# Gross value added and worker salary

I'm trying to figure out how the Gross value added is calculated. The first question that I have encountered is "Does the Gross value added of an activity includes workers salary?" If not, what is the difference between GVA and an activity profit?

I assume that you're interested in gross value added as a national accounting concept (which is the most frequent use of the term). In that case, it is formally defined by the UN's System of National Accounts as "the value of output less the value of intermediate consumption". Here is a table from the freely available old version of Understanding National Accounts showing this breakdown for the nonfinancial corporate sector of France:

This definition is made on the production side, but gross value added can also be broken down into income. On the income side, it includes worker salaries, as another account excerpted from Understanding National Accounts shows:

As we can see above, gross value added is decomposed into compensation of employees (of which "wages and salaries" is the most important part), other taxes less subsidies on production, and gross operating surplus. Gross operating surplus can further be decomposed into consumption of fixed capital (basically depreciation) and net operating surplus.

Combining Tables 3 and 4, we see how the initial "output" accruing to a firm can be progressively whittled down:

• First, we subtract intermediate inputs to obtain gross value added.
• Then, we subtract compensation of employees and taxes less subsidies on production to obtain gross operating surplus.
• Finally, we subtract consumption of fixed capital to obtain net operating surplus.

Of all these concepts, the final one ("net operating surplus") is closest to our usual concept of profit, since it subtracts payments for intermediates, compensation of employees, production taxes, and depreciation. Nevertheless, there are a number of conceptual and technical differences between this and profit as it is usually defined: for instance, the net earnings of a corporation subtract interest payments, while "net operating surplus" does not. Instead, "net operating surplus" can be viewed as a broader measure of capital income. (Indeed, when Piketty and Zucman (QJE 2014) plot "capital shares" of national income in Table XII, they are actually plotting net operating surplus as a share of national income for each country, taken from the national accounts.)

Finally, note that all these definitions are quite generic and meant to apply to many levels of aggregation: firms, industries, areas, sectors, or entire economies. The tables with gross value added above show the "production" and "generation of income" accounts for the non-financial corporate sector, but all national accounts constructed using the same principles provide an analogous account for other sectors—including households, government, the total economy, etc.

Looking at a Profit & Loss statement of a company,

Value Added = Personnel Costs (+) Depreciation Charges (+) Profits (or (-) Losses)

It essentially is this concept that coincides exactly (in a narrow sense) to the fundamental production function with constant returns to scale, and factors of production only Capital and Labor, that moreover are being paid their marginal product:

Due to homogeneity of degree $1$, we have the production function

$$Y = F(K,L) = \frac {\partial F(K,L)}{\partial K}K + \frac {\partial F(K,L)}{\partial L}L$$

So if the gross rate of return to capital equals its marginal product, and the wage equals labor's marginal product,

$$r= \frac {\partial F(K,L)}{\partial K}, \;\; w=\frac {\partial F(K,L)}{\partial L}L$$

we get

$$Y = rK + wL$$

So all of $Y$ goes to the factors of production that appear in the right-hand side.

But $rK=$ Depreciation Charges + Profits (or minus Losses), and $wL=$ Personnel Costs. So in reality, $Y$ is Value Added rather than Gross Sales (and most econometric studies where production functions are estimated, regress Value Added on labor and capital, rather than Gross Sales). An issue here could be how one views interest costs, which are also returns to capital (irrespective of the fact that they do not belong to the shareholders -the company employs this capital and pays a fee for its use)

Of course the concept of production function can be enhanced to include separately materials and energy for example, in which case the appropriate dependent variable becomes Gross Sales.