• Desierto and Koyama (with ungated earlier version here) explain the economics of medieval castles in Europe
• Ordali and Rapallini (with ungated earlier version here) conduct a meta-analysis of the relationship between age and risk aversion, and confirm that there is a positive relationship in studies using survey data and lotteries
• Singh and Mukherjee conduct a replication of an earlier study that established 'action bias' among goalkeepers facing a penalty kick, and find that jumping left or right rather than staying in the centre of the goal is not a sub-optimal action for goalkeepers in FIFA World Cup matches, and so the high frequency of jumping is not indicative of action bias (it is good to see a replication study published in a good journal)
• Lindkvist et al. (open access) investigate attitudes toward research misconduct and questionable research practices among researchers and ethics reviewers across academic fields, and find that researchers and ethics reviewers in medicine, as well as more senior and female researchers and reviewers, took a more negative view of questionable research practices
• Lei et al. use China’s Compulsory Schooling Law as a quasi-natural experiment to investigate the effect of education on HIV/AIDS, finding that mass education significantly enhances knowledge about HIV/AIDS, and that each additional year of exposure to the law reduces HIV/AIDS and mortality rates by 6.51 percent and 2.15 percent respectively
• Daoud, Conlin, and Jerzak (open access) study the differential effects of World Bank and Chinese development projects in Africa between 2002 and 2013, using data across 9899 neighbourhoods in 36 African countries, and find that both donors raise wealth, with larger and more consistent gains for Chinese development projects
• Stoelinga and Tähtinen (open access) find that conflict exposure, on average, increases support for democracy in African countries, but the effects vary by ethnicity and regime type, but interestingly, violence increases trust in ruling institutions in autocratic regimes
• Ruiz et al. (with ungated earlier version here) find that, following the exodus of Cuban doctors from Brazil in 2018, the reduction in doctors was associated with persistent reductions in the care of chronic diseases, while service utilization for conditions requiring immediate care, such as maternal-related services and infections, quickly recovered
• Geddes and Holz (open access) investigate the effect of rent control on domestic violence in San Francisco, and find that there was a nearly 10 percent decrease in assaults on women for the average ZIP code (some good news for advocates of rent control, but it hardly offsets the bad outcomes)
• Clemens and Strain (with ungated earlier version here) add further to the literature on the disemployment effects of minimum wages, this time looking at the difference between large and small minimum wage changes, finding that relatively large minimum wage increases reduced usual hours worked per week among individuals with low levels of experience and education by just under one hour per week during the decade prior to the onset of the Covid-19 pandemic, while the effects of smaller minimum wage increases are economically and statistically indistinguishable from zero

Anticipating higher future petrol prices, consumers actually push up petrol prices now

In his 1984 book The Evolution of Cooperation, Robert Axelrod suggested that people cooperate in repeated games because of 'the shadow of the future'. They alter their behaviour by cooperating now, because they anticipate that will lead to greater gains for them in the future. I really like this analogy of the shadow of the future affecting our decisions now, and not just in the context of game theory and repeated games. In fact, we've seen it play out in a different context this past week, as reported by the New Zealand Herald:

Kiwis are rushing to fill up their cars across the country amid fears of price increases at the pump because of escalating conflict in the Middle East.

Video sent to the Herald of Waitomo Tinakori petrol station in Wellington today showed a queue of cars waiting for fuel, with vehicles spilling out on to the road.

Waitomo Group CEO Simon Parham said there has been a similar increase in demand at stations across the country, with sales increasing by 10-15% this week.

“People are filling up and filling their cars ahead of the price increase that will flow through the market over the coming weeks because of the Iran conflict,” he said.

To see what is going on here, let's consider the retail market for petrol, as shown in the diagram below. Before the current conflict in the Middle East, the equilibrium price of petrol was P0, and Q0 petrol was traded per week. Then the conflict begins. Consumers anticipate that the price of petrol will increase in the future, so they decide to fill up their vehicles now. That increases the demand for petrol from D0 to D1. The equilibrium price of petrol increases to P1, and there is Q1 petrol traded in the week. 

Notice that by trying to avoid the high petrol price in the future, the consumers cause the price to rise today, which is exactly the outcome they were trying to avoid! In effect, when consumers rush to fill up early, they bring some of the future price pressure forward into the present. Expectations about future prices can cause self-fulfilling prophecies like this, which is a point I will make in my ECONS101 class in several weeks, when we talk about financial markets (where self-fulfilling prophecies are a clear and present danger at all times). The shadow of the future matters - consumers' actions based on trying to avoid future price rises make those price rises happen now instead.

Consumers can't tell the difference in audio quality between high-end audio cables and a banana

Consumers are not very good judges of quality. They can't tell the difference between bottled water and tap water. They can't even tell the difference between pâté and dog food. And now, according to this article by Futurism last month, they can't tell the difference between audio cables and a banana:

High-quality cables have long been marketed as a key way to get the most out of high-end equipment, such as expensive studio-grade monitor speaker cables and gold-plated HDMI cables for cutting-edge TVs.

In the high-end audiophile world, which is renowned for eye-bulging prices, cables can cost tens of thousands of dollars for ultra-pure copper with silver plating, specialized insulation, and dozens of individual conductors that manufacturers claim will squeeze the most out of a luxury-grade sound system aimed at the uber-wealthy.

The laws of physics, however, have long dictated that spending that kind of cash on cables simply isn’t worth it in the vast majority of circumstances — as long as you don’t go for the cheapest option from the dollar store, of course.

To put the decades-long debate to the ultimate test, a moderator who goes by Pano at the audiophile enthusiast forum diyAudio conducted an eyebrow-raising experiment back in 2024, which was rediscovered by Headphonesty late last month and Tom’s Hardware last week.

Pano ran high-quality audio through a number of different mediums, including pro audio copper wire, an unripe banana, old microphone cable soldered to pennies, and wet mud. He then challenged his fellow forum members to listen to the resulting clips, which were musical recordings from official CD releases run through the different “cables.”

The results confirmed what most hobbyist audiophiles had already suspected: it was practically impossible to tell the difference.

Consumers are not fully informed about the quality of the products that they buy. When they lack quality information before they buy, but that information is revealed after the consumer buys the good, we say that quality is an experience characteristic (and goods like that are called experience goods). A used car is an example of an experience good - the consumer doesn't really know if it is a high-quality car until they drive it. However, for some goods, the quality isn't revealed even after the good is purchased. In that case, quality is a credence characteristic (and goods like that are called credence goods). Health care is a credence good, because patients don't know for sure what would have happened to them without treatment, so it is impossible to judge the quality of the treatment.

Coming back to using an unripe banana as an audio cable, it appears that the quality of audio cable may also be a credence characteristic. At least, that's what this research tells us.

Why does this matter? The thing about credence goods is that the buyer may be reliant on the seller telling them about the quality. In the case of audio cables, the industry has a strong incentive to convince buyers that a 'high-quality' audio cable matters for sound quality, even if the consumer can't tell the difference. That changes the nature of competition in the industry. When buyers cannot verify quality for themselves, sellers can't compete on quality, and instead rely on reputation, branding, expert language, and the seller’s ability to sound convincing. They aren't going to want to sell banana cables, even if the banana cable would be produce audio of equivalent quality to a 'fancier' cable. Overall, this is a good reminder that in some markets, what consumers pay for is not better quality, but a more persuasive story about quality.

[HT: Marginal Revolution]

Read more:

• Can people tell the difference between bottled water and tap water?