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C-92 Appendix C
TABLE 2
External Demands*
Steel
308 units
Coal
275 units
Electricity 830 units
*These are the demands for steel, coal,
and electricity exclusive of the production
requirements listed in Table 1.
(While it’s clear that coal and electricity would be required in the production of
steel, you may be wondering why steel itself appears as one of the inputs.
Think of the steel as being utilized in the building of equipment or factories for
use by the steel industry.) The second and third columns of figures in the table
are interpreted similarly. In particular, the second column of figures in Table 1
indicates that the production of 1 unit of coal requires 0.02 unit of steel, no
units of coal, and 0.10 unit of electricity. The third column indicates that the
production of 1 unit of electricity requires 0.16 unit of steel, 0.25 unit of coal,
and 0.04 unit of electricity.
Table 1 can also be interpreted by reading across the rows, rather than
down the columns. The first row of figures tells how much steel is required to
produce 1 unit of output from each industry. In particular, to produce 1 unit of
steel, 1 unit of coal, or 1 unit of electricity requires 0.04 unit of steel, 0.02 unit
of steel, or 0.16 unit of steel, respectively. The second and third rows of figures
are interpreted similarly.
Table 1 shows the demands that the three sectors place on one another for
production. Now, outside of these three sectors, in other industries or in government,
for example, there are, of course, additional demands for steel, coal,
and electricity. These additional demands, from sources outside of the three
given sectors, are referred to as external demands. By way of contrast, the
demands in Table 1 are called internal demands. Let us suppose that the
external demands are as given in Table 2. The problem to be solved then is as
follows.
An Input-Output Problem
How many units should each of the three given sectors produce to satisfy both
the internal and external demands on the economy?
To solve this input-output problem, let
x the number of units of steel to be produced
y the number of units of coal to be produced
z the number of units of electricity to be produced
We’ll use the information in Tables 1 and 2 to generate a system of three linear
equations involving x, y, and z. First, since x represents the total number of
units of steel to be produced, we have
(internal demands for steel) (external demands for steel) x
(internal demands for steel) 308 x
using (1)
Table 2
Regarding the internal demands for steel in equation (1), we’ll make use of
the first row of figures in Table 1 along with the following proportionality
assumption. (For clarity, we state this for the case of steel output, but it’s
assumed for coal and electricity as well.) If the output of one unit of steel
requires n units of a particular resource, then the output of x units steel requires