Identified by English economist Philip Wicksteed (1844-1927) among others, adding-up problem refers to the difficulty of ensuring that the income earned by different factors of production when added together equals national income.

If each factor of production is paid the value of its respective marginal product, cetris paribus, a situation will eventually arise in which total product (total income) will be exhausted.

Wicksteed studied the problem in the model of a long-run economy in perfect competition.

The Swiss mathematician Leonhard Euler (1707-1783) argued that certain assumptions had to be made the production function (that is, how factors of production are combined to produce output) to make national income equal to the sum of income earned by individual factors of production.In any theory of income distribution in which one type of return is determined residually, it will be tautologically true that the various different incomes, as determined by the theory, will add up so as to exhaust the total product. By contrast, any theory which provides a ‘positive’ explanation for every category or return, treating none as a residual, must show that the various returns so explained do indeed exhaust the product. In practice, it has been with reference to the marginal productivity theory that this consistency requirement has received considerable attention. By the early 1890s a number of authors had sought to extend the ‘principle of rent’ into a completely general theory of distribution but it was P.H. Wicksteed, in his Co-ordination of the Laws of Distribution (1894) who first clearly stated, and attempted to resolve, the resulting adding-up problem.

You got a very fantastic website, Glad I noticed it through yahoo.