Chapter 1.1, Problem 24E

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 demandfor all products? Here, we consider a very simple example of input—output analysis, an economy with only twoindustries, A and B. Assume that the consumer demandfor their products is, respectively, 1 ,000 and 780, in millions of dollars per year.

What outputs a andb (in millions of dollars peryear) should the two industries generate to satisfy thedemand? 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 demandas well. Let us say that industry A produces electricity.Of course, producing almost any product will requireelectric power. Suppose that industry B needs 10 worthof electricity for each $1 of output B produces and that industry A needs 20 ¢ worth of B’s products for each $1of output A produces. Find the outputs a andb neededto satisfy both consumer and interindustry demand.