Input-Output Analysis, Linear Programming and Modified Multipliers

(10) α = [i',0]B^-1 = i'(In - A)^-1{In + D'FD(In - A)^-1}

Similarly the modified employment and income multipliers can be derived. It is
noteworthy that some elements in matrix in equation (10) are zero due to D matrix of
which elements are zero and ones, and the modified multipliers are always smaller than
the original multipliers. This indicates that economic impact would be overestimated
when the original multiplier is used with additional capacity limitations on production.

Numerical Example

An example application of equation (8) through (10) is shown in this section. The
hypothetical data from table 4.2 in Schaffer (1999) is used (See Table 1). In this
hypothetical economy, there exist five sectors; Extraction, Construction, Manufacturing,
Trade and Service. Suppose that the central government imposes production limit on
manufacturing sector for some reasons, for example to reduce air pollution, by 10%.

From equation (8) we set up the LP problem as follows:

x₁

x₂

s.t

where Z = [12,745] and D = [0 0

1 0 0]. Using equations (9) and (10)

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