Question

The consumption matrix C for the U.S. economy in 1972 has the property that every entryin the matrix \({\left( {I - C} \right)^{ - 1}}\) is nonzero (and positive). What does that say about the effect of raising the demand for the output of just one sector of the economy?

Short answer

An increase in the final demand for any sector will increase the demand for all sectors.

Step-by-step solution

State the \(\left( {i,j} \right)\) entry in \({\left( {I - C} \right)^{ - 1}}\)

From Exercise 8, the \(\left( {i,j} \right)\) entry in \({\left( {I - C} \right)^{ - 1}}\) corresponds to the effect on the production of sector \(i\) if the final demand for the output of sector \(j\) rises by one unit.

Find the effect of raising the demand for the output of one sector

An increase in the final demand for any sector increases the production of all sectors because all the entries are positive.

Therefore, an increase in the final demand for any sector increases the demand for all sectors.