Money and prices -- Part II
andrea.parisi | Published: 14 Dec 2023, 10:01 a.m.
In my previous post, I discussed how economic theory rarely deals with the definition of money. I pointed out that any measurement of money (GDP, monetary mass, any quantity dealing with money) is nothing more than counting the number of currency units: scientifically, this is not a complete operational definition. That is because we have no method to unequivocally and independently 'measure' what I called the 'intrinsic quality' of a dollar bill, a euro bill, whichever currency we wish to refer to. There are no instruments that allow to compare a euro bill to a yuan bill: the very fact that the relation between currencies changes in time and space means that they are not a reliable foundation for any economic theory. Money, as appearing in economic equations, is ill-defined.
In order to understand this issue, and better define money, we will use a common thought experiment used in economic theory, where we imagine an isolated island and somebody being stranded there owing to a shipwreck. This thought experiment was used by E. Böhm Bawerk, a funding father of the Austrian School, but it was reprised several times by different authors of various economic schools, including modern economic theory. It is quite a useful way to illustrate basic economic facts. Let us consider a stranded inhabitant on a deserted island: we will call our main character, not surprisingly, Robinson Crusoe – or RC for short. RC is lost on an isolated island and needs to survive. He starts by catching fishes: he is alone on the island abundant of life, and there is also a large pool of fishes available to him. Here and in the following, I will use estimates for fishing rates: these estimates are probably not realistic, but are adapted to have round numbers for easy calculations. Specifically, I will follow the set-up described in "The Dao of Capital", by Mark Spitznagel. In his description, RC catches fishes and increases his productivity by building a spear. The author focusses on the use of capital to increase productivity, and the economic calculation that determines its feasibility. Here, I stretched the story further, focussing on production, use of time and trades.
Like the protagonist in Mark Spitznagel's story, RC needs to catch 5 fishes in one day to survive. Catching fishes with bare hands is extremely difficult, as fishes escape quickly: suppose he needs 10 hours on average to get all those fishes: that means that each fish costs him 2 hours of work. This is, of course, a lot of work. To make his life easier, he decides to use part of his time to build a spear. Building a spear requires time (following Spitznagel, you need to find a good rock for the spearhead, work it with some other stone to sharpen it, find a proper wood stick, work it, attach the spearhead to the wood stick in a way that it will not make it fall off into water). Suppose it takes 20 hours to build a spear: RC sacrifices 2 hours per day (1 fish) to work on it. In 10 days he has a proper spear, and now he can catch the same number of fishes in half of the time: just 5 hours for 5 fishes, that is 1 hour per fish. At this stage there has been no exchange between individuals, but RC has done some important exchanges: he has exchanged some of his bare-hand fishing time for spear-building time, and has used the final product to increase his fishing rate. Overall, he has exchanged some fishes (the ones he did not catch) for a future increased rate of fishing. If fishes represent goods of exchange, then we could value him for this fishing capability. At the start of this story RC was worth 1/2 a fish per hour. He invested 1 fish every day for 10 days to build a spear (thus costing him 10 fishes or 20 hours of work), which is a tool that makes him worth 1 fish per hour. So the tool has made RC more valuable in terms of productivity. His higher productivity means that now he has 5 hours per day available as leisure time. He might also decide to use this time to get more fish, thus increasing his fish income. Alternatively, he might use his 5 hours to build extra tools, a house or a shelter, or a river fishing net. Each of these new items would affect his life in different ways. A fishing net would increase his fish catch and would thus increase the value of his time (in productive terms). A house/shelter will make his life more comfortable; to some extent, a house/shelter, despite not directly affecting his catch, will serve as a way to improve his health and survival, so it will contribute to the value of his catches (he might need fewer days off). Even not doing anything has its benefits, as he will be resting and enjoying the beauty of nature.
At some point, his spear will need replacing, and he will need to build a new one. He need to sacrifice 20 hours to build a new spear, but if he uses his fishing time, that would correspond to 20 fishes, as each hour he can now catch 1 fish on average. That means that those 20 hours will cost him 20 fishes, since his time-worthiness (or productivity) is 1 fish/hour. It is clear though that there is no rule that sets this value, as there is no true exchange here: beyond discussing the productivity per hour of the individual, we are not able to set any price. Moreover, differently from the previous case, the time dedicated to the production of the spear is now in excess to the time required for the survival. In other words, RC can use his free time to produce a new spear. Because he is not subtracting time from his sustenance, the cost of the new spear is the cost of his free time. He will need to renounce to something he could have done instead, during his free time. If RC were able to put a cost on that alternative activity, then we would know what the cost of the replacement spear is. The key point here is not to identify the cost of the spear, but to understand that building that spear means using a certain amount of time that might have been used for something else. Thus, the true exchange is time with time. If RC was going to rest and doing nothing, he will be exchanging 20 hours of his doing-nothing time with 20 hours of spear-building time.
A new spear will not increase productivity (but would avoid a fall in productivity). A fishing net on the river instead might allow RC to get 20 fishes in 5 hours: that would make him worth 4 fishes/h. At that point, RC will be able to dry some of the fishes (say for simplicity 50%) as a long-term reserve for bad days (maybe when he is ill), so that now he can work on alternate days, when half a day he gets fishes, and the next half-day he builds his long-term storage. This storage will allow RC to further reduce his work some time in the future.
Now let us imagine that someone else ends up on the very same island. The new guy (let’s refer to him as RC2) will be in the same position as our first arrival. We can reasonably expect that human empathy will lead RC to lend a helping hand to the newcomer. For the sake of understanding, though, let us imagine that the new arrival receives no initial help. In this case, he will have to start fishing with his bare hands, and we may assume for simplicity that he is as good as RC in this activity. For the first few days, he will manage to survive by getting 5 fishes with 10 hours of hard work. He then meets RC, and sees one of his spears: with one of those he would be able to catch many more fishes. So, he asks RC for one spear.
Things now get a bit complicated. The time needed to build a spear is 20 hours, but since in one hour RC can catch 4 fishes, should he trade his fishing time with spear production, the fish-cost of the spear would be 80 fishes. If RC needed this time to sustain himself, he would require RC2 to compensate him. On the other hand, he could build the spear during his free time, since he now has plenty: a new spear could be provided out of generosity by RC at no cost. Any outcome is right as there is no rule here that set prices, and it is all in the hands of RC. It is quite clear that we cannot do much economic calculation with just two people. However, thinking on a much larger scale, if RC were to produce spears often, he would require some sort of compensation for the efforts he places in building them. For example, if RC can easily produce 4 fishes per hour, he might make this his main activity, at which point building a spear in 20 hours would require a lost production of 80 fishes. This is a big number of fishes, and if RC2 was asked to pay for the lost production, he would have to give two fishes per day for 40 days in order to compensate for it. If RC allows him to have the spear and be payed afterwards, he could achieve this by working 10 hours per day for 16 days using the new spear (5 fishes for sustenance and 5 to repay his debt). RC2 realizes that it might be cheaper for him to build a new one instead of buying a replacement from RC. So after paying back his debt (if he got his first spear from RC) he quickly builds a new spear before the one he is using wears off.
New shipwreck victims arrive on the island, and after seeing spears in use, they decide to buy new ones. RC2 can now sell his spears at, say, 20 fishes each, which is a fair exchange for the amount of fishes he is currently able to catch with his spear. Actually, getting material for multiple spears at once, he is able to greatly reduce the costs of each spear and can sell them for 10 fishes each. That means now that spears are convenient for all newcomers. All the fishes that RC2 obtains by selling his spears require storage, but RC2 now decides that he can ask RC to dry some fish for him. In fact, for RC some extra 10 fishes to dry are just a small addition to his drying schedule, and cost him just 15 mins more of work. Thus, with just one extra fish, of cost he can dry 10 fishes for RC2). So, we arrive at a subdivision of enterprises, where RC is now drying fish (and occasionally replacing fishnets), RC2 is in the spear business, while the newcomer might start new activities. For instance, one of the newcomers might take over fishnet production, so that RC can focus on drying fishes. All exchanges now are based on some kind of money: fishes. Each fish, however, has value because it represents its time-cost. In such an economy thus, fish-money represents time.
We have thus reached three important hints: first, when individuals exchange staff, they are effectively exchanging their time. When RC builds a spear for RC2, he is using his time to build it. When it gives to RC2, the latter will receive a good that costed him no time. He might compensate back RC either voluntarily, or by force (because he needs to pay RC for the spear) using his own time to provide some other good to RC (for instance fishes). Exchanges of goods are indeed exchanges of time among individuals. Note that we are not yet discussing how much time should be exchanged for a given amount of time (for a given good or service): we are just setting an equivalence between goods and the amount of time that was required to produce them.
The second hint is that individuals have an intrinsic worthiness (productivity) that is measured by how much they can produce/extract/craft per unit of time. If $p_h^i$ is the per-hour productivity of individual $i$ with respect to product $h$, the total yield of the person is $p_h^i \times T_h^i$, where $T_h^i$ is the amount of hours dedicated to work by individual $i$ on product $h$. Thus, production of $h$ for individual $i$ is: \begin{equation} P_h^i = p_h^i T_h^i \end{equation}
The third hint is that productivity increases for those who benefit from innovations: their productivity improves, and consequently their free time increases. That is because innovations allow the beneficiary to get things done in a fraction of the time. However, innovations need to be produced first, and that requires an investment, as time must be set aside to develop them.
Individuals will also consume items: for instance, as we assumed above, each individual will consume 5 fishes per day. We call the consumption rate of good $h$ by individual $i$, $c_h^i$, which gives $C_h^i = c_h^i \mathcal{T}_h^i$, where $C_h^i$ is the total consumption, and $\mathcal{T}_h^i$ is the time interval during which the total consumption is measured. For the moment, one can assume that, given we are only dealing with fishes, $c_h^i$ is a constant equal to all individuals, set to 5 fishes per day. Also, it is reasonable (but not required) that produced goods also need to be consumed, leading to some balance between production and consumption. This, however, is not straightforward: we focussed on fishes, but we might be producing staff that will not be consumed. Additionally, nobody is preventing RC or RC2 to get fishes and throw them in the bin instead of eating them.
