LACHLAN SMITH 12R

YEAR 12 MATHS C

MRS SWAN

EXTENDED MODELLING TASK

QUESTION 1

Consider the 4-sector economic system consisting of petroleum, textiles, transportation and chemicals. The production of 1 unit of petroleum requires 0.2 units of transportation, 0.4 units of chemicals and 0.1 unit of itself. The production of 1 unit of textiles requires 0.4 units of petroleum, 0.1 units of textiles, 0.15 units of transportation and 0.3 units of chemicals. The production of 1 unit of transportation requires 0.6 units of petroleum, 0.1 unit of

itself and 0.25 units of chemicals. Finally, the production of 1 unit of chemicals requires 0.2 units of petroleum, 0.1 units of textiles, 0.3 units of transportation and 0.2 units of chemicals.

a) P

Te

Tr

Ch

P

Te

Tr

Ch

Write a technology matrix to represent this information.

0.10.40.60.200.100.10.20.150.10.30.40.30.250.2

b) On what sector is petroleum most dependent? Least dependent?

Petroleum is most dependent on the chemicals sector as it requires the most units out of the other three sectors that make up petroleum. The least dependent sector is textiles as it does not feature in the economic system in the production of petroleum. Both these findings can be identified by looking at the technology matrix above in Part a).

c) If the textiles sector has an output of $4 million, what is the input in dollars from petroleum?

The total output from the textiles sector is $4 000 000. Petroleum has a sector that valued at 0.4 in the total production of textiles. This number can be multiplied by 4 000 000 to find the total input dollars from petroleum.

Textiles = $4 000 000

Petroleum sector = 0.4

∴0.4×4 000 000

=$1 600 000

d) Suppose the production matrix is:

P=Petr.TextTrans.Chem.800200700750

i. What is the internal consumption matrix?

Internal consumption = A x P

A=0.10.40.60.200.100.10.20.150.10.30.40.30.250.2 × P=800200700750

=...

YEAR 12 MATHS C

MRS SWAN

EXTENDED MODELLING TASK

QUESTION 1

Consider the 4-sector economic system consisting of petroleum, textiles, transportation and chemicals. The production of 1 unit of petroleum requires 0.2 units of transportation, 0.4 units of chemicals and 0.1 unit of itself. The production of 1 unit of textiles requires 0.4 units of petroleum, 0.1 units of textiles, 0.15 units of transportation and 0.3 units of chemicals. The production of 1 unit of transportation requires 0.6 units of petroleum, 0.1 unit of

itself and 0.25 units of chemicals. Finally, the production of 1 unit of chemicals requires 0.2 units of petroleum, 0.1 units of textiles, 0.3 units of transportation and 0.2 units of chemicals.

a) P

Te

Tr

Ch

P

Te

Tr

Ch

Write a technology matrix to represent this information.

0.10.40.60.200.100.10.20.150.10.30.40.30.250.2

b) On what sector is petroleum most dependent? Least dependent?

Petroleum is most dependent on the chemicals sector as it requires the most units out of the other three sectors that make up petroleum. The least dependent sector is textiles as it does not feature in the economic system in the production of petroleum. Both these findings can be identified by looking at the technology matrix above in Part a).

c) If the textiles sector has an output of $4 million, what is the input in dollars from petroleum?

The total output from the textiles sector is $4 000 000. Petroleum has a sector that valued at 0.4 in the total production of textiles. This number can be multiplied by 4 000 000 to find the total input dollars from petroleum.

Textiles = $4 000 000

Petroleum sector = 0.4

∴0.4×4 000 000

=$1 600 000

d) Suppose the production matrix is:

P=Petr.TextTrans.Chem.800200700750

i. What is the internal consumption matrix?

Internal consumption = A x P

A=0.10.40.60.200.100.10.20.150.10.30.40.30.250.2 × P=800200700750

=...