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SIRI KERTAS KERJA WORKING PAPER SERIES FEA Working Paper No. 2009-20 The Measurement of the National Production Function: Theoretical Framework Mario Arturo Ruiz Estrada Fakulti Ekonomi dan Pentadbiran Universiti Malaya Faculty of Economics and Administration http://www.fep.um.edu.my/ University of Malaya 50603 Kuala Lumpur MALAYSIA Faculty of Economics and Administration University of Malaya 50603 Kuala Lumpur MALAYSIA 1

FEA Working Paper No. 2009-20 The Measurement of the National Production Function: Theoretical Framework Mario Arturo Ruiz Estrada May 2009 All Working Papers are preliminary materials circulated to promote discussion and comment. References in publications to Working Papers should be cleared with the 2

The Measurement of the National Production Function: Theoretical Framework Mario Arturo Ruiz Estrada Faculty of Economics and Administration, University of Malaya, 50603 Kuala Lumpur, MALAYSIA Email: marioruiz@um.edu.my Website: www.econonographication.com Tel: +006012-6850293 Abstract. This paper proposes an alternative graphical and mathematical modeling approach to find the national production function (NP-Function) of any country based on the uses of Econographicology. The NP-Function is willing to measure the final national output under the construction of four sub-production functions, each sub-production function is originated from the agriculture, industry, manufacturing and services outputs. The modeling of the NP-Function requests the application of the economic modeling in real time in the same graphical space. The main objective to build the national production function is to analyze and visualize the total national output from a multidimensional perspective. Keywords: Econographicology, Macroeconomic Policy Modeling, Production Function, Multidimensional graphs, Cartesian Spaces. JEL: E60 1. Introduction In the study of the production function, we find that the use and combination of labor (L) and capital (K) is not enough variables to quantified and analyze the final output (Y). In fact, the NP-Function includes land (L) and capital (K) plus n number of variables together into its analysis. Basically, the NP-Function is formed by four sub-production functions. But each sub-production function represents each production sector such as agriculture, industry, manufacturing and services. The same NP-Function requests the uses of economic real time modeling framework, it based on the application of dynamic growth rates that we applied in all variables into each sub-production function. We assume four sub-production functions into the NP-Function keep on a constant dynamic imbalance state (Ruiz, 2008.a.). It is to explain and analyze the behavior of complex dynamic changes of each sub-production function until we find our final national output. However, this paper proposes the construction of the NP-Function under the application of Econographicology (Ruiz, 2007) and economic real time modeling framework. The NP-Function can facilitate the analysis and visualization of four sub-production functions by production sector (agriculture, industry, manufacturing and services) in constant movement into the same physical space in real time; it is to observe the fast and abrupt changes of the four sub-production functions by production sector develop in real time. Finally, the NP-Function is available to offer an alternative economic modeling to measure the final national output. 3

2. The National Production Function (NP-Function) The construction of the national production function will be explained by this section of our paper. Initially, the NP-Function is build by four sub-production functions; each subproduction function has its quadrant. Each quadrant show a single dependent variable represented by a vertical line the in center part of its quadrant by Y ij and n number of independent variables X ij on the bottom part of the quadrant by horizontal lines. Finally, we join all Xji to the dependent variable Y ij under the application of linkage of axes. All axes in each quadrant are running on real time under the application of dynamic growth rates (See Expression 1.5). Therefore, we have four quadrants or four sub-production functions, each quadrant has its dependent variable Y ij by n number of independent variables X ij respectively. In our case, we have four outputs from agriculture sector (Y 0 ), industrial sector (Y 1 ), manufacturing sector (Y 2 ) and services sector (Y 3 ) from each sub-production function. Finally, we can observe that among the four quadrants exist a single axis that we call the final national output Y*. It is based on join the four outputs from each sub-production sector by the application of the linkage of quadrants by strait lines (See Figure 1), the idea is to build a single surface based on link the four outputs together in the same physical space. In the NP-Function objective is to build a large and single surface that is moving in real time in the same physical space. In fact, the application of the Omnia Mobilis assumption (Ruiz, Yap and Shyamala, 2008.b.) is a basic condition to generate the real time effect of the NP-Function. Hence, the final national output Y* always keeps in dynamic and multi-dimensional behavior according to the economic modeling in real time into its multi-dimensional space. Finally, the analysis of the final result from the NP-Function depend on the position of the surface can help to determinate the situation of any economy. Additionally, the final result of the NP-Function is going to be determinate by the position of the surface. If the surface is located into the positive level then we can observe economic stability (See Expression 1.7). If the surface keeps zero level then we can observe economic stagnation (See Expression 1.8). If the surface keeps negative or positive levels then it is possible to observe economic recession (See Expression 1.9). Finally, if the surface is located on the negative level then we find an economic crisis (See Expression 1.10). 4

3. Model The NP-Function offers to us an alternative graphical and mathematical modeling approach to analyze the final national output from a multi-dimensional perspective. This new multi-dimensional graphical modeling can show the final national output. The NP- Function offer to policy makers an alternative methodological approach to measure the final output of any country from the national production function. The NP-Function is follow by four sub-production functions, there are: Sub-Production Function 0: (1.1) Y 0 = ƒ ( X 00, X 01,.., X 0 ) Sub-Production Function 1: (1.2) Y 1 = ƒ ( X 10, X 11,.., X 1 ) Sub-Production Function 2: (1.3) Y 2 = ƒ ( X 20, X 21,.., X 2 ) Sub-Production Function 3: (1.4) Y 3 = ƒ ( X 30, X 31,.., X 3 ) = Real Time Y i = Output = Dynamic Growth Rate All variables in each sub-production function request the application of the dynamic growth rate follow by: (1.5) X ij = X ij <t+1> - X ij<t0> x 100% X ij<t0> i = {1,2,..., } and j = {1,2,... } <t+1> = Future period of time <to> = Initial period of time Therefore, the final mathematic structure to build the NP-Function is based on expression (1.6.) (1.6.) Y* Y 0 Y 1... Y... = linkage of quadrants The final results in the NP-function depend on the location of the surface (See Figure 1). Hence, we have four possible results that can be classified by Economic Stability (See Expression 1.7), Economic Stagnation (See Expression 1.8), Economic Recession (See Expression 1.9) and Economic Crisis (See Expression 1.10): 5

(1.7.) Y* +Y o +Y 1 +Y 2 +Y 3 {if +Y* R + then the surface Economic Stability} (1.8.) Y* +Y o +Y 1 +Y 2 +Y 3 {if Y* 0 then the surface Economic Stagnation} (1.9.) Y* ±Y o ±Y 1 ±Y 2 ±Y 3 {if Y* R +/- then the surface Economic Recession} (1.10.) -Y* -Y o -Y 1 -Y 2 -Y 3 {if Y* R - then the surface Economic Crisis} Figure 1: The National Production Function (NP-Function) 4. Conclusion Now we are available to measure the total output of any country under the application of the national production function. This new approach shows an alternative approach under the construction of four sub-production functions ant the final national output. In the construction of the national production function request the application of Econographicology (multidimensional graphical modeling) and economic modeling in real time. 6

5. References Ruiz Estrada, M. A. (2007). Econographicology, International Journal of Economics Research (IJER), Volume No. 4/1. Ruiz Estrada, M.A., (2008.a.). Is the Market in Dynamic Imbalance State?. International Journal of Economic research (IJER), Vol. 5-2. Ruiz Estrada, M.A., Nagaraj, S. and Ya, S.F. (2008.b.). Beyond the Ceteris Paribus Assumption: Modeling Demand and Supply Assuming Omnia Mobilis. International Journal of Economic research (IJER), Vol. 5-2. 7

FEA Working Paper Series 2009-1 Shyamala NAGARAJ, Goh Kim-Leng, Tey Nai-Peng and Rohana Jani, HUMAN CAPITAL FORMATION AND LABOUR MARKET DYNAMICS: A GENDERED PERSPECTIVE, January 2009. 2009-2 Mario Arturo RUIZ ESTRADA, The Economic Waves Effect of the U.S. Economy on the World Economy, January 2009. 2009-3 Mario Arturo RUIZ ESTRADA, The Application of Prototypes in the Teaching-Learning Process of Multi-Dimensional Physical Spaces, January 2009. 2009-4 Mario Arturo RUIZ ESTRADA, The Multi-Level Investment Flows Monitoring Model (MIF-Model), January 2009. 2009-5 Mario Arturo RUIZ ESTRADA, The Mega-Space Distributed Lag Model, January 2009. 2009-6 Mario Arturo RUIZ ESTRADA, The Visualization of Complex Economic Phenomena from a Multi-dimensional Graphical Perspective: The U.S. Economy (1929-2008) Case Study, January 2009. 2009-7 Mario Arturo RUIZ ESTRADA, Multi-dimensional Economic Modeling, January 2009. 2009-8 Mario Arturo RUIZ ESTRADA, Multi-Dimensional Games (MD- Games), January 2009. 2009-9 Mario Arturo RUIZ ESTRADA, The Application of the Mega-Dimensional Cartesian Coordinate System in the Economic Policy Modeling, January 2009. 2009-10 Mario Arturo RUIZ ESTRADA, Alerting or Forecasting Economic Crisis?, January 2009. 2009-11 Mario Arturo RUIZ ESTRADA, Economic Modeling in Real Time, January 2009. 2009-12 Mario Arturo RUIZ ESTRADA, The Food Security Function Surface (FSF-Surface): An Economic Note, January 2009. 2009-13 Evelyn S. DEVADASON, ASEAN-CHINA trade Flows: Moving Forward with China, May 2009. 2009-14 Mario Arturo RUIZ ESTRADA, Multidimensional Differentiation, May 2009. 2009-15 Mario Arturo RUIZ ESTRADA, Measuring the Energy of Economics (Ё): Theoretical Framework, May 2009. 8

2009-16 Mario Arturo RUIZ ESTRADA, The Input-Output Multi-Dimensional Analysis: Theoretical Framework, May 2009. 2009-17 Mario Arturo RUIZ ESTRADA, The Idea about Zero and Infinity in the Multi-Dimensional Graphical Modeling, May 2009. 2009-18 Mario Arturo RUIZ ESTRADA, From a Global Financial Crisis to a Global Poverty Crisis, May 2009. 2009-19 Mario Arturo RUIZ ESTRADA, Economic Graphical Modeling from 2-Dimensional Graphs to Multi-Dimensional Graphs, May 2009. 2009-20 Mario Arturo RUIZ ESTRADA, The Measurement of the National Production Function: Theoretical Framework, May 2009. 2009-21 Mario Arturo RUIZ ESTRADA, Is Possible to Plot Matrices into a Multi- Dimensional Coordinate System?, May 2009. 2009-22 Mario Arturo RUIZ ESTRADA, The Application of the National Production Function (NP-Function) in the Analysis of Regional Trade Agreements, May 2009. 2009-23 Mario Arturo RUIZ ESTRADA, How to Evaluate the Creation of an Economic Joint Venture through the Application of the Box Negotiation Diagram, May 2009. 2009-24 Mario Arturo RUIZ ESTRADA, The Study of Economic or Natural Phenomenon Behavior under the Application of Multi-dimensional Real Time Modeling Framework, May 2009. 9

FEA Working Paper Series Objective and Scope: The Faculty of Economics and Administration (FEA) Working Paper Series is published to encourage the dissemination and facilitate discussion of research findings related to economics, development, public policies, administration and statistics. Both empirical and theoretical studies will be considered. The FEA Working Paper Series serves mainly as an outlet for research on Malaysia and other ASEAN countries. However, works on other regions that bear important implications or policy lessons for countries in this region are also acceptable. Information to Paper Contributors: 1) Two copies of the manuscript should be submitted to: Chairperson Publications Committee Faculty of Economics and Administration University of Malaya 50603 Kuala Lumpur MALAYSIA 2) The manuscript must be typed in double spacing throughout on one side of the paper only, and should preferably not exceed 30 pages of A4 size paper, including tables, diagrams, footnotes and references. 3) The first page of the manuscript should contain (i) the title, (ii) the name(s) and institutional affiliation(s) of the author(s), and (iii) the postal and email address of the corresponding author. This cover page will be part of the working paper document. 4) The electronic file of the manuscript must be submitted. The file can be a Word, Word Perfect, pdf or post-script document. This will be posted at the Faculty s website (http://www.fep.um.edu.my/) for public access. 5) Contents of the manuscript shall be the sole responsibility of the authors and publication does not imply the concurrence of the FEA or any of its agents. Manuscripts must be carefully edited for language by the authors. Manuscripts are vetted and edited, if necessary, but not refereed. The author is, in fact, encouraged to submit a concise version for publication in academic journals. 6) When published, the copyright of the manuscript remains with the authors. Submission of the manuscript will be taken to imply permission accorded by the authors for FEA to publicize and distribute the manuscript as a FEA Working Paper, in its hardcopy as well as electronic form. 10