Leontiff Models

Question

. A Leontief input-output model has two goods, steel and oil. The production processes
are such that .8 units of steel and .1 unit of oil are required to produce 1 unit of steel, and
.4 units of steel and .5 units of oil are required to produce 1 unit of oil. Suppose that the
economy is meeting an external demand of 2 units of steel and 1 unit of oil. Then

 

 

a) The level of production of steel is at two times the level of production of oil.
b) The level of production of steel is at 4.5 times the level of production of oil.
c) The level of production of steel is at 2.5 times the level of production of oil.
d) The level of production of steel is at 3.5 times the level of production of oil.
e) None of the above

 

 

 

 

 

The answer is D but why?

Answer 1

Let S = total steel production and O = total oil production.

The Leontief model says total production must cover both:

1. the amount industries use internally, and
2. the external demand.

For steel, producing 1 unit of steel uses 0.8 unit of steel, and producing 1 unit of oil uses 0.4 unit of steel. There is also an external demand of 2 units of steel.

So:

S = 0.8S + 0.4O + 2

Rearranging:

0.2S - 0.4O = 2

S - 2O = 10

Therefore:

S = 2O + 10

For oil, producing 1 unit of steel uses 0.1 unit of oil, and producing 1 unit of oil uses 0.5 unit of oil. There is an external demand of 1 unit of oil.

So:

O = 0.1S + 0.5O + 1

Rearranging:

-0.1S + 0.5O = 1

-S + 5O = 10

Therefore:

S = 5O - 10

Now set the two expressions for S equal:

2O + 10 = 5O - 10

20 = 3O

O = 20/3

Then:

S = 2(20/3) + 10 = 70/3

Now compare the production levels:

S/O = (70/3)/(20/3) = 70/20 = 3.5

Therefore, the level of steel production is 3.5 times the level of oil production.

Answer: D