# Leontief Input Model

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LEONTIEF INPUT OUTPUT MODEL
Leontief input output model is base on the idea that which level of output should produce in an economy in order to satisfy the total demand for that product. By this model we can clearly see how the national economy is affected by the production of output in one industry. Also, in order to produce given amount for final demand , we can easily obtain industriesâ€™ total output. By this model one can say that the economy is whether efficient or not. Structure of an input-output model:
We aplly this model to large number of industries and it could be complicated. Thus, to simplify the problem following assumptions must be take into consideration. 1) Each industry produce only one homegeneous commodity. For example, food industry only produce bread. 2) Each industry uses a fixed input ratio for the production of its output. 3) Production in every industry is subject to constant returns to scale.
These assuptions are unrealistic. Also, from these assumption we can assume that in order to obtain each unit of jth commodity ith input needed which can be show by aij.

It is the input-output coefficient matrix. To produce a unit of output ann is required amount of product from industry Sn.
For example, We can see that there are three industries; agriculture, manufacturing, and labor. In order to produce a unit of food the industry need 0.2 units of food 0.5 manufacturing goods and 0.3 labor etc. This matrix shows that whether the economy can satisfy the certain demand for their goods. The Open Leontief Model:
If the economy consitituted by the n industries than these industries purpose will be satisfy the input demand of the same n industries.We include in the model an open sector. In the open model...

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