# Law of demand with time component

As I understand it the law of demand works at one particular instant. I.e. it make a claim that the higher the price of an item at time t, the lower the quantity that will be purchased. Is there an equivalent theory which takes time into account. So for example it may be postulated that if the price of an item has been rising steadily over some extended period then the desire to purchase the item (as an investment) would remain high despite the higher price.

As a real world example, you hear people (non-economists) all the time saying that house prices can only ever go up. This appears to be based on decades of this being mostly true rather than any analysis of demographics or the rate of house building. Is there even a name for this kind of thinking? My feeling is that the existence of these kind of thought processes sits outside of (or perhaps on the periphery of) mainstream economics but maybe I've just been looking in the wrong places.

There is no dynamic first law of demand because demand function has to be specified at some point of time. As time passes demand function changes and as a consequence over time it is impossible to claim that increase in price leads to lower quantity demanded.

Thus over time increase in price could plausibly lead to:

• decrease in quantity demanded (e.g. if price increases from \$1 to \$2 and demand at t=0 is given by $$Q=10-p$$ and demand at $$t=1$$ is given by $$Q=10-2p$$).
• increase in quantity demanded (e.g. if price increases from \$1 to \$2 and demand at t=0 is given by $$Q=10-p$$ and demand at $$t=1$$ is given by $$Q=20-p$$).
• quantity demanded could remain unchanged (e.g. if price increases from \$1 to \$2 and demand at t=0 is given by $$Q=10-p$$ and demand at $$t=1$$ is given by $$Q=10- \frac{1}{2}p$$).

As a consequence in dynamic setting it is impossible to claim that increase in price should always lead to decrease in quantity (in fact even in static case there are Giffen Good that violate the first law of demand but at least for regular goods it holds).

As a real world example, you hear people (non-economists) all the time saying that house prices can only ever go up. This appears to be based on decades of this being mostly true rather than any analysis of demographics or the rate of house building. Is there even a name for this kind of thinking? My feeling is that the existence of these kind of thought processes sits outside of (or perhaps on the periphery of) mainstream economics but maybe I've just been looking in the wrong places.

If it would be truly based just on past empirical data the name for it would be adaptive expectations. Adaptive expectations are hypothesized expectations where people form their expectations about what will happen in the future based on what has happened in the past (see Evans & Honkapohja, 2001). Hence if someone believes future house price will get higher just because in the past house prices got higher that would be an example of adaptive expectations.

However, even layman typically understand 101 supply-and-demand. The sort of thinking can be justified with basic supply and demand model where we assume that demand will shift to the right in the future and supply will not as plotted below. If most laymen would be asked to justify their claim that house price will increase they would probably not pull out statistics but try to reason that they believe demand will keep getting higher while supply wont keep up.

• In the paper you cite it says: "In the 1950s and 1960s, the adaptive expectations hypothesis was employed widely in both empirical and theoretical work. In the 1970s and 1980s the ‘rational expectations (RE) revolution’ led to a fundamental reformulation." - so at first glance it appears that adaptive expectations used to be part of mainstream thinking but has now been pushed to the fringes. Would you say that's a fair assessment?
– Mick
Apr 3, 2022 at 16:27
• @Mick they are not completely fringe because they are still used in behavioral macro models in which rational expectations are combined with adaptive expectations, but in models that only use one kind of expectations adaptive expectations are no longer used because models with pure adaptive expectations perform very poorly compared to models based on rational expectations or mix of rational and adaptive in behavioral macro
– 1muflon1
Apr 3, 2022 at 18:35
• Re: "models with pure adaptive expectations perform very poorly compared to models based on rational expectations" - would you have a reference for that?
– Mick
Apr 5, 2022 at 7:44
• @Mick there is no single paper that covers entire corpus of economic theory. In macro, you can have look at Sargents Macroeconomic Theory, especially the chapter on lucas critique. You can have also look at this blogpost mainlymacro.blogspot.com/2013/11/…
– 1muflon1
Apr 5, 2022 at 8:07
• It might depend on what economic variables you are looking at. So for example in the housing market things may be reversed. In this paper researchgate.net/publication/… it states "The hypothesis of adaptive expectations is found to explain the data quite well. The rational expectations hypothesis, however, does very poorly."
– Mick
Apr 7, 2022 at 16:00