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Unformatted text preview: em the is no unique "correct" output m s ere mix. 230 _ _ _ _ We c determine the outp levels x0, x1, x2, an x3 in proportion to o another can put nd one r, but w cannot fix their abs we f solute levels unless ad s dditional res strictions ar imposed re on th model. We will see that this is much less useful (no really very useful at he W e s s ot y all!) t than our res sults from t open model since we cannot invert the t the technology matrix in the clo osed model. odel A Nu umerical E Example The Closed Mo Supp pose that we have the same exam w mple as we solved in t open m e the model above e, but w convert the primary input into "just another industry" and appro we y " oach the problem as a closed input output m model. all s e efficient ma atrix for the open mode is as el Reca that we said that the input co-e follow ws: and i we denote by a0j the dollar amo if e ount of the primary inp (labour) used in put producing a dollar's worth of the jth co ommodity, w can writ (by subtr we te racting each h colum sum in the above m mn t matrix from 1): m a01 = 0.3 0 a02 = 0.3 a03 = 0.4 ow e nput into "ju another industry" by adding ust y so no we can convert the primary in these elements to the inpu co-efficient matrix as follows: e ut s With the matrix A above, th closed in he nput outp system c be exp put can pressed in the fo we der orm rived earlier...Tx = (I A)x = d as follows: 231 Or sp pecifically, we ove get ) o em So, w said abo that to g a specific (unique) solution to the proble the techn nology matrix must be invertible.. e .. We k know that fo the close model th it won't b invertible but let's confirm this or ed hat be e, s by fin nding the determinant of the tech hnology mat trix. We wi use the fi row to ill irst expa along to evaluate t determi and o the inant... f minants is si imply the de eterminant that we Now, the first of the four 3 3 determ figure out in th open ver ed he rsion of the model. Th first one works out to be 0.384 his 4. 232 The second term of this de m eterminant c be foun as follow can nd ws: The t third term of this deter o rminant can be found as follows: n 233 The f fourth term of this...
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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