2 each industry uses a fixed input ratio or factor

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Unformatted text preview: j. To clarify, the production of each unit of the jth commodity will require a1j of the first commodity, a2j of the second commodity,..., and anj of the nth commodity. The order of the subscripts in aij is easy to remember: the first subscript refers to the input and the second refers to the output so that aij indicates how much of the ith commodity is used for the production of each unit of the jth commodity. For our purposes, let's assume that prices are given and this allows us to adopt "a dollar's worth" of each commodity as its unit of measurement. Then the statement a32 = 0.35 will mean that 35 worth of the third commodity is required as an input for producing a dollar's worth of the second commodity. This means that the aij symbol can be referred to as the input coefficient. For an n-industry economy, the input coefficients can be arranged into a matrix A = [aij], as in the table on the next page. Each column specifies the input requirements for the production of one unit of the output for a particular industry. The second column, for example, states that to produce a unit (one dollar's worth) of commodity 2, the inputs needed are: 221 a12 units of commodit 1, a22 un of com ty nits mmodity 2,... and an2 units of ..., com mmodity n. . ses s then the ele ements in th principal he l If no industry us its own product as an input, t diago onal of mat A will all be zero. trix del The Open Mod esides the n industries the model also conta s, ains an "ope sector ( en" (say, If, be hous seholds) wh hich exogen nously dete ermines a fin demand (i.e. a non nal d n-input dema and) for the product of each industry and wh e f hich supplie a primar input es ry (say, labour) no produced by the n in , ot d ndustries th hemselves, then the model is an open model. n With the case of the prese o ence of an o open sector the sum o the eleme r, of ents in eac ch colum of the in mn nput coeffic cient matrix A must be less than 1 Each column sum 1. repre esents the partial i...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.

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