# William petty

6th April 2021

William Petty (Romsey, UK, 1632-1687) was an English mercantilist, founder of political arithmetic, a method consisting in the application of quantitative methods to the analysis of social and economic phenomena. Such method reflected the innovation happened in his time concerning the the field of quantitative science, and he was particularly influenced by Bacon’s inductive method. His aim was to move in the analysis of science from qualitative arguments to quantitative ones, namely number, weight and measure. Nevertheless, Petty acknowledges the limits of mathematics and induction when applied to social sciences, hence he supported a method where both induction and deduction were equally important and possess complementary value.

## Labor-theory of value #

Petty focused his studies on the concept of value. According to him, the value of a good fluctuates around what he calls natural value, which corresponds to the costs of production: labor ($L_{t}$), land ($T_{t}$) and other previous factors ($V_{t}$) exploited in the production process

$p_{a,t} = L_{t} + T_{t} + V_{t}$

where:

• $p_{a,t}$:= value of a commodity $a$ at time $t$;
• $T_{t}$:=land used at time $t$;
• $V_{t}$:= quantity of additional inputs, different from labor and land, employed at time $t$.

assuming that $V_{t}$ was produced in a previous production process which took place one year before:

$p_{a,t} = L_{t} + T_{t} + \underbrace{L_{t-1} + T_{t-1} + V_{t-1}}_{V_{t}}$

continuing a substitution of the values, assuming that something of those inputs was produced before, the previous year, too:

$p_{a,t} = L_{t} + T_{t} + L_{t-1} + T_{t-1} + V_{t-1} + \cdot{} \cdot{} \cdot{} + L_{t-n} + T_{t-n} + V_{t-n}$

As $n$ grows larger, it is plausible to assume that $V_{t-n} \approx{} 0$. In this case, we can rewrite the previous formula as

$p_{a,t} = \sum_{j=0}^n L_{t-j} + \sum_{j=0}^n T_{t-j}$

Therefore, the value of the commodity is equal to the sum of the labor and land exploited at a given time and the ones used before.

Nevertheless, this approach showed two main problems:

1. it was not possible to determine the exchange values of goods, since it was not possible to pinpoint which one between land and labor was the most valuable. Petty could not find a way to quantify land as labor and vice-versa.
2. Petty could never get more clarity concerning what the convergence mechanism of the above equations is about

## Division of labor #

Petty considered society as a complex organism where different groups of workers have different roles; such subdivision ensures the functioning and survival of such society.

According to him, it was possible to define a hierarchy based on the kind of goods produced among different works citizens do. At the top of such hierarchy there was agriculture, since it was considered to be the only one capable of producing a surplus sufficient to support the entire population.
For Petty, even the existence of a rent was an indirect proof that agriculture produced a surplus of goods.

Petty also introduced the idea of technical division of labor, at a firm level: a better organization of work inside the firm itself; this comes as an anticipation of Adam Smith’s groundbreaking theory concerning division of labor.

Petty’s view concerning international trade was in line with the scholars contemporary to him: since he lived in the period of mature mercantilism, his primary purpose was to counterbalance the plunging inflow of gold from the colonies, and the only way to do so was favoring the export of surplus.

## Fiscal regulations #

Petty proposed the introduction of a proportional taxation levied on consumption, since it alone constitutes “actual” riches. Such criterion was considered to be fair, since it could not alter the distribution of income. Furthermore, this could solve the problem of double taxation, meaning that firms and their owners would be sanctioned twice, one time personally, and one time for their firm.

## Money #

Concerning money, Petty highlighted a connection between investment expenditures and interest rates: he believed that a higher circulation of money could lead to a lowering of interest rates. More money would hence indirectly stimulate investments through reduced interest rates.

email