Thou Shall Not Experience Relative Utility!

Some consumption, it seems, rewards the consumer differently depending on the consumption of others. It may feel quite good to own a reasonably new car, at least until all the others buy brand new SUV's. To my knowledge, in economics this phenomenon is studied under the name of "relative utility", or "keeping-up-with-the-joneses-utility". Probably, this is something that could help to narrow the gap between the dismal science and real life. Unfortunately though, it complicates matters, as people's economic discussions via relative utility gets much tighter intertwined. It might, from a technical perspective, look like any other externality to the market. Polluters degrade the air without compensating those who breathe it; SUV drivers impose increased traffic risk on others without compensating them. And - buyers of conspicuous consumption goods make each others goods look less conspicuous in comparison; they degrade each others experience of "relative utility".

Now, that's another big problem for the concept of "relative utility". Unlike other externalities, they might look as closely linked to a certain less generous and not so pleasant feeling - envy. Here in the welfare state, it's not only envy, it's "The Royal Swedish Envy". Quite natural when most of us pay and receive quite a lot of our household incomes in a big zero-sum game that is our local and central government budgets. But to support what to me looks like a welcome precision to the far to course-axed models of our economy, I would rather think of "relative utility" as something that has to do with social compatibility. You simply have to posses a basic equipment in terms of clothing, housing etc. to manage your social life. Even if falling behind or advancing ahead really wouldn't deprive you of or give you any crucial stuff, it would certainly make a difference when being together with others.

Are our consumption then best described as being conspicuous or basic, do we derive relative or absolute utility from it? I began to think of this in the context of leisure versus consumption (below), starting from a post and later a comment by Arnold Kling, and got further into it reading a NYT-article pointed to by Anne.Therefore, it was natural to look at labor data from the US and from other countries in the OECD. It actually seemed to me that absolute utility does a good job in describing the various tradeoffs between leisure and consumption. Nonetheless, as relative utility may add to describe phenomenon ranging from things like segregation and government interventions to redistribute income, to the home bias in equity investments it should be an interesting field of study. Perhaps even more so as we are hopefully approaching standards of living where increasing shares of our consumption is devoted to show off wealth.

Here are my calculations:

C is the total volume of consumption
PC is the total price for it (in hours worked per day to buy it) and
pC is the price per consumption unit (in hours worked).
PC=C*pC
L is the total volume of leisure in hours per day and
PL is the total price for it (in hours you cannot spend at work)
PL=L

The stylized facts for the US is that leisure (for people employed) for the last 25 years or so have been fairly constant, but that the volume of consumption each worked hour buys have increased.

So L is constant and PC is constant (L+PC=24 per definition). Now, the optimal distribution of consumption and leisure is reached when the marginal utility of consumption equals the marginal utility of leisure.

UL is used for utility of leisure;
UC is used for utility of consumption as a function of the volume of consumption, C. Both's derivatives with respect to total cost should optimally equal:

dUL/dPL = dUC/dPC (note that dUL/dPL is constant)

As the unit price of consumption decreases, more utility is gained from consumption per worked hours, we thus have to get more consumption to arrive at a point where marginal utility of consumption volume is lower:

dUC/dPC = dUC/dC*dC/dPC = dUC/dC*1/pC

so

dUC/dC = pC * dUL/dPL
dUC/dC = PC/C * dUL/dPL
UC = constant + dUL/dPL*PC*ln(C)

The utility is a function of the logarithm consumed volume C, although the total price (in hours) paid for it stays constant, its volume increases (with the decrease in prices), the utility derived from it increases, but as the utility function quickly flattens, its marginal utility stays constant. As does marginal *and* total utility from leisure. Absolute utility, increased consumption and constant leisure seem to fit together.

((Internationally though, leisure varies widely in the OECD, both across countries and over time. It seems however that these variations are highly correlated with variations in effective marginal tax on labor. If these in turn are indicative of the progressiveness of the taxation - the absolute utility framework outlined above may still fit))