# Product Exhaustion Problem or Adding Up Problem

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**Product Exhaustion Problem or Adding Up Problem**

The marginal productivity theory of distribution states that each factor of production is paid remuneration equal to its marginal product. It has been urged out that if that were so, the total product would be just exhausted without leaving any surplus or deficit. This problem is called the adding-up problem. The following figures numbering 31.7 and 31.8 illustrate the product exhaustion problem. We assume that there arc only two Factors; labour and capital, used in production. Let A stand for Labour and B for Capital. The marginal product of a factor can be found by varying its quantity and keeping the other factor constant. The reward of a variable factor is equal to its marginal product when a certain quantity of it is used. Then the reward for the filled factor can be shown as surplus (or residual income) of the total product over the marginally determined reward of the variable factor. In figure 31.7, labour (i e. A has been treated as a variable factor and is shown on the X-axis whereas capital has been taken as a fixed Factor. When OL is the equilibrium amount of the labour employed, its marginal product is LM and the wage rate determined is Ow. The total wage bill is OLMW. The total product is the whole area under the marginal productivity curve i.e. OSML. After paying the total wage hill i.e. OLMW, the residual income SWM will go to capital as interest. In the. when we have paid the total wage bill OL 1\’ and interest SWM. nothing is left. i.e. the total product i: exhausted. In order to show that the total product is exhausted, we may now take capital a the fixed factor and labour as the variable fa t r. ital gets ORNK as the margm /I determined interest out of the total product 01 K La ur receives the residue in the form of the wage \I i.e. RTN. Here, again the total product is JU e ansted by the rewards paid to labour and capital. 1’3 ing no surplus or deficit.c have now to prove that the area OKNR in Figure 31.8 is equal to the area WMS in figure 31.7 and area RNT in figure 31.8 is equal to OI.M Only in this way we can show that the payments made in accordance with marginal productivity to both labour and capital exactly exhaust the total product. We can thus show that the marginally and Walras which assumes that the firms operated at the lowest point of the long-run average cost curve.