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Note that cach column sum in A is less than I, as it should be. Further, if we denotc by aj 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]: ao 0.3 ao2-0.3 an0.4 (5.23) With the matrix A of (5.22), the open input-output system can be expressed in the form (1-4)x = d as follows: 0.8-0.3-0.2 di (5.24) -0.4 0.9-0.211x21=1d2 03 0.8 LJ Ld Here we have deliberately not given specific values to the final demands di, d2, and d3. 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 a 30, c2 15, and 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-industry 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 Il; and the open sector demands $1,000 billion of commodity I and $2,000 billion of commodity E (o) 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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