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Indigo Algebra and Discrete Mathematics for Economics: Numbers, Graphs and Matrices in Input-Output Economics | Erin Mills Town Centre
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Algebra and Discrete Mathematics are essential tools also for economists.
Globalization makes that goods and services are exchanged worldwide. Input-output analysis uses the advantage of a relatively stable flow of commodities and services. The essential principles can be described by input-output tables. Such tables correspond to systems of linear equations, written as single equations consisting of matrices whose entries are non-negative rational numbers. The flow itself can be described by a directed edge-valued graph where the sets of values consist of positive rational numbers. Therefore numbers, especially non-negative rational numbers, multiple-partite graphs and matrices with non-negative rational entries play an important role in input-output analysis. Thus knowledge from Algebra and Discrete Mathematics becomes more and more useful in this area.
We will consider a particular set of graphs, the so-called input-output graphs and a particular set of matrices, the input-output matrices, define a partial binary operation on each of these sets and prove that we obtain weakly isomorphic weakly partial semigroups. The result of considering this situation can be applied to multiple-step production processes, to material reqirements planning and to internal cost allocation of a business.
The results show that Algebra and Discrete Mathematics are quite useful for mathematical modeling in Economy.
Algebra and Discrete Mathematics are essential tools also for economists.
Globalization makes that goods and services are exchanged worldwide. Input-output analysis uses the advantage of a relatively stable flow of commodities and services. The essential principles can be described by input-output tables. Such tables correspond to systems of linear equations, written as single equations consisting of matrices whose entries are non-negative rational numbers. The flow itself can be described by a directed edge-valued graph where the sets of values consist of positive rational numbers. Therefore numbers, especially non-negative rational numbers, multiple-partite graphs and matrices with non-negative rational entries play an important role in input-output analysis. Thus knowledge from Algebra and Discrete Mathematics becomes more and more useful in this area.
We will consider a particular set of graphs, the so-called input-output graphs and a particular set of matrices, the input-output matrices, define a partial binary operation on each of these sets and prove that we obtain weakly isomorphic weakly partial semigroups. The result of considering this situation can be applied to multiple-step production processes, to material reqirements planning and to internal cost allocation of a business.
The results show that Algebra and Discrete Mathematics are quite useful for mathematical modeling in Economy.
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