Von Neumann raised the intellectual and mathematical level of economics in several stunning publications. For his model of an expanding economy, von Neumann proved the existence and <answer>uniqueness of an equilibrium using his generalization of the Brouwer fixed-point theorem</answer>. Von Neumann's model of an expanding economy considered the matrix pencil  A − λB with nonnegative matrices A and B; von Neumann sought probability vectors p and q and a positive number λ that would solve the complementarity equation
What did von Neumann prove with his model of expanding economy?
uniqueness of an equilibrium using his generalization of the Brouwer fixed-point theorem