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the russian-born u.s. economist and nobel laureate wassily leontief (1906–1999) was interested in the following question: what output should each of the industries in an economy produce to satisfy the total demand for all products? here, we consider a very simple example of input–output analysis, an economy with only two industries, a and b. assume that the consumer demand for their products is, respectively, 1,000 and 780, in millions of dollars per year. industry a industry b consumer 1,000 780 what outputs a and b (in millions of dollars per year) should the two industries generate to satisfy the demand? you may be tempted to say 1,000 and 780, respectively, but things are not quite as simple as that. we have to take into account the interindustry demand as well. let us say that industry a produces electricity. of course, producing almost any product will require electric power. suppose that industry b needs 10c/ worth of electricity for each $

Sagot :

Output a=400 and Output b=300

Let

     Output of industry A=a

    Output of industry B=b

Now industry A shall produce output required by customer i.e. 310

But, industry A also have to supply 0.36 output to industry B

Then we obtain   a-0.36=310

Similarly industry B shall produce output required by customer i.e. 100 while also supplying 0.5a output to Industry A.

Then we obtain    b-0.5a=100

Thus, we obtain set of linear equations

a-0.36=310-----------eq1

-0.5+b=100-----------eq2

Solving the linear system, we multiply equation 1 by 0.5

eq 1×0.5 ⇒ 0.5a-0.15b=155

eq2×1     ⇒ -0.5a+b=100

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                   0.85b=255

                           b=255/0.85=300

Then putting in eq 1        

a-0.3(300)=310

              a=310+90

             a=400

Thus, output a=400, output b=300  

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