## Fossil fuels, bio fuels, and food: ranking priorities

Input-output models Inter-industry flows in a specific economy are determined by technological and economic factors, and these flows can be described by a system of simultaneous equations represented by:

X = AX + Y(1)

where X is a vector (n x 1) of total production by sector; Y (n x 1) is the final demand; and A is a (n x n) matrix of technical coefficients, Leontief (1951) and Miller and Blair (2009). In the model above, the final demand vector is usually considered exogenous to the system; thus, the total production vector is determined only by the final demand vector, that is:

X + BY (2)

and

B = (I – A)–1 (3)

where B (n x n) is the Leontief inverse matrix. Working with the information contained in the input-output systems it is possible to conduct a structural analysis of the economy. The next section sets this out.