Consumer demand: a function of present endowment?

Question

I don't know about you, but each time I go shopping for groceries, my purchasing decision takes into account what I already have at home. I don't make only one demand decision for my entire life the day I become a consumer, and afterward never buy anything ever again. Rather, each and every day, my daily demand for goods is a different function than it was yesterday. Similar to the concept of marginal utility, my daily demand for goods depends in part on what goods I have already have acquired yesterday (and all the days before that in which I have been a consumer).

Let's take a concrete example. Whether I want to buy a soda today depends partly on whether or not I already have one in my possession at home that I could drink. Namely, if I purchased a soda yesterday and it's still in my fridge, I don't want to buy one today; on the other hand if I don't have a soda in my fridge, I do want to buy a soda today. My particular demand function for soda, as I just described it, depends on my present endowment of soda.

However, in the way demand is traditionally modeled, the amount of a good $x$ you wish to buy, $x(p,w)$, is a function only of prices $p$ and wealth $w$. The amount of each good you already have in your possession does not enter as a parameter in the demand function.

(Admittedly, your wealth, which enters in your demand function as a single parameter $w$, CAN be calculated from your present endowment of goods, as a linear combination of their respective market prices. But it's not the actual quantities of those endowments that enter into the demand function -- only the total money-value of all your endowments, in units of the numeraire good. That is, only the amount of the numeraire good you possess actually enters as a parameter into the demand functions for non-numeraire goods.)

I am sure that classical demand theory is not flawed. At the same time, there is a disconnect in my mind between how I think about demand (which makes sense to me only in the context of one's present endowments), versus how demand is traditionally modeled. Can someone help me bridge this gap?

Answer 1

Although it's often left unstated, demand for a good is measured as quantity per unit of time. Broadly, the longer the time period over which demand is measured, the smaller the (proportional) effect on demand of the initial endowment. Whether you have a soda in your fridge one morning may make the difference between your demand for soda that day being $0$ or $1$. But over the next year, if you often consume sodas, it may make the difference between your demand being $n-1$ or $n$, only a very small proportional difference if $n$ is large. For this reason, even at the individual level it can often be appropriate to ignore endowments as a determinant of demand for frequently consumed goods.

At market level, a further consideration is that the effect of endowments may average out over many individuals. At a certain time, for example, A has a recently purchased washing machine, B's washing machine is in mid-life, and C's is old and needs replacing soon. In the absence of changes in income or major improvements in washing machines, it may be that in any year approximately the same proportion of people have a demand for a new washing machine, so that both the aggregate endowment of washing machines and the market demand for new washing machines are approximately stable. Again, therefore, it could be appropriate to ignore endowments.

But there are also many situations where neither of the above apply and it is important to consider endowments as a factor affecting demand. These include: in consumer markets, take-up of goods embodying new technologies; in housing markets, the size and condition of the existing housing stock; and in commodity markets, stocks of for example wheat or copper held by commodity traders.