TEMPLATE DESIGN © The economic impact of a limitation on production in a linear programming input-output model Wolfgang Koller, Institute for Industrial Research (Industriewissenschaftliches Institut), AbstractModel I: no importsModel III: competive imports Applications and conclusions Contact information 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. 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. 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. 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), 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), 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),  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 What is new in our approach? 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 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 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. Notation and definitions Model Ic: maximize subject to with Wolfgang Koller Istitute for Industrial Research (Industriewissenschaftliches Institut), Vienna, Austria 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 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 II: non-competitive imports Model IIb: maximize subject to Model IId: maximize subject to with The last restriction concerns the trade balance. Model III: maximize subject to with