Economic analysis has been hobbled by its ignorance of a simple fact of nature: change. Time is missing from the mental models that most economists use to study most economic problems. To remedy this problem, some part of economic analysis will have to be rebuilt from scratch.
If we started from scratch, what would be the most sensible atomistic unit to choose for our analysis of markets and firms? I suggest that it should be individual people. Others will object that people are difficult to model with numbers. This is true. The success of economics as a theory can largely be attributed to the success of the fundamental rational hypothesis as a description of the behavior of aggregated groups of people over long periods of time. What other hypotheses could be as fundamental? Here I propose one:
The needs of a person change in time according to rhythms that, in the aggregate, and over long periods of time, have a characteristic frequency.
Examples will help illustrate my point. Although not all of these rhythms will have a Gaussian distribution in frequency, there will nonetheless be a mean time that people need to sleep every day, a mean amount of time people may go without eating, a mean amount of time people may go without drinking, a mean amount of time people may walk without resting, a mean amount of time that people may live without dying.
When we talk about the market for a good or service in economics, we're talking about the aggregate supply and demand for that good or service across an economy of people. Yet the supply and demand curves taught in introductory economics are static. It is true that good economists have the ability to understand how supply and demand curves change in time in response to changes in supply and demand for other goods and services. But the simple model of supply and demand taught in introductory economics does not include time as a variable. What I have been arguing in the past few weeks is for an alternative means for modeling market prices that takes into account the rhythms of people in supplying and demanding goods and services.
Let's take as an example one of the very simplest models possible for a market -- two people in a market for food during the waking hours of one day. We need at least two for there to be a market. We can ignore for now the fact that our two people will sleep before and after.
Each of these people needs to eat about three meals per day. So the demand cycle for each person has amplitude = one meal, and frequency = 3 per day. As an aside, the demand cycle is not sinusoidal. It probably looks more like an exponential growth from zero followed by a precipitous drop back to zero shortly after each meal. A transaction needs to take place for the drop back to zero to occur (i.e., a meal needs to be eaten). If not, the demand cycle will continue to increase exponentially until the person starves to death, at which point it will again drop back to zero regardless of whether any transaction takes place.
The supply cycle for food has a different amplitude and frequency. Gathering raw ingredients might take each person an hour per meal. Cooking raw ingredients into a meal might also take about an hour for each person. Thus, the amplitude and frequency of the supply cycle for each person working alone is amplitude = one meal and frequency = 6 per day -- i.e., (12 hours awake/day) / (1 hour gathering + 1 hour cooking).
Consider now what happens when we put the two people together: Both have a demand cycle of 3 meals / day. Both have the ability working alone to supply up to 6 meals / day. But so long as the quantity cooked or gathered doesn't much affect the frequency of the supply cycle for the respective activity (a crucial assumption), it makes sense for one person to do the cooking while the other does the gathering.
First, by phase shifting the two supply cycles and increasing their respective amplitudes -- i.e., by timing the gathering of twice as many raw ingredients to be finished just before the cooking of two meals begins -- the two people can synchronize their supply activities such that each spends at most six hours meeting the total demand for both (of 6 meals per day). More likely, each spends far less than six hours because it doesn't take twice as much time to gather or cook for two meals when you're already gathering or cooking for one. In fact, it's not at all unreasonable to guess that gathering for two meals would take only 50% longer than gathering for one and that cooking two meals might take approximately the same amount of time as cooking one. So the amplitude and frequency after a division of labor might be one meal / 45 minutes (gathering) and one meal / 30 minutes (cooking) for an aggregate one meal per 1 hour 15 minutes -- 45 minutes faster than would be possible for each working alone.
This explains how divisions of labor work. When supply activities are synchronized into an assembly line, divisions of labor multiply the rate of supply while decreasing the total required labor. So long as the amplitude for each supply cycle can be increased faster than frequency decreases and successive supply cycles can be kept synchronized, divisions of labor multiply the rate of supply. Without a division of labor, added units of labor lead only to proportional additions to supply.
Second, over longer periods of time, by specializing in either gathering or cooking, we can reasonably expect that the frequency of the supply cycle may be still further shortened. Instead of the gatherer taking an hour and a half to gather two meals and the cook an hour to cook two meals, the gatherer might learn how to gather for two meals in an hour, and the cook to cook two meals in 45 minutes. This observation helps in understanding the relationship between divisions of labor, learning, and endogenous growth.
Within this simple model of supply and demand, "market price" is a function of the supply and demand of each person at a moment in time (the time of the transaction), and is measured in the same units of meals per day. The demand cycle requires 3 meals per day per person. The supply cycle permits at least 6 meals per day per person (as explained above supply cycle frequency may be increased by divisions of labor and learning). What shape should the function of market price take?
First, supply must exceed demand and demand must be above some threshold level before a transaction takes place. If there isn't any meal to eat or nobody is hungry, then no transaction can take place even if someone is hungry. Thus, if we want market price to be a positive number, then it should be a function of supply minus demand. In addition, supply should reflect the cumulative supply that hasn't been consumed in earlier transactions. I'll ignore the possibility of spoilage since we're looking only within a one-day time window.
A corollary to this first point is that price will be undefined in an economy in which each person gathers and cooks for herself. No transactions take place so long as each human can rely upon herself to synchronize and meet her own supply and demand. No market will develop until there is a division of labor.
Second, the phase and frequency of supply and demand -- i.e., the relative position of peaks and relative frequency of cycles -- will affect market price. For example, because meals can be prepared before eating and at a rate faster than demand for them increases, the supply cycle doesn't need to be running continuously to meet the demand cycle. If the supply cycle runs twice as fast as the demand cycle, the supply cycle can be idle for at least 50% of the time and both humans will still get enough meals. But the supply cycle does need to lead the demand cycle on average in order to ensure that meals are ready when people get hungry.
Third, averaged over long periods of time, voluntary transactions will tend to occur at a price that both humans agree fairly represents the respective contributions made to the supply cycle. For example, all else being equal, if I've spent two hours gathering and you've spent one hour cooking the same two meals, I might reasonably expect you to give me more than one of the meals you've cooked. I can't expect to get two. You wouldn't agree to that because then you'd go hungry. But over time, surplus or leftovers will be transferred to the person who is mutually perceived to add more value to the supply cycle. And the supply cycle will naturally tend to that amplitude and frequency that matches output to the mutual perceptions of value.
This explains the principal of diminishing marginal utility. Given a demand cycle, the closer that each person gets to matching their share of aggregate supply to personal demand, the less incentive each actor has to continue learning and increasing the amplitude and frequency of the supply cycle.
The model also explains market failures. If I ask too much, you may tell me to cook for myself. At worst if you don't already have the raw ingredients, you go hungry for a few hours while you go out and gather for yourself. Although I won't have to gather again until tomorrow, I still have to spend two hours cooking. By tomorrow, I may miss your cooking and lower my asking price. If not, we'll be back where we started, with no division of labor, spending twice as much time scrambling around and cooking as we would otherwise need to.
Last, notice that although the relative amount of time spent on supply is a good starting point for estimating value of each person's contribution, the market price might also reflect a variety of other things, such as the quality of the ingredients gathered, the timing in which they were supplied to the cook, along with past track record of and future expectations for similar transactions. Even in a two-person economy, price is a complex, multivariable function, which is nonlinear in time.
Let D1 and D2 represent the demand functions for person 1 and person 2. Both are a function of time with amplitude 1 meal and frequency 3 / day. Let Di represent either D1 or D2.
Let S1 and S2 represent the individual supply functions for person 1 and person 2. Working alone, these functions have amplitude 1 meal and frequency 6 / day. Working together, the functions will shift so that S1 (gathering) leads S2 (cooking). Frequency and amplitude will increase by the division of labor, and (over many days) learning.
Let t* equal the moment in time when a transaction occurs.
Let Sum(S1)dt and Sum(S2)dt equal the integrated sum of S1 or S2 individually over the period of the single demand cycle immediately preceding t*.
Let Sum(S1 + S2)dt equal the integrated sum of S1 plus S2 over the period of the single demand cycle immediately preceding t*.
Given that Di(t*) > 1 meal and S12 - Di > 0 (see the first point above):
Let P1 and P2 represent the price paid by person 1 or person 2, respectively.
P1(D1,S1, S2, t*) = Sum[(S1/S2)*(S1+S2)]dt/(period of single D1 demand cycle) - D1(t*)
P2(D2, S1, S2, t*) = Sum[(S2/S1)*(S1+S2)]dt/(period of single D2 demand cycle) - D2(t*)
As a result,
P1 = P2 when D1(t*)=D2(t*) and Sum(S1/S2) = Sum(S2/S1) = 0.5