An evolutionary explanation of consumption

Since Thorstein Veblen’s 1899 book Theory of the Leisure Class, the economics profession has taken a somewhat mixed approach to consumption. In areas such signalling theory, Veblen’s argument that conspicuous consumption must be wasteful and expensive to be a reliable signal of wealth is well recognised. Conspicuous consumption has a purpose as a signal. However, the typical economic model is built on the simple concept that more consumption brings more utility. There is no benefit beyond consumption itself.

The absence of a rationale for consumption appears even less satisfactory when considered from an evolutionary perspective. If people trade consumption against the use of resources for survival or reproduction, why does a trait which involves excessive consumption exist in the population? An individual could boost their fitness if they reallocated resources to increasing their fertility.

In this light, Gianni De Fraja’s explanation of conspicuous consumption through an evolutionary lens is a useful addition to the literature. Using a modified version of Grafen’s model on the use of biological signals as handicaps (see also), De Fraja showed that under certain conditions conspicuous consumption could be explained as a signal to the opposite sex. De Fraja further described how utility maximisation (as used by economists) is formally equivalent to the maximisation of fitness through signalling. This provides a biological basis for economists to include consumption in utility functions.

De Fraja’s model incorporated two sexes that mate during a mating season that consists of two “periods” (although the result could be extrapolated to more periods). De Fraja assumed that men make no investment in offspring, so they are free to mate in both periods, while if a woman mates in either period, they are removed from the mating population for the rest of the season. On this basis, men are willing to mate with any woman they are paired with, while women are choosy.

The choosiness of women is with good reason, as men vary in quality. With a mate of higher quality, the female can expect more of her children to survive to adulthood. Females do not vary in quality, but they face a chance of death in each period. In the first period, men and women are matched one-to-one. Given the varying quality of the men, the women need to decide whether the man they are paired with is of high enough quality to mate with, or whether they should take their chances and wait until the next period in the hope of finding a better mate. If their chance of death is high, the woman may drop her standards.

This choice is complicated, however, as male quality is not directly observable. What women can see is the man’s level of conspicuous consumption. Putting this in terms of choices we face today, and ignoring the possible approach of bringing your bank statement or pay slip to the dinner date, total wealth is unobservable. Instead it is conspicuous consumption on the car you drive to the date, your clothes, your watch and the cost of the restaurant that will show one’s wealth. The question the woman must address is whether the signal from the man as to his wealth is reliable. Has he arrived in a BMW that he will also have to sleep in tonight as he has no resources left for accommodation? Or is he actually wealthy?

To make this choice, the woman needs to infer the man’s level of quality. In De Fraja’s model, the strategy employed by the women is heritable. In equilibrium, all women would adopt the same strategy (a function of the perceived quality of the male and their chance of death), as no alternative strategy would be able to increase the female’s fertility.

The choice faced by men is how divide resources between conspicuous consumption and survival activities, which reduce the male’s chance of death. De Fraja assumes that investment in survival activities is unobservable, leaving consumption as the only feature that the female can see. A higher quality male will have more resources to allocate between consumption and investment in survival activities. In the model, the way men allocate resources to consumption (their signalling strategy) is genetically inherited. Quality itself is not inherited but randomly allocated to each new generation.

So, how does this work out? De Fraja did not study the dynamics of the model but, as is the case of most consideration of preferences in economics, the model was solved for the steady state population equilibrium. In the first period of the steady state, a female will agree to mate with a man only if they above a perceived quality, with that threshold level of quality decreasing as the woman’s chance of death increases. In the second period, the women will mate with whoever they are matched with as there are no further breeding opportunities.

For the men, De Fraja found that for certain combinations of environmental constraints, men would split into a separating equilibrium, whereby men of above a certain quality would signal that they are of high quality (those who meet this threshold all signal at the same level of consumption). Those below that level do not signal. Put simply, the lower quality men will sacrifice too much investment in survival if they tried to match the high quality male’s level of conspicuous consumption. As a result, low quality men do not engage in conspicuous consumption and focus on surviving. If the BMW will have low quality men starving and sleeping on the streets, a low quality male will not buy it and ownership of a BMW will be a signal that women can rely on.

In this equilibrium, the strategy by women of believing the signal, and by men of signalling true quality (that is, low or high quality) was found to be stable as neither the men nor women can use an alternative strategy and increase their level of fitness.

I would like to say more about the conditions under which this separating equilibrium holds, but as De Fraja notes, the mathematical proof of the separating equilibrium is not readily interpretable. Even after solving through the equations, it is not clear to me how feasible the required conditions are.

Once De Fraja establishes his separating equilibrium result and provides an evolutionary basis for conspicuous consumption, he moves to explaining whether this result is consistent with the utility maximising approach of economics. Is the maximisation of utility subject to a budget constraint equivalent to maximising fitness subject to environmental constraints? Under conditions of similar mathematical opacity to those for the separating equilibrium, De Fraja showed that they could be equivalent. The common strategy of all men could be thought of as common indifference curves, which in economics are the bundles of goods (in this case, consumption and survival activities) between which the man is indifferent. What determines where the man is on the indifference curves (his choice of consumption and survival activities) varies according to his quality. As a result, and assuming the conditions held, a model which involves a basic utility function that has utility increasing with consumption could be said to be biologically sound.

De Fraja’s paper left me with a number of questions. The most obvious one was why no-one had done this before. This issue had been known at least since the time of Veblen, and Grafen had laid the mathematical framework in 1990. I can only suggest that most economists are not overly concerned about the biological basis of their models, particularly if they have reasonable predictive power.

The second question relates to the range of conditions under which a separating equilibrium can arise and whether these are broad enough to be realistic. Having not got to the bottom of De Fraja’s mathematics, I am not sure of whether an alternative mathematical approach might yield more intuitive and easier to interpret results. Perhaps simulation could be used as a starting point to get a feel for how specific these conditions are.

A further issue relates to dynamics. While De Fraja’s work should allow economists who use consumption in utility functions to argue that their approach is biologically consistent, this is restricted to static situations. Can we learn anything further from the dynamic processes that lead to equilibrium (if a dynamic process would lead to equilibrium)? Take Galor and Moav’s argument of natural selection being a trigger for economic growth. While natural selection is at the core of their model, the model’s agents’ desire to consume above subsistence levels is not subject to selection and has no biological justification. This leaves some scope for extensions to the model, or indeed any other long-term growth model that represents a period sufficiently long for selection to occur.

That links to the question I always ask when I see a static model which explains the equilibrium of preferences shaped by natural or sexual selection. What are the macroeconomic effects of the move to equilibrium? For example, suppose there was initially no conspicuous consumption but the separating equilibrium proposed by De Fraja evolved over a few thousand (or tens of thousands of) years. Does a preference for conspicuous consumption drive us to gather more resources, which in turn increases in economic growth? This is nothing but speculation (at this stage), but it is a question that could yield interesting answers. (Since I first wrote this post, I have developed a dynamic scenario building of De Fraja’s work.)

De Fraja, G. (2009). The origin of utility: Sexual selection and conspicuous consumption Journal of Economic Behavior & Organization, 72 (1), 51-69 DOI: 10.1016/j.jebo.2009.05.019

Comments

  1. says

    From your description (I haven’t read the paper), the result relies completely on their being two periods. It is not nearly as easy as you say to generalize to more periods (since the decision procedure now has to solve a dynamic variant of the secretary problem), and the result disappears completely if there isn’t a clear “last period”. We could adapt either of the following reproductive rules (both being more reflective of human mating, which is not as clearly seasonal and correlated as the models): (1) at each time step, female is paired with a male and can mate or wait, if she mates then she can’t mate for the next m time periods (we will need m > 1 to get interesting strategies, in humans you’d expect m >= 9), or (2) we still have seasons, but instead of being of a fixed length, there is a probability p of the mating season ending on this period (i.e. the length is sampled from the geometric distribution). Note that the second scenario cannot be approximated by a fixed length mating season of 1/p periods (for the same reason that you can’t approximate an iterated-PD by a fixed-length PD). Both of these approaches eliminate the “sure chance to mate if you survive” part of the model, making honest signaling sub-optimal.

    This “sure chance to mate if you survive” is not an innocent assumption for males. Being male in almost any species is characterized by the fact that most of them do not get to mate (most females do mate by contrast). If you plotted how often males mated as a function of their quality in this figure, you would never get an inequality in mating-frequency that is anywhere close to real populations. Also, having non-heritable quality is a pretty silly, although probably excusable if all we care about is solving for equilibrium.

    Finally, from your description, it isn’t clear to me if the author proved that this is a unique equilibrium, or just proved that this particular form is an equilibrium. If he didn’t establish uniqueness and didn’t explore dynamics then the result is pretty useless, so I will assume he did. I also agree with you that these sort of results are a bit pointless if you don’t present when they fail. I feel like any study that shows “random cool effect”, should also show how to make it disappear in their model, that way we can have some idea of robustness. It is just too easy to build a just-so model otherwise.

    • says

      I’m not sure either of those alternative model approaches would make signalling sub-optimal. In either case, if a woman is more likely to mate with a male which she perceives as high quality – which can happen in cases of multiple periods or uncertain numbers of periods (not that there would ever be no information about the number of periods) – the signalling behaviour could pay off.

      I’m not sure what you mean by the “sure chance to mate if you survive” assumption. Low-quality males who survive may not mate.

      The assumption of non-heritable quality is done throughout biology in studies of handicaps etc. If quality is heritable, selection drives everyone to the maximum quality, in which case there is no point signalling as there is no variation in quality. To have heritable quality, you then need to introduce mutations, or parasites, or something that creates variation in quality.

      The equilibrium is not unique, and De Fraja notes this. However, showing something is possible is worthwhile. Sure, it’s worth looking at when it fails. That is at least partly captured in De Fraja’s mathematical condition, which in De Fraja’s case was unfortunately uninterpretable.

      I agree on the need for dynamic analysis on this. There is a lot of work happening on this in biology (the whole Fisherian versus handicap selection debate), but its a big question, I don’t blame De Fraja for not personally solving it. He took a result from biology and applied it. A decent first step. Ultimately, if you have problems with this approach, the point of attack is the evolutionary biology literature, starting with Grafen.

Comments, thoughts, suggestions?