Flexible capital-labor assignment model

This paper constructs an assignment model that allocates a variable number of labor to a variable amount of capital. Sattinger introduced an assignment model in which a worker is coupled with a machine. In Sattinger's model, workers and machines differ in quality, e.g., ability, productivity, efficiency, or size. In the model in the present paper, the number of workers and the number of machines also differ from assignment to assignment. First, I introduce a model that assigns a different number of workers with different abilities to a different amount of capital with the same quality, then extend that model to a case in which quality is different among the capital.