Two sectors of some economy are Sector 1 and Sector 2. The input-output table involving these two sectors results in the following value for $$( I - A ) ^ { - 1 }$$ $$( I - A ) ^ { - 1 } = \left[ \begin{array} { c c }
1.0965 & 0.04361 \
0.00536 & 1.07515
\end{array} \right]$$
How many additional dollars worth of production of Sector 2 must be produced to meet a $1 increase in the demand for products of Sector 2

A)$0.00536
B) $0.54825
C) $1.07515
D) $1.0965
E) $0.04361

Question

Two sectors of some economy are Sector 1 and Sector 2. The input-output table involving these two sectors results in the following value for $$( I - A ) ^ { - 1 }$$     $$( I - A ) ^ { - 1 } = \left[ \begin{array} { c c } 
1.0965 & 0.04361 \
0.00536 & 1.07515
\end{array} \right]$$  
How many additional dollars worth of production of Sector 2 must be produced to meet a $1 increase in the demand for products of Sector 2 
 
A)$0.00536
B) $0.54825
C) $1.07515
D) $1.0965
E) $0.04361

Quizplus · Accepted Answer

The matrix $( I - A ) ^ { - 1 }$ represents the total output required from each sector to meet one unit of final demand in the economy. To find how many additional dollars worth of production of Sector 2 must be produced to meet a $1 increase in the demand for products of Sector 2, we look at the second column, second row entry of the matrix, which is $1.07515. This means for a $1 increase in demand for Sector 2's products, Sector 2 must increase its production by $1.07515.

Two Sectors of Some Economy Are Sector 1 and Sector (I−A)−1( I - A ) ^ { - 1 }(I−A)−1

Two Sectors of Some Economy Are Sector 1 and Sector $( I - A ) ^ { - 1 }$