The correct answer is: A. Homogenity of a factor.
The marginal productivity theory of distribution is a theory of income distribution that states that the distribution of income is determined by the marginal productivity of the factors of production. The theory assumes that factors of production are homogeneous, that there is perfect competition in the factor market, and that all factors, except one, are variable.
Homogeneity of a factor means that all units of a factor are identical in terms of quality and productivity. This assumption is not realistic, as factors of production are often heterogeneous. For example, workers with different skills and experience will have different marginal products.
Perfect competition in the factor market means that there are many buyers and sellers of factors of production, and that there is no collusion or price discrimination. This assumption is also not realistic, as there are often few buyers and sellers of factors of production, and there may be collusion or price discrimination.
All factors, except one, are variable means that all factors of production can be increased or decreased in the short run, except for one factor, which is fixed. This assumption is not realistic, as all factors of production are often variable in the long run.
Given stock of each factor and full employment means that the stock of each factor of production is fixed, and that all factors of production are fully employed. This assumption is not realistic, as the stock of factors of production can change over time, and factors of production are often not fully employed.
Therefore, the assumption of homogeneity of a factor is not realistic, and it is the only assumption that is not necessary for the marginal productivity theory of distribution to hold.