Transcript Poster - IIOA!

The economic impact of a limitation on production in a linear
programming input-output model
Wolfgang Koller, Institute for Industrial Research (Industriewissenschaftliches Institut), www.iwi.ac.at
Abstract
What is new in our approach?
In this paper a linear programming model is used to analyze the
impact on the overall economy of a bottleneck in the production of a
group of goods, e.g. basic materials or energy resources, when the
technology is a Leontief technology. The impact is shown by
comparing a base scenario, given by the input-output-table as
observed in the base year, when no limitation is assumed to exist, and
the bottleneck scenario, which obtains as the solution of the linear
program after the introduction of the limitation. A further necessary
restriction used in the model is that the final demand in no group of
goods may exceed the final demand of the base scenario.
Extension of the basic model for further restrictions, e.g.:
• limitation on production of a certain commodity
• limitation on imports of a certain commodity
• limitation on primary resources and regulation-induced limitation
such as maximum allowed carbon emissions
• minimum final demand for certain or all sectors
The objective function to be maximized is the sum of the final demand
over all groups of goods. Extensions of the basic model consider also
an open economy and allow for the introduction of other limitations,
e.g. on primary inputs.
In models II and III we account for behavioral restrictions concerning a
trade balance deficit: the ratio of the trade balance to GDP may not fall
under a predetermined value.
The analysis reveals how a progressive tightening of the bottleneck
brings about a more than proportionalreduction of the final demand
able to be satisfied.
Overview on previous research linking LP and IO
Approaches that use linear programming (LP) and input-output (IO)
with the assumption of one technology for the production of each
commodity (Leontief technology) to model the (optimal) reaction of an
economy facing a bottleneck:
Part of chapter 4 in: Chenery, H.B. and Clark, P.G. (1959), Interindustry
economics. New York: John Wiley and Sons.
Schluter, G. and Dyer, D. (1976), The economic interpretation of
constrained input-output solutions. Review of Economics and Statistics,
58 (2), 245-248
Wang, T.-F. and Miller, R.E. (1995), The economic impact of a
transportation bottleneck: An integrated input-output and linear
programming approach. International Journal of System Science, 26
(9), 1617-1632
Rose, A., Benavides, J., Chang, S.E., Szczesniak, P., and Lim, D. (1997),
The regional economic impacts of an earthquake: Direct and indirect
effects of electricity lifeline disruptions. Journal of Regional Science, 37
(3), 437-458
 These approaches are similar to our approach.
 Some differences in the choice of the objective function:
- Sum of sectoral final demand (favored by us)
- Sum of sectoral value added
- Sum of sectoral gross outputs
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Model I: no imports
Model III: competive imports
Model Ic:
Model III:
maximize
maximize
subject to
subject to
Extension of the basic model for an open economy:
• Model I: no imports assumed
• Model II: non-competitive imports assumed
• Model III: competitive imports assumed
with
Model II: non-competitive imports
Notation and definitions
The models aim at the comparison of a (unconstrained) base scenario
and a bottleneck scenario. The LP-IO model with an ineffective
constraint reproduces the base scenario, i.e. the result of the demand
driven IO model for the base year.
0 denotes variable in base scenario
 denotes bottleneck-constrained variable
* denotes solution for a variable
Model IIb:
with
maximize
subject to
Applications and conclusions
production
imports
final demand (including consumption, capital
formation and exports)
final consumption
gross capital formation
final demand, excluding exports
exports
intermediate demand
intermediate demand for domestic goods
pollution
Imports into final demand, into intermediate demand,
etc. (but: imports into exports are assumed to be 0)
(matrix of) intermediate input flows
interm. input flows of domestic goods
intermediate imports
technical input coefficients
domestic inout coefficients
import input coefficients
Leontief inverse matrix
Leontief inverse matrix for domestic
production
Model IId:
maximize
subject to
Applicaition 1: Limitation of the production and importation of mineral
oil products by xx% in the Austrian economy.
Application 2: Limitation of the CO2 emissions of sectors underlying
ETS in Austria by xx%.
Computation of the models for varying degree of limitation shows that
a progressive tightening of the bottleneck brings about a more than
proportional reduction of the final demand able to be satisfied.
Many further extensions of the model are possible, e.g. for
endogenous price formation and more general objective functions.
Contact information
with
Wolfgang Koller ([email protected])
Istitute for Industrial Research (Industriewissenschaftliches
Institut), Vienna, Austria
The last restriction concerns the trade balance.