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					Scientific Estimation of Crude Oil Price with Input-Output
Analysis Method
Shou Ying Lu
 Petroleum Division of China Statistic Society Beijing .P.R.China
65# Fanyang Street / p.o.box 11
Zhuozhou Hebei P.R.China

Hongbin Cheng
Planning Department, Liao He Oil Field
Shi You Street, Xing Long Tai District
Beijing, China



      A well developed market economy must be accompanied by a scientific and reasonable price
mechanism. If a petroleum enterprise competes in a market, crude oil price, the price of its main
product, should be reasonable, so that the enterprise could stand firm in an intense market
competition. But there are many differences between crude oil and other industrial products. Not
only is crude oil produced in very different outdoor places, but also its production is often affected
by natural environment. Also crude oil is not regenerated resource. Therefore, the price of crude oil
could not be fixed with the method on ordinary industrial product and the marginal cost analysis
method. This paper tries to fix the price using an economic mathematical model, i.e., input-output
analysis method.
      Input-output analysis method, on the basis of the Max’s theory on labor value, for fixing a
product price is to find an economic mathematical model which describes the price composition;
Product is of value because it is an outcome of labor, and the amount of value of a product is
determined by the amount of labor consumed during production. To be sure, it is not the amount of
labor consumed in an individual company but the amount of the social average labor or the amount
of social necessary labor which determines the amount of product value. The value of a product is
measured based on the social necessary labor. The amount of labor is measured by labor time.
Labor time is measured by hours, days and other natural time units.
      Assume there are several kinds of products produced in an oil field economic system, let
       a ij ≥ 0(i , j = 1,2 ,⋅ ⋅ ⋅, n )
represent the amount of product i consumed for producing unit product j in material amount, for
example, producing 1 ton crude oil while consuming 100 tons geological reserve. So aij is a
material direct consumption coefficient, i.e., a direct consumption norm.
     Now let T j ( j = 1,2,⋅⋅⋅, n)
represent the total labor time (natural hours) consumed for producing unit product j . They are
unknown.
      Let t j ( j = 1,2,⋅⋅⋅, n)
represent the live labor time (natural hours) consumed in producing unit product j .
      So that the objective process of price composition can be described as follows,
      T1 = a11T1 + a 21T2 + ⋅ ⋅ ⋅ + a n1Tn + t1
      T2 = a12T1 + a 22T2 + ⋅ ⋅ ⋅ + a n 2Tn + t 2
      … … …
      Tn = a1nT1 + a 2 nT2 + ⋅ ⋅ ⋅ + a nnTn + t n
     This is a set of linear equations which consists of n equations. These equations can be
simplified as:
                 n
      Ti = ∑ a ij Ti + t j         ( j = 1,2,⋅ ⋅ ⋅, n) → ∞
               i =1
where aij T j is the labor time involved in product i consumed for producing unit product j . To be
concrete , a1 j T1 , a 2 j T2 , …, a nj Tn are respectively the material labor consumption involved in
production material 1, 2, …, n, as parts of labor consumption in producing unit product j . And
           n
the sum   ∑a
          i =1
                       T is the total material labor consumption of unit product j . The sum of material
                      ij i


labor consumption and live labor consumption is the total labor consumption of unit product j ,
i.e., the total amount of labor consumption accumulated in unit product j . Therefore, according to
the deduction of the economic mathematical model of price composition, we find
        lim { T(k) } = lim {AT(k-1)+t}
         k →∞             k →∞
and get
        T*=AT*+t
        The economic mathematical model of price composition is dependent on the computation of
the total labor consumption of unit product. The key step is relevant to the different value of free
term estimated for the iteration computation. If the free term takes the social necessary live labor
consumption vector t, then the result of iteration is the total labor consumption vector T*; if the
free term takes the wages vector of unit product, then the result of iteration is the cost vector of
unit production excluded the profit, and so on. It is evident that mathematical method is able to
completely and reasonably describe the objective process of price composition.

RESUME
     Le petrole brut est un produit special dont le prix ne peut pas etre determine par la methode
de produits ordinaires industriel. Cet article apporte une methode de model economique
mathematique—l’analyse d’input-output pour l’estimation du prix de petrole brut.
     La determination du prix de petrole brut avec l’analyse d’input-output est basee sur la
quantite de travail de toutes types et les relations entre ces types de travail pendant toute la duree
de la production de petrole brut. Cette methode mathematique peut simuler precisement le
processus objectif de la production, donc elle apparait plus scientifique que d’other methodes
ordinaires.




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