industries through capital flow matrix by industry. In virtue of technology limitation, the dynamic input-output model was nowadays merely united in linear programming rather than dynamic programming for making some long-term decisions. Na (2006) and Zhang (2001) made the multi-goal programming on the basis of the dynamic input-output model for economic term forecast. All of above models are aimed at maximizing the sum of over the planning term, but simplicity application of linear programming have no consideration the efficient growth theory (i.e“turnpike indeed, their objectives and constraints with the time theorem”); sequence ought to be used the sequential constrained technique in dynamic programming in place of simply linear programming. Using the optimal technology to overcome the unbalance system can be also traced back to the origin of turnpike theorem. The Dorfman, Samuelson, Solow (1958) first combined the linear programming with dynamic input-output model in and “Linear Programming and Economic Analysis” demonstrated that the solution is exactly Leontief trajectory, which is the efficient growth path, so called turnpike. is concerned with efficient paths of accumulation of economic expansion. Turnpike theorem Efficiency is defined with reference to the terminal stocks paths, namely, a path of accumulation lasting N periods is efficient if no other path, starting from the same initial stocks and complying with the technical restrains, reaches larger terminal stocks after N periods. Their concept is contrast to von-Norman (1932), who proofed the existence of a balance, where the price just compensate the cost so as to no profit exist, stimulatingly, the expand of economy activity make the capital stock expanding at maximum rate, meanwhile the optimal model with objective function takes no effect. Samuelson (1949) thought that it is necessary to introduce optimal in the case of economy unbalance. He also first put the concept of turnpike forward from von-Norman model, in which exist a turnpike, and of which the maximum objective function is the scale of capital stock in final term. Put another way, turnpike is the speediest path of capital balance growth, so-called von-Norman equilibrium. Later, Dorfman, Samuelson, Solow (1958) demonstrated the turnpike theorem in the model with two capital goods, and found the efficient capital growth path is consist with Leontief trajectory. The technology advance make the Leontief trajectory became a curve.
industries through capital flow matrix by industry. In virtue of technology limitation, the dynamic input-output model was nowadays merely united in linear programming rather than dynamic programming for making some long-term decisions. Na (2006) and Zhang (2001) made the multi-goal programming on the basis of the dynamic input-output model for economic forecast. All of above models are aimed at maximizing the sum of over the planning term, but simplicity application of linear programming have no consideration the efficient growth theory (i.e“turnpike theorem”); indeed, their objectives and constraints with the time sequence ought to be used the sequential constrained technique in dynamic programming in place of simply linear programming. Using the optimal technology to overcome the unbalance system can be also traced back to the origin of turnpike theorem. The Dorfman, Samuelson, Solow (1958) first combined the linear programming with dynamic input-output model in “Linear Programming and Economic Analysis” and demonstrated that the solution is exactly Leontief trajectory, which is the efficient growth path, so called turnpike. Turnpike theorem is concerned with efficient paths of accumulation of economic expansion. Efficiency is defined with reference to the terminal stocks paths, namely, a path of accumulation lasting N periods is efficient if no other path, starting from the same initial stocks and complying with the technical restrains, reaches larger terminal stocks after N periods. Their concept is contrast to von-Norman (1932), who proofed the existence of a balance, where the price just compensate the cost so as to no profit exist, stimulatingly, the expand of economy activity make the capital stock expanding at maximum rate, meanwhile the optimal model with objective function takes no effect. Samuelson (1949) thought that it is necessary to introduce optimal in the case of economy unbalance. He also first put the concept of turnpike forward from von-Norman model, in which exist a turnpike, and of which the maximum objective function is the scale of capital stock in final term. Put another way, turnpike is the speediest path of capital balance growth, so-called von-Norman equilibrium. Later, Dorfman, Samuelson, Solow (1958) demonstrated the turnpike theorem in the model with two capital goods, and found the efficient capital growth path is consist with Leontief trajectory. The technology advance make the Leontief trajectory became a curve. term
2392_20160603031_2392_63-TurnpikeOptimality.docx