Chapter 2.6, Problem 24E

(a)

To determine

The input-output matrix A if there is a three sector economy which consists of wood, steel and coal.

Wood requires input of $30\text{<menclose notation="updiagonalstrike">c</menclose>}$ from wood, $20\text{<menclose notation="updiagonalstrike">c</menclose>}$ from steel and $10\text{<menclose notation="updiagonalstrike">c</menclose>}$ from coal for $\$1$; steel requires no input from wood, $30\text{<menclose notation="updiagonalstrike">c</menclose>}$ from steel and $20\text{<menclose notation="updiagonalstrike">c</menclose>}$ from coal for $\$1$ and coal requires input of $10\text{<menclose notation="updiagonalstrike">c</menclose>}$ from wood, $20\text{<menclose notation="updiagonalstrike">c</menclose>}$ from steel and $5\text{<menclose notation="updiagonalstrike">c</menclose>}$ from coal for $\$1$.

(b)

To determine

The matrix ${\left(I-A\right)}^{-1}$ if there is a three-sector economy which consists of wood, steel and coal.

Wood requires input of $30\text{<menclose notation="updiagonalstrike">c</menclose>}$ from wood, $20\text{<menclose notation="updiagonalstrike">c</menclose>}$ from steel and $10\text{<menclose notation="updiagonalstrike">c</menclose>}$ from coal for $\$1$; steel requires no input from wood, $30\text{<menclose notation="updiagonalstrike">c</menclose>}$ from steel and $20\text{<menclose notation="updiagonalstrike">c</menclose>}$ from coal for $\$1$ and coal requires input of $10\text{<menclose notation="updiagonalstrike">c</menclose>}$ from wood, $20\text{<menclose notation="updiagonalstrike">c</menclose>}$ from steel and $5\text{<menclose notation="updiagonalstrike">c</menclose>}$ from coal for $\$1$.

(c)

To determine

To calculate: The levels at which each sector should produce if the demand for wood, steel and coal is worth $\$200$, $\$300$ and $\$800$.

There is a three sector economy which consists of wood, steel and coal.

Wood requires input of $30\text{<menclose notation="updiagonalstrike">c</menclose>}$ from wood, $20\text{<menclose notation="updiagonalstrike">c</menclose>}$ from steel and $10\text{<menclose notation="updiagonalstrike">c</menclose>}$ from coal for $\$1$; steel requires no input from wood, $30\text{<menclose notation="updiagonalstrike">c</menclose>}$ from steel and $20\text{<menclose notation="updiagonalstrike">c</menclose>}$ from coal for $\$1$ and coal requires input of $10\text{<menclose notation="updiagonalstrike">c</menclose>}$ from wood, $20\text{<menclose notation="updiagonalstrike">c</menclose>}$ from steel and $5\text{<menclose notation="updiagonalstrike">c</menclose>}$ from coal for $\$1$.

(d)

To determine

To calculate: The amount of output of each sector is used to meet internal consumption if the demand for wood, steel and coal is worth $\$200$, $\$300$ and $\$800$.

There is a three sector economy which consists of wood, steel and coal.

Wood requires input of $30\text{<menclose notation="updiagonalstrike">c</menclose>}$ from wood, $20\text{<menclose notation="updiagonalstrike">c</menclose>}$ from steel and $10\text{<menclose notation="updiagonalstrike">c</menclose>}$ from coal for $\$1$; steel requires no input from wood, $30\text{<menclose notation="updiagonalstrike">c</menclose>}$ from steel and $20\text{<menclose notation="updiagonalstrike">c</menclose>}$ from coal for $\$1$ and coal requires input of $10\text{<menclose notation="updiagonalstrike">c</menclose>}$ from wood, $20\text{<menclose notation="updiagonalstrike">c</menclose>}$ from steel and $5\text{<menclose notation="updiagonalstrike">c</menclose>}$ from coal for $\$1$.