# Marginal value product

The value marginal product (WGP for short; or value limit productivity ; English value of marginal product , VMP for short) is the physical marginal product valued at the market price in price theory .

## General

The entrepreneur needs to know how sales change when he changes one or more factors of production . The business key figure of the marginal value product provides information on this. Above all, the production factors labor and capital are examined . The marginal product of value is the product of the goods price or interest level and marginal productivity . If a company is a quantity adjustor on the goods and factor market , the maximum profit corresponds to the marginal product of the market price of the corresponding production factor .

Since, from an economic point of view, the price level of goods and the price of capital (interest) are identical, the optimal use of capital means that the interest rate corresponds to the marginal productivity of capital. Every production factor, including the land , is economically rewarded as high (in the case of land through rent or rent ) as can be gained from the last unit used in additional income (marginal value product). The prerequisite for this consideration is always the perfect labor market or perfect capital market , where the factors of production are rewarded according to their marginal value product. Assuming complete competition , the marginal value product corresponds to marginal costs . Accordingly, in a monopoly case, the WGP is larger than the WGP on the competitive market with the same marginal costs.

## detection

The marginal value product is the amount by which a company's sales revenue ( value product ) changes through the use of an additional production factor. The marginal value product therefore consists of the two components of the (physical) marginal product (the marginal revenue is identical to it ), which is multiplied by the product or market price : ${\ displaystyle \ Delta Q}$${\ displaystyle \ Delta A}$${\ displaystyle WGP}$${\ displaystyle GP}$${\ displaystyle P_ {q}}$

${\ displaystyle WGP = {\ frac {\ Delta Q} {\ Delta A}} \ cdot {P_ {q}}}$.

For example, a company hires so many workers until the marginal value product equals the wage rate (given for the company) .

## economic aspects

According to neoclassical theory , the marginal value product of a factor of production determines its reward. This is to be examined for the production factors labor (remuneration: wages ) and capital (remuneration: cost of capital).

If, for example, an additional worker is hired, the marginal product consists of the increased sales generated by this worker. A profit-maximizing enterprise will therefore employ just enough workers until the marginal product of the production factor labor equals the wage rate. Under the application of the law of decreasing marginal income , the marginal value product also decreases with each additional worker employed. The profit maximum is reached when the marginal value product is identical to the wage rate. If wages are lower than the marginal value product of labor, additional workers can be employed. This also applies in the event of falling wages.

For the production factor capital, the marginal product is the change in sales due to the increase in the capital employed by one unit: ${\ displaystyle WGP_ {K}}$${\ displaystyle \ Delta K}$

${\ displaystyle {WGP_ {K}} = {\ frac {\ Delta Q} {\ Delta K}} \ cdot {P_ {q}}}$.

For example, a company increases its equity until its marginal product equals its cost of capital. If the cost of capital is lower than the marginal product of capital, then a profit-maximizing company strives for a capital increase . This also applies in the event of falling interest rates. If work becomes more productive relative to capital, it is worthwhile to use more work with unchanged wages; this saves capital.

## Analytical example

A company produces with the factor labor as follows: Due to the functioning pricing mechanism on the goods markets, the company assumes that it can sell the amount it produces. The decision is therefore only based on the given goods and factor prices. The profit function looks like this (difference between sales and costs): ${\ displaystyle x = {\ sqrt {L}}}$

${\ displaystyle \ Pi = p \ cdot xK (x) = p \ cdot x (L) -w \ cdot L}$.

This includes the price of goods and the price of labor (wages) , as well as the production function. The optimality condition then results in a profit maximum for the following condition: ${\ displaystyle p}$${\ displaystyle w}$

${\ displaystyle \ Pi '= p \ cdot x' (L) -w = 0 \ Leftrightarrow p \ cdot x '(L) = w}$.

The marginal value product can now be found here. The marginal value product of labor ( ) must correspond to the nominal wage rate . ${\ displaystyle p \ cdot x '(L)}$ ${\ displaystyle w}$