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Application of maths in economics

What are the branches of maths where we can see undoubtful connections with economics? Where can we use mathematical methods or models and apply them to analyze economic concepts?
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Find a price vector p for various prices of industries.

( Leontief input-output model ) Suppose that three industries are interrelated so that their outputs are used as inputs by themselves, according to the $3 \times 3$ consumption matrix A = ...