Contents (0) Preliminaries (0) Preliminaries We have given the overview of Quesnay's Tableau. Now let us return to the seven stages and consider them in more detail with a numerical example. Before proceeding, it might be worthwhile to keep our overview picture of the Tableau from our summary section open (open summary picture in new window) All assumptions are as before. We have five representative protagonists of Quesnay's three classes: in the "proprietary" class we have a Landlord, in the productive class we have a Farmer and Farm Laborer, in the sterile class we have an Artisan and a Foreign Merchant. We have several goods. Farmers produce grain. Artisans produce crafts. Farm Labourers provide labor inputs. Foreign Merchants provide foreign inputs. Landlords provide, well, the right to use their land. But above everything, floating through the entire system, is a stock of cash. Prices are assumed given. For the sake of simplicity, let us suppose that a unit of grain costs $1, a unit of crafts costs $1 and a unit of foreign inputs costs $1, where $ is the monetary unit of account. We shall have more to say on this later. For this section, we will also make the strange assumption (to be relaxed later) that the wages of Farm Labourers and trade with the Merchant is not in cash but in barter. We shall change this in our "expanded zig-zag" section later. (1) The Initial Position The economy begins with the Farmer having just produced 1500 units of "grain" and the Artisan having produced 750 units of "crafts". Let us suppose, for reasons we shall see, the Landlord holds $600 in cash. We can depict the initial balances owned by the farmer, landlord and artisan as follows: 
where $ denotes units of cash, g denotes units of grain and c are units of crafts. (2) The Initial Injection To sustain his extravagant lifestyle during the year, the Landlord must buy substantial amounts of grain and crafts for himself. So, the next step in the Tableau is the initial injection of income: the expenditures by the Landlord on the products of the Farmer and the Artisan. Remember that we assumed that a unit of grains costs $1 and a unit of crafts costs $1. So, let us suppose the spendthrift Landlord spends $300 to buy 300 units of grain and $300 to buy 300 units of crafts. Notice how the stocks of grain, crafts and cash are adjusted in the columns of the three classes.  The 300g and 300c received by the Landlord will be gradually consumed by him throughout the year. We shall let him do so in peace, and so leave him out of the remainder of the story. (3) The Zig-Zag Process After this initial injection by the landlord, the "zig-zag" process commences as the Farmer and the Artisan proceed to spend half of their income on each other's goods. In the first line of the zig-zag, the Farmer spends $150 (half of the $300 he received from the Landlord) to buy 150 crafts, while Artisan spends $150 (half of the $300 he received) to buy 150 grain. Notice how the stocks adjust as a result. 
The Farmer and Artisan continue to spend half of their income on each other. So, in the next line of the zig-zag, the Farmer (who has just received $150 in income from the Artisan) will turn around and spend $75 to buy 75 crafts. Similarly, the Artisan (who also just received $150) will spend $75 to buy 75 grain.
The process continues in the next line. Having just received $75 in income, the Farmer spends half of that, namely $37.5 to buy 37.5 crafts; similarly, Artisan spends $37.5 to buy 37.5 grain.
And so on ad infinitum. Now, let us sum up the entire expenditures. The Farmer spent $150 in the first round, $75 in the second, $37.5 in the third, etc., so his total expenditures on crafts are:
Or, letting a = 0.5 be the propensity (marginal = average) of the Farmer to spend on crafts, we can express is total expenditures on crafts as:
Now, as 0 < a < 1 then the geometric series (1 + a + a2 + a3 + .....) converges to 1/(1-a), i.e.
so the total expenditures of the farmer on crafts can be expressed as:
So, from the initial $150 injection, we will find that, after the zig-zag process has worked itself through, the farmer will have spent a total of $300 worth of crafts, which at our prices ($1 per unit), means he acquired a total of 300 crafts. This convergent income-expenditure process is reminiscent of the "multiplier process" introduced by John Maynard Keynes (1936) and so familiar to us from macroeconomics. Similarly, let b = 0.5 be the propensity of the Artisan to spend on grain. So, from the initial $150 injection, the Artisan will buy 300 units of grain via the zig-zag process, i.e. (1 + b + b2 + b3 + .....)$150 = $150/(1-b) = $150/0.5 = $300 is the total spent by the Artisan on grain. The entire zig-zag process depicted in the Tableau can thus be summarized more simply by the following aggregate transactions:  So, at the end of the zig-zag process, the Farmer and the Artisan have the stock positions noted in the columns above. (4) Capital Stage The expenditure and goods acquired in the zig-zag process happen during the course of the year. But the Farmer and the Artisan must pay attention to setting aside capital for next year's production cycle. This part of the theory is discussed by Quesnay in his Explication du Tableau, rather than in the diagram of the Tableau itself. The Physiocrats assumed a self-replicating economy. In other words, our agents must be able to produce next year exactly what they produced this year. The Farmer needs to set aside enough capital this year this year to produce 1500 units of grain next year. In other words, he needs to set aside just enough goods, crafts and cash to maintain himself, his workers, his cattle and seed during the production process, i.e. before next year's harvest. Similarly, the Artisan needs to have enough goods set aside to maintain himself and use as raw materials in order to produce 750 units of crafts next year. The capital requirements of the Farmer (productive sector) and the Artisan (sterile sector) are summarized in the following table:
where g denotes units of grain, c denotes crafts and f denotes foreign imports. We will explain these requirements as we go. (A) The Sterile Sector Let us begin with the Artisan. The Artisan's capital requirements are the following. To produce 750 units of crafts next year, the Artisan needs 150 units of foreign implements and 300 units of grain for raw material. This is his direct non-wage capital needs. In addition, he needs to set aside 150 units of grain and 150 units of crafts for his own personal consumption. How does he go about meeting these requirements? Let us take this a step at a time. The Artisan acquires his raw materials by a single non-reciprocated purchase of 300g from the Farmer (note: this is after the zig-zag).
 [Note: How is grain a raw material in manufacturing? Remember that we are using the term "grain" to denote the generic output of the agricultural sector, so we are really referring to wool, leather, timber, silk, cotton, flax, iron ore, precious metal, etc.] Now, the Artisan acquires his foreign inputs (e.g. Baltic wood, Asian silk, Venetian beads, Flemish lace, Russian furs, etc.) by buying them from an import-export Merchant. Again, to abstract from prices, we shall assume that a unit of a foreign good costs $1. The Merchant provides 150 units of foreign inputs to the Artisan in exchange for 150 units of grain (which the Merchant will proceed to export out of the country).
[Note: If we don't believe that goods are exchanged for goods directly, but rather stipulate that goods must always be exchanged for money, then this cannot happen here. See our discussion of the "Expanded Zig-Zag" below to see how to fit this.] The Artisan is now ready to start setting his capital aside. He allocates 150 foreign goods and 300 grain as non-wage capital (raw materials and tools) for next year.
The Artisan also sets aside 150 units of grain and 150 units of crafts for his own consumption next year. (incidentally, notice that the Artisan's yearly consumption requirements are half of the consumption requirements of the Landlord we dealt with earlier -- an acceptable assumption in light of 18th Century social reality).
So, in the end, after accounting for all his regular and capital expenditures and storing them away, the Artisan has nothing left over. In other words, the sterile class has no net product. (B) The Productive Sector Let us now turn to the Farmer's capital requirements. The Farmer needs to hire Labor for next year. So he allocates 150 grain and 150 crafts for his laborer's consumption. This is the Farmer's wage-capital requirement.
[Note: Again, if we insist on a pure monetary economy, then the Laborer's services should be paid in cash and not in kind. This is dealt with in our "Expanded Zig-Zag" section below.] The Farmer also needs to set aside 300 units of grain for cattle feed and seed for next year's harvest. These are his non-wage capital requirements:
Finally, the Farmer needs to allocate 150 grain and 150 crafts for his own consumption next year.
Notice that the Farmer has $600 left over. This is his net product. (5) Production Stage We have noted in the previous section how, by a series of trades, the sectors acquire the necessary capital. After setting aside their capital requirements for the next year, the final positions of the Farmer and Artisan are the following:
Notice that the capital requirements table and our price assumption ($1 = 1 unit of crafts = 1 unit of grain = 1 unit of foreign implements) mean that the total value of capital requirements by the agricultural sector is $900 and its output is worth $1500. Thus, the production process in the agricultural sector yields $600 in surplus ("net product"), which we clearly see sitting in the Farmer's column. In contrast, the manufacturing sector uses $750 worth of capital to produce $750 worth of output, and thus yields no surplus -- which is why the Artisan's column is empty. Production can now begin. Next year, with his $900-worth of agricultural capital, the Farmer will produce 1500 units of grain. This agricultural production process can be summarized as follows:
Similarly, from his $750-worth of manufacturing capital, the Artisan will produce 750 units of crafts. The manufacturing production process can be summarized as:
So, after production, the final positions are:
Notice that the capital stocks of both our Farmer and are Artisan are entirely used up in the production process But now they have stocks of output. Notice that the farmer has all the cash. (6) Closing the Circuit: Rent stage Finally, there is payment of rent by the Farmer to the Landlord. The payment is a total of $600 cash. It gives the farmer the right to use the land for one year. We depict this payment as follows:
Why is rent $600? We shall discuss this line in a little more detail later. For now, let us just assume that this is it. The payment of rent closes the circuit. The final stock positions of the Farmer, Landlord and Artisan are exactly what we began with, no more and no less.
[Note: if you look carefully, you will see that in Quesnay's original Tableau picture, the payment of rent occurs right before the initial injection of Landlord spending, whereas in our depiction, we started off assuming the rent has already been paid. It doesn't really matter where we place this transaction. It closes the circuit.] (7) Expanding the Zig-Zag We have not monetized every transaction in this process. In particular, the Artisan & Merchant barter grains and foreign goods with each other while the Farmer pays the Laborer in crafts and grain. This was merely convenient way so that we'd only have to deal with a simple zig-zag between Farmer & Artisan and deal with the Laborer and Merchant separately at a later stage. But the proper way to do it - the fully monetized economy - would be where Merchants & Farm Laborers are paid in cash. That would merely involve adding a few more steps and a more expanded zig-zag between one sector (Farmer + Laborer) with another sector (Artisan + Merchant), so they'd get paid along the way. If we insist on cash at every step, it is easy to adjust the sterile sector in the very first line of the capital stage: (1) the Artisan conducts a non-reciprocated purchase of $150 (rather than $300) worth of grain from the Farmer, thus leaving him with a stock of 150c, 450g and $150; (2) the Artisan uses his remaining $150 to buy 150 foreign implements from the Merchant; (3) the Merchant then uses this $150 to buy 150 grain from the Farmer which he then exports. So, in sum, the entire sterile class (Artisan + Merchant) have made a non-reciprocated payment to the Farmer of $300 for 300 grain -- exactly as we had it in that line - and the Merchant carries off 150 units of grain for export. Our conclusion is unchanged. Adjusting the productive sector is only slightly trickier. Here, we'd have the farmer pay the laborer 150 grain (which he has) plus $150 cash and let the laborer himself use the cash to buy the necessary 150 crafts from the Artisan. Of course, the Artisan only produced 750 crafts, of which we said 300 go to the Landlord, 150 are retained by the Artisan himself and 300 go to the Farmer. It seems there are no crafts left for the laborer to buy. But that is, of course, misleading. If the laborer is going to be paid in cash, then the Farmer doesn't really need 300 crafts, but only 150 crafts for himself. So there are enough crafts left over - 150 - for the Laborer to buy. If this is the case, then we must modify the earlier zig-zag process. We must have it that, over the course of the year, the Farmer only spends $150 to buy 150 from the Artisan, using the remaining $150 to pay his laborers, but the laborers simultaneously use the $150 to buy crafts. So an expanded zig-zag process, up to the allocation of non-wage capital, would, in the end, look something like this:  Which is no different than the conclusion we came to before. Notice the goods in the Farmer & Artisan columns will be exactly the capital needed to produce next year. And the full $600 cash is in the Farmer's hands. Finally, we can compact the above into sectors, where Productive = Farmer + Laborer and Sterile = Artisan + Merchant, so the flows become:  Where, notice, the sterile sector spends more on productive sector than the other way, so, on net, the productive sector drains $300 from the sterile sector - the very $300 paid by the Landlord to the artisan, leaving Sterile sector with no cash and the Farmer with the entire sum of $600 - a sum, we must note, that is exactly equal to 600g, the net product of agriculture (i.e. the 600g not needed by productive sector as capital, but sold to the sterile sector.)
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