The Planner and the Market: The Takayama Judge Activity Model
The linear programming formulation of the Leontief input–output model, established as the linear activity analysis model, represents an advancement in the construction of applied general equilibrium models, because it introduces a great deal of flexibilit
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The Planner and the Market: The Takayama Judge Activity Model
The linear programming formulation of the Leontief input–output model, established as the linear activity analysis model, represents an advancement in the construction of applied general equilibrium models, because it introduces a great deal of flexibility into the basic linear input–output structure. The lack of price-induced substitution was overcome by the development of the linear activity model. By allowing inequality constraints and the introduction of an endogenous mechanism of choice among alternative feasible solutions, the effects of sector capacity constraints and primary input availabilities may be investigated in the model. However, the linear programming formulation retains the assumptions of horizontal supply functions (up to the point where capacity is reached) and vertical final demand functions for each sector as well as fixed proportion production functions. Hence, the demand for commodities and supply of factors are assumed to remain constant no matter what happens to prices. In the linear programming framework it is natural to interpret the shadow prices that result as a by-product of the solution as equilibrium prices. However, these prices cannot be interpreted as market-clearing prices of general equilibrium theory because endogenous prices and general equilibrium interaction to simulate competitive market behaviour cannot be achieved using the linear programming specification. Thus, by using a linear programming formulation, without representing a realistic price system in which endogenous price and quantity variables are allowed to interact, the interplay of market forces cannot be described properly. These are simplifying assumptions which severely restrict the usefulness of the linear programming formulation of the input–output model. In linear programming problems, the solution is guaranteed to occur at one (or more) of the vertices, of the feasible set. This implies that the optimal solutions are always to be found at one of the extreme points of the feasible set, and the solution will constitute a basic feasible solution of the linear programming problem. Consequently, all we need is a method of determining the set of all extreme points, from
R. Nore´n, Equilibrium Models in an Applied Framework, Lecture Notes in Economics and Mathematical Systems 667, DOI 10.1007/978-3-642-34994-2_3, # Springer-Verlag Berlin Heidelberg 2013
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which an optimum solution can be selected.1 However, this constitutes a significant drawback of the applicability of the model because the linear programming specification restricts the field of choice to the set of extreme points. Unlike the points of tangency in differential calculus, the extreme points are insensitive to small changes in the parameters of the model. That reduces the attractiveness of the model for comparative static experiments. In order to include some elements of flexibility within the system and make the
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