Question: Write down the input matrix for the simple Leontief model of Example. Compare the condition for efficient production discussed in that example with the requirement that the sum of the elements of each column in the input matrix be less than 1.
Example: Once upon a time, in an ancient land perhaps not too far from Norway, an economy consisted of three industries-fishing, forestry, and boat building. To produce 1 ton of fish requires the services of α fishing boats. To produce 1 ton of timber requires β tons of fish, as extra food for the energetic foresters. To produce 1 fishing boat requires γ tons of timber. These are the only inputs needed for each of these three industries. Suppose there is no final (external) demand for fishing boats. Find what gross outputs each of the three industries must produce in order to meet the final demands of d1 tons of fish to feed the general population, plus d2 tons of timber to build houses.