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Note that cach column sum in A is less than I, as it should be. Further, if we denotc by a) thc dollar amount of the primary input used in producing a dollars worth of the jth com- modity, we can writc [by subtracting each column sum in (5.22) from 1]: aoi - 0.3 0.3 and a0.4 (5.23) With the matrix A of (5.22), the open input-output system can be expressed in the form (I - A)x - d as follows: 0.8-0.3-0.2x 0.4 0.9-0.2x2-d2 0.1 -0.3 0.8x (5.24) Here we have deliberately not given specific values to the final demands di, d2, and dj. In this way, by keeping the vector d in parametric form, our solution will appear as a formula into which we can feed various specifie d vectors to obtain various corresponding specific solutions.1. On the basis of the model in (5.24), if the final demands are d30, d2- 15, anod d 10 (all in billions of dollars), what are the solution output levels for the three in- dustries? (Round off answers to two decimal places.) 2. Using the information in (5.23), calculate the total amount of primary input required to produce the solution output levels of Prob. 1. 3. In a two-ndustry economy, it is known that industry uses 10 cents of its own product and 60 cents of commodity to produce a dollars worth of commodity l industry lI uses none of its own product but uses 50 cents of commodity in producing a dollars worth of commodity ll; and the open sector dernands $1,000 billion of commodity I and $2,000 billion of commodity Ii. (a) Write out the input matrix, the Leontief matrix, and the specific input-output matrix equation for this economy (b) Check whether the data in this problem satisfy the Hawkins-Simon condition. (c) Find the solution output leveis by Cramers rule.

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