Unformatted text preview: nput cost (not i p including th cost of th primary input) he he incur rred in prod ducing a dollar's worth of some co ommodity; if this sum is greater than or equal to 1 then pro o oduction wo ould not be economica justifiable. ally Symbolically, th fact can be stated a follows: his as 222 re mation is ov i, that is over the e ver s, elements appearing in the variou n us wher the summ rows of a specif column j s fic j. Takin this line of thought a step furth it may also be sta ng her, ated that, sin the nce value of output ($1) must b fully abs e be sorbed by th payment to all fact he ts tors of production, the amount by which the column sum falls shor of $1 mus be the y m rt st value of the pay e yment to the primary in e nput (labou of the op sector. ur) pen Thus the value of the prim s, mary input n needed in p producing a unit of the jth comm modity shou be: uld If ind dustry 1 is to produce a output ju sufficien to meet the input req o an ust nt quirements s of the n industries as well a the final demand of the open s e as f sector, its o output level l x1 must satisfy the followin equation: t ng x1 = a11x1 + a12x2 + a13x3 +... a1nxn + d1 ...+ or (1 a11) x1 a12x2 a13x3 - ... - a1nxn = d1 re es or t epresents t input the wher d1 denote the final demand fo its output and a1jxj re 3 dema from th jth industry. Notice that, exce for the f and he e ept first coefficie (1 ent a11), the remain ning coeffici ients in the last equation are exac the first row of the ctly t e matrix on page 3 above ex xcept they a all nega are ative. Similarly, the corre esponding equation for industry 2 will have t same co e the oefficients a in the as seco row of the matrix o page 3 a ond on above, exce that the variable x2 will have ept the c coefficient (1 a22) ins stead of a22. For t entire se of n indu the et ustries, the "correct" ou utput levels can be sum s mmarized by th following system of n linear eq he g quations: 3 Do n add up the input coeffic not e cients across a row; such a sum say, a11 + a12 + a1 +...+ a1n is 13 devoid of economic meaning. T sum of...
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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.
- Spring '10