Allocation Models and their Use in Economic Planning

Three different lines of approach have contributed to the theory of optimal planning. One approach considers the problem from the view-point of a national government and its adviser, the econometrician planning speci­ alist. The government can, if this is thought to be desirable, stimulate investment in certain directions and discourage other economic activities. By various fiscal devices, it can influence both the total level and the distribution of investment funds over different sectors of production. Also, in many countries, a public agency plays some kind of coordinat­ ing role in the formulation of long-term plans for output by the enter­ prises sector; this may range from administrative direction in so-called centrally planned economies, to persuasion and advice in 'capitalist' economies. Accordingly, the public planner wishes to know what dis­ tribution of the nation's resources would be 'optimal'. This leads to the construction of various models which may be described under the general heading 'input-output type models'. This type of model has been largely developed by practitioners, among whom Sandee [B2] is probably the most outstanding and the earliest. A later, well-developed example of a model based on this approach is, for example, the Czech model by Cerny et al. [Bl]. A second approach considers the problem from the point of view of the private entrepreneur and his adviser, the manager and financial accountant.

I. Allocation, Investment and Efficiency Prices in Input-Output Type Models.- I. What is Efficiency?.- 1.1. The Preference Function.- 1.2. The Efficiency Frontier.- 1.3. Dynamic Efficiency.- 1.4. Efficiency Prices and Limiting Prices.- II. The Generalized Input-Output Model.- 2.1. The Primal of the Static Model.- 2.2. The Zero Profit Requirement.- 2.3. The Maximization of G.D.P..- 2.4. Public versus Private Preferences.- 2.5. Arrow’s Theorem on the Choice of Processes.- 2.6. Factor Substitution and Output Composition.- 2.7. The (Non) uniqueness of the Price Structure.- 2.8. The Adjusted Plan.- 2.9. The Plan-Orientated Preference Function.- 2.10. Price Adjustment in Input-Output Type Models.- 2.11. External Economies and Non-Convexity.- 2.12. Capacity in Transportation Problems.- III. Inter-Temporal Allocation in the Generalized Model.- 3.1. The Multi-Period Model.- 3.2. The Principle of Discount.- 3.3. The Recursive Formulation.- 3.4. An Example of a Multi-Period Allocation Model.- 3.5. The Dynamized Dual Restrictions.- 3.6. Interest Discount and Depreciation.- 3.7. Technical Change.- 3.8. The Plan-Orientated Intertemporal Preference Function.- 3.9. Some Questions for the Student.- IV. The Balanced Growth Frontier.- 4.1. The Exogenous Rate of Growth.- 4.2. A Demonstration Example of a Balanced Growth Path.- 4.3. The (Balanced Growth) Rate of Interest.- 4.4. The Balanced Growth Transformation Ridge.- V. The Dynamized Leontief Model.- 5.1. Formal Specification of the Model.- 5.2. The Turnpike Rate of Growth.- 5.3. The Turnpike rate of Interest.- 5.4. The Dynamic Input-Output Model and Its Limiting Prices.- VI. Foreign Trade in the National Economy Model.- 6.1. The Accounting Framework.- 6.2. Export and Market Limits.- 6.3. The Dynamic One-Factor Model with Foreign Trade.- II. The Evaluation of Individual Projects.- VII. The Costing Problem.- 7.1. The Investment Decision.- 7.2. The Econometrician and the Accountant.- 7.3. A Short Summary of Methods of Investment Evaluation.- 7.4. Project Evaluation and the Zero Profit Requirement.- 7.5. Natural Limits to Projects.- VIII. Discounted Cash Flow in the Standard Case.- 8.1. Present Value.- 8.2. How to Find the Rate of Interest.- 8.3. Input-Output Plan and Price Adjustment.- 8.4. Sector-Wise Discount.- 8.5. Clusters of Projects.- 8.6. Direct Coordination of Projects.- 8.7. Summary of a Planning Procedure.- 8.8. Some Questions for the Student.- IX. Increasing Returns to Scale.- 9.1. Discussion of the Problem.- 9.2. Planned Surplus Capacity.- 9.3. Project Size and Efficiency Price.- X. Some Special Evaluation Problems in Particular Sectors.- 10.1. Investment in Transport Production.- 10.2. Education.- 10.3. Hospitals.- III. Capita Selecta on Economic Policy.- XI. The Distribution of Outputs.- 11.1. The Functions of Prices.- 11.2. Profits.- 11.3. Duties on Final Outputs.- 11.4. Revenue Taxes.- 11.5. Redistributive Taxation.- 11.6. Rationing.- XII. Opportunity Cost and Exchange Price.- 12.1. Discussion of the Problem.- 12.2. Costing versus Programming.- 12.3. Macro-economic Equilibrium.- 12.4. Technical Change.- 12.5. Import Substitution and the Cost of Foreign Exchange.- 12.6. Underutilization of Resources.- Appendix A. Optimality Conditions.- a.1. The Additive Property of Inequalities.- a.2. The Programming Problem and Its Lagrangean.- a.3. John’s Theorem.- a.4. Aggregate Restrictions of Allocation Models.- a.5. The Kuhn-Tucker Theorem for Convex Programming.- Appendix B. Some Conventions of Notation.