Leontief Matrix. Robert M. Hayes 2002. Nobel Prize in Economics. The following slides list the persons who have received the Nobel Prize for Economics since its inception in 1969.
Robert M. Hayes
X = A*X +D
where the matrix A represents the requirement for input (from each sector into each sector) that will generate the output to serve the needs in production of output X. The resulting “internal consumption” is represented by A*X.
XTt (I - A) - (XTt+1 - XTt )B = DTt,
where I is the nxn identity matrix, A is the usual Leontief input matrix, B is the matrix of fixed capital coefficients, X is the vector of total outputs and D is the vector of final deliveries, excluding fixed capital investment; t refers to the time period. It deserves to be stressed that in this approach time is treated as a discrete variable. The coefficient bij in the matrix B defines the stock of products of industry j required per unit of capacity output of industry i and is thus a stock-flow ratio.