Look at interrelationships between industries in a given economy.

A sector of the economy will use resources from itself and other sectors in its production run.

Leontief Input–Output Model

Open model: production uses some commodities, the rest not used are considered surplus.

Closed model: production uses 100%, all inputs/outputs are part of the economy, no surplus

Two models

X

DAXX

Gross production, a column vector

A Technology (or consumption) matrix,

describes relationship between inputs/outputs

D Surplus, another column vector

Open Model

0 AXX

Closed Model

Example 1

45.3.

2.2.A

Given an economy made of Agriculture and Manufacturing.

Technology matrix describes inputs (rows) needed for outputs (columns).

DAXX

1 unit of Agr. requires units of Agr. and units of Man.

1 unit of Man. requires units of Agr. and units of Man.

If 100 units of each is produced, what is left in surplus?

units of Agriculture and

units of Manufacturing are left in surplus.

Example 1 – cont. DXAI )(

45.3.

2.2.A If a surplus of 80 Agr. units and 540 Man.

units is desired, what should be produced?

Produce units of Agr. and units of Man.

Example 2

5.6.2.

2.3.4.

3.1.4.

A

Given a closed economy, find the budgets(outputs) for government, industry and households.

Here the first column represents:

1 unit of Gov. requires units of Gov., units of Ind. and units of House.

3

2

1

x

x

x

X

0)( XAI

0)( XAI

0

0

0

_________

_________

_________

Example 2 – continued

0

0

0

000

19/1210

38/2301