Feasible Set and the Transformation of Values

This paper proposes a shift in perspective on two long-standing problems in political economy: the reduction of complex labor and the transformation problem. Rather than searching for a unique constant solution, we reframe both problems as characterizing the space of feasible distributions under the constraints imposed by the objective physical-production network. We build an input--output model that includes fixed-capital stocks and prove mathematically that, as long as the macroeconomy generates a physical surplus, all reduction ratios that can sustain the subsistence floor of the labor force form a bounded value feasible set. Within this multi-dimensional space, the classical two macro-aggregates equalities can be satisfied simultaneously for a well-defined range of profit rates, so that the Law of Labor Value and the nominal price system are logically consistent without violating the physical reproduction floor. We validate the theoretical framework with an empirical test based on China's 199-sector input-output network for 2023.