Question

14. An economy consists of three sectors: agriculture, industry, and services. To produce $1 worth of agricultural output, the agricultural sector requires $0.3 of its own output, 0.1 of industrial output and $0.4 of services output. On the other hand, to produce $1 worth of industrial output, the industrial sector requires $0.4 of agricultural output, $0.3 of its own output and $0.2 of services output. Finally, to produce $1 worth of services output, the services sector requires $0.1 of agricultural output, $0.4 of industrial output and $0.4 of its own output. a) Derive the technology matrix A from the above information $\begin{bmatrix} 20,000 \\ 30,000 \\ 40,000 \end{bmatrix}$ b) Given that the vector of the final production $X = \begin{bmatrix} 20,000 \\ 30,000 \\ 40,000 \end{bmatrix}$, find the vector of final demand $d$ in the economy

          14. An economy consists of three sectors: agriculture, industry, and services. To produce $1 worth of
agricultural output, the agricultural sector requires $0.3 of its own output, 0.1 of industrial output
and $0.4 of services output. On the other hand, to produce $1 worth of industrial output, the
industrial sector requires $0.4 of agricultural output, $0.3 of its own output and $0.2 of services
output. Finally, to produce $1 worth of services output, the services sector requires $0.1 of
agricultural output, $0.4 of industrial output and $0.4 of its own output.
a) Derive the technology matrix A from the above information
$\begin{bmatrix} 20,000 \\ 30,000 \\ 40,000 \end{bmatrix}$ 
b) Given that the vector of the final production $X = \begin{bmatrix} 20,000 \\ 30,000 \\ 40,000 \end{bmatrix}$, find the vector of final demand $d$
in the economy

14. An economy consists of three sectors: agriculture, industry, and services. To produce 1 worth of
agricultural output, the agricultural sector requires0.3 of its own output, 0.1 of industrial output
and 0.4 of services output. On the other hand, to produce1 worth of industrial output, the
industrial sector requires 0.4 of agricultural output,0.3 of its own output and 0.2 of services
output. Finally, to produce1 worth of services output, the services sector requires 0.1 of
agricultural output,0.4 of industrial output and 0.4 of its own output.
a) Derive the technology matrix A from the above information
< b m a t r i x >
b) Given that the vector of the final productionX =
< b m a t r i x >
, find the vector of final demanddin the economy

Added by Paul E.

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