Find the outputs a and b needed to satisfy the consumer and interindustry demands given...

Find the outputs a and b needed to satisfy the consumer and interindustry demands given in the following figure. See Exercise 24:

See Exercise 24:

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.

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 10 ? worth of electricity for each $1 of output B produces and that industry A needs 20? worth of B’s products for each $1 of output A produces. Find the outputs a and b needed to satisfy both consumer and interindustry demand.