This type of analysis has been used extensively in economic planning, but it has many other uses as well.
II. The Closed Leontief Model.
2.1 An Introduction to the Models.
The matrix is set up to represent interdependent industries. The coefficients represent the the materials necessary for each industry to produce one unit of their goods. This is why the matrix is often referred to as the consumption matrix. The coefficients in row one correspond to industry the coefficients in row 2 are the amounts necessary for industry to produce something, and so on. Each column in the coefficient matrix models the output from each industry that is consumed. This means that the summation of the entries in a given column will give the total amount of product from a given industry that is consumed by the economy modelled.
Now each coefficient has meaning in the matrix:.
is the amount of product from industry required for that industry to create a unit of output. This is what the industry consumes of itself.
is the amount of product from industry required for industry to produce anything.
For example, consider this economy:.
There are three sectors in this economy: agriculture, manufacturing, and labor. To produce a unit of food, the industry needs .2 units of food, .5 units of manufactured goods, and .3 units of labor. The manufacturing industry needs .3 units of food, .3 units of its own goods, and .6 units of labor. The sector that contains the work force needs .5 units of food, .2 units of manufactured goods, and .1 units of its own labor to produce more labor.
The matrix is meant to model the flow of goods and services in the economy. The matrix will also show whether or not an economy can produce enough to fulfill a certain demand for their goods. There are two types of demand: an inside demand and an outside demand. The inside demand consists of the demand from the industries contained within the model.