# 2.6 - 2.6 The Leontief Input-Output Model This is a basic...

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2.6 The Leontief Input-Output Model This is a basic model for studying the economies of coun- tries, or provinces, or cities, or ... Assumptions: (i) One part of economy is divided into n sectors of producers that produce goods or services: production vector vectorx ∈ R n is the annual output of each sector (ii) Another part of economy is consumers that consume goods and services from the others (and don’t produce anything): this is the open sector, and final demand vector vector d ∈ R n is the value of goods and services demanded by these nonproductive sectors (e.g., consumer demand, government consumption, exports, surplus production) (iii) Producers of goods and services themselves create an additional demand for goods and services as inputs for their production (that is, they also consume goods and services). This is the intermediate demand For an equilibrium , total produced equals total consumed, that is, vectorx = ( · ) + vector d amount produced = intermediate demand + final demand 1

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Measuring all inputs and outputs in currency (say, mil- lions of dollars), there is a unit currency vector ∈ R n giving input needed per unit of output for each sector. Therefore, there is a consumption matrix C = bracketleftBig vector c 1 | · · · | vector c n bracketrightBig such that intermediate demand = x 1 vector c 1 + x 2
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