Several Types Of Random Input-output Model And Example Analysis

"Input-output analysis" also known as sectoral linkages balance method, which was first raised by the American economist · Leontief (Wassily Leontief) proposed in the 20th century to the 1930s ,to seeks to explore and explain the structure and operation of the national economy. In 1936,Leontief published the first Input-Output Analysis paper "the number of input-output system of the United States economic relations", marked the birth of the input-output analysis. For the next 70 years, the input-output technology has developed tremendously and it has become an important tool for the analysis of the contemporary economy.Early in the input-output analysis., the model is based on input-output coefficients fixed the basic assumption that all consumption. However, the actual situation is not[1-2]. Large- scale economic input-output system, the complex and diverse objectives of many factors, there were a lot of factors at play, and using the amount of uncertainty to explain the phenomenon of uncertainty will cause a lot of difficulties. If we simply use classical mathematical methods for the law to reveal the operation of the economy,it is difficult. Therefore, if we thingk to simulate and analysis the macroeconomic developments quantitatively and truely, it would be necessary to study the input-output model with random factors. With the continuous development of science and technology,we can use more complicated but more effective theory and technology to explain complex and socio-economic phenomenon. For the uncertainty of the changes and the phenomenon reflecting the laws of changes ,we can use random variables to describe and analysis the phenomenon ,it will be more objective and effective. Therefore, some scholars put forward random input-output model to be studied and analyzed[3 - 9]. Randomness is the general demand for direct consumption or final random coefficient.This article also discussed the completely random coefficient of consumption and investment factor, because these variables is not correct. The practical numerical is estimated, so using random variables to measure short, more in line with the objective reality.In this paper ,there are a few random input-output model to analysis and discussion. First of all we study the input-output model.of departments with direct consumption coefficients and final demand are subject to normal distribution and uniform distribution,; After, we discussed the radom input-output model of various department's entirely consumption coefficients are subject to normal distribution, and the random prices model corresponding is established , secondly, we discussed the various departments and direct investment to consumption coefficient obey normal random coefficients input-output model; Finally, the twin goals of random input-output model is studyed, and then the method is given.This paper is divided into four chapters.Chapter I is an introduction, and an account of the birth and development of the input-output method and its significance and role is given.This chapter also gives a brief introduction to the main structure and content.Chapter II gave an analysis of the input-output theory, the application of latest developments and prospects and analysis,it is the theoretical foundation behind the chapter.Chapter III and IV is the main content of this paper. In the third chapter, First of all we study the input-output model.of departments with direct consumption coefficients and final demand are subject to normal distribution and uniform distribution; After, we discussed the radom input-output model of various department's entirely consumption coefficients are subject to normal distribution, and the random prices model corresponding is established ,secondly, we discussed the various departments and direct investment to consumption coefficient obey normal random coefficients input-output model; Finally,the twin goals of random input-output model is studyed, and then the method is given. The main conclusions were as follows :Theorem 3.1 Assuming z_it =m_ij +m_i.j+1, j=1, 2, …, n (for n is odd, the lastone is z_i(n+1)/2 = m_m ) 1=1,2,..., n/2 (for n is odd, it is (n+1)/2)(1) If λ_ij≤λ_ij+1, Theorem 3.2 Established department i early input to x_i volume, the sector's demand for the ultimate is y_i , so it can satisfy its demand for intermediate and final demand probability is α_i,Theorem 3.3 Assuming a_ij and y_i obey normal distribution, but also for a fixed i, a_ij and y_i independent of each other and charged a_in+1 = y_i x_n+1 = 1 , z_? =a_ijx₁, +a_i2x₂+...+(a_i1-1)x_i+...+a_inx_n+ a_in+1x_n+1, probability density function is So the probability equation into the text uncertainty equation :Theorem 3.4 Assuming entirely expendable coefficient c_ij obey normal distribution N(μ_ij,σ_ij), the expected price for the products sector i is μ_i, or p_i is subject to normal distribution N(μ_ij, σ_ij)Theorem 3.5 Based on this assumption, including years of delay can be improved following the general input-output model:Theorem 3.6 Assuming A(k) and B(k + l,l) s Nonzero elements obeynormal distribution, in other words so the additional expectations of the finalproduct sector i is Application : Construction random input-output model of the twin goals:max X(k)^T P(k)min‖x(k)-X|^(k)‖ Solving the optimal output of various departments, and give the related examples of the note.