Hawkins–Simon condition

The Hawkins–Simon condition refers to a result in mathematical economics, attributed to David Hawkins and Herbert A. Simon, that guarantees the existence of a non-negative output vector that solves the equilibrium relation in the input–output model where demand equals supply. More precisely, it states a condition for ${\displaystyle [\mathbf {I} -\mathbf {A} ]}$ under which the input–output system

has a solution ${\displaystyle \mathbf {\hat {x}} \geq 0}$ for any ${\displaystyle \mathbf {d} \geq 0}$. Here ${\displaystyle \mathbf {I} }$ is the identity matrix and ${\displaystyle \mathbf {A} }$ is called the input–output matrix or Leontief matrix after Wassily Leontief, who empirically estimated it in the 1940s. Together, they describe a system in which

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