Input-Output Analysis, Linear Programming and Modified Multipliers

makers attempt to analyze the compensation or recovery of impact (mostly economic
loss) from production restrictions using promoting other sectors’ final demand or
increasing government spending. This is important because the conventional IO analysis
with additional restrictions is apt to overestimate multipliers and lead insufficient
investment to recover the loss from production change.

In order to obtain the modified multipliers responding to direct restrictions on
production the IO transaction matrix should be rebuilt, which is not possible before
implementing policies. In this sense, it is required to figure out how to derive the
modified multipliers without rebuilding the transaction matrix and explore the regional
impact analysis. We suggest that the linear programming (LP) approach is one of the
candidates. In the LP, the shadow price has the same meaning as multipliers in the IO
analysis (Brink and McCarl, 1977). Previous works using the LP in place of the IO
analysis are Wilfred and Boehlje (1971) who analyzes the capital budgeting with multiple
goals, and Penn et al. (1976) for modeling and simulating the U.S economy with
alternative energy availabilities. These papers use the LP approach mainly because of
computational problem rather than inflexibility of the IO analysis. As argued in Brink and
McCarl (1977) the LP algorithms are simpler, easier and more accurate than matrix
inversion algorithms. During 1970’s and early 1980’s, the computer system doesn’t allow
invert the huge Leontief matrix, which is essential in the IO analysis. The advent of the
fast and stable computer removes advantages to use the LP approach in the regional
impact analysis.

In this paper, the LP approach is recalled. The multipliers in the conventional IO
analysis are fixed and constant regardless of restrictions such as reduction of production

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