Marginal Productivity Theory (Neoclassical Approach)

Before understanding the marginal productivity theory, first know what the theory of distribution.

This is the neo-classical theory of distribution, which argues that the price of any input depends on its marginal productivity.
Marginal productivity refers to the additional product produced by a factor in its next unit. If the marginal product of the factor is higher, it gets a higher price.
When a firm decides to employ or use the factor, it compares the price to be paid to the factor and the value of the products produced by the factor.
If the price of the factor is less than the additional value, the firm benefits, and it then demands more of the factor.
For example, consider labour as a factor, and the wage rate per hour is Rs. 500, and the value of the product produced by the labour in an hour is Rs. 800, then it is profitable to hire more labour. But if the value of the product produced by labour is only Rs. 400, then the firm does not hire more labour.
The market determines the price of any factor based on its marginal productivity.

In the perfectly competitive market, we are assuming both the factor and product markets are perfectly competitive. So, the prices of factors and products are given to the firm, and the firm is a profit maximizer.
In such a case, the price of the factor is determined by the interaction between market demand and supply of the factor. The market demand of the factor is the summation of the factor demand by individual firms, and the market supply of the factor is also the summation of the supply of the factor.
However, the demand for the factor is the derived demand, which depends on the demand for the goods and services produced by it. Similarly, the supply of the factor is also different from the product supply.
To explain factor pricing in the perfectly competitive market, assume that labour is such a factor, then the market demand of labour is summation od labor demand by the individual firm, which demands labour based on the value of the marginal product of labour (VMP_L) and the wage rate (W).
If VMP_L>W, it is profitable to employ more labour, and so the firm demands more labour.
Similarly, if VMP_L<W, then the firm reduces labour. So, the firm attains equilibrium when VMP_L=W.

Labor demand by a firm

Here,

If the wage rate is Wo, then the firm employs OLo units of labour at which VMP_L=W.
If the wage rate declines to w1, then the firm is in equilibrium at E1 with OL1 units of labour.
This shows that is wage rate declines, then the firm employs more labour. Such an inverse relationship between wage rate and quantity of labour. So, the VMP_L=curve itself represents the labour demand curve by the firm if labour is a single variable factor.

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