can the marginal product of capital be negative
Marginal product In the "law" of diminishing marginal returns, the marginal product initially increases when more of an input (say labor) is employed, keeping the other input (say capital) constant. Here, labor is the variable input and capital is the fixed input (in a hypothetical two-inputs model). As more and more of variable input (labor) is employed, marginal product starts to fall. Finally, after a certain point, the marginal product becomes negative, implying that the additional unit of labor has decreased the output, rather than increasing it. The reason behind this is the diminishing marginal productivity of labor.
Production–possibility frontier In the PPF, all points on the curve are points of maximum productive efficiency (no more output of any good can be achieved from the given inputs without sacrificing output of some good); all points inside the frontier (such as A) can be produced but are productively inefficient; all points outside the curve (such as X) cannot be produced with the given, existing resources.[2] Not all points on the curve are Pareto efficient, however; only in the case where the marginal rate of transformation is equal to all consumers' marginal rate of substitution and hence equal to the ratio of prices will it be impossible to find any trade that will make no consumer worse off.[3]