Mathematics of the market. Service random flow. Alexandr Berlin
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Название: Mathematics of the market. Service random flow
Автор: Alexandr Berlin
Издательство: Издательские решения
Жанр: Математика
isbn: 9785448592393
isbn:
In this case, the main exit is the agreement to reduce output. This agreement applies to the type of “Nash equilibrium” [3.4]. This agreement brings to all parties to the losses, but the abandonment leads to even greater losses. Such agreements can be reached with great difficulty. This is true in general for the industry.
However, if we consider individual participants of market, the decline in the prices can increase number of groups of consumers which use product this participants reducing the number of consuming products of the other group manufacturers. Competition in the form of lower prices between manufacturers can limit only prime cost. This contest wins by the party that has the least cost, or he can get outside support (from government, banks, etc.).
Non-price factors that affect real consumption [4.4], and which can be influenced a relative consumption:
• The level of income in the society;
• The size of the market;
• Fashion, seasonality;
• Availability of substitute products (substitutes);
• Inflationary expectations.
Resume
So we have established General properties of the concept “the goods”.
It is despite of the large variety of goods, we reduced quantitative characteristics of the goods up to the two indicators.
1. The maximum possible consumption.
2. The real consumption.
However, if we consider the individual participants of market, the decline the prices individually participants of the market (by manufacturers) can increase number of groups of consumers which use his products by reducing the number consuming of products of the other group manufacturers. Competition in the form of lower prices between manufacturers will is limit only prime cost. This contest wins by the party that has the least cost, or he can get outside support (from government, banks, etc.).
In the future we will divide incoming supply of goods and supplies goods which already were serviced. (by analogy with the concepts of the theory of mass service [2.1] – the offered load and. the carried out load).
Incoming supply of goods in the time interval (t1, t2) denoted by Ainc. (t1, t2), it is represents the sum of the quantities of goods handled by this consumer group during the period (t1, t2).
Supplies of goods which already were serviced. over a period of time (t1, t2) is called such the supply of goods if each incoming goods will immediately purchased by the consumer – in moment. (t1, t2). Sometimes this supply will be called – a potential supply.
The difference between the incoming supply of goods and supplies goods which already were serviced will be called a” the losses supplies of goods” :
Alost (t1, t2)=A income (t1,t2)– Aserved.. (t1, t2)
1.4. Numerical characteristics of flows supplies of goods
1.4.1. The intensity of the supplies of goods
By analogy with the concepts of instantaneous and average intensities of random flow may to considered instantaneous and the average intensity of the supply of goods. However, in the theory and practice of calculation of the capacity of the market it is advisable to use the average intensity of the flows offers supply of goods. The intensity the incoming supply of goods means the offer of goods per unit of time. As a unit of measurement of the intensity of the supply of goods adopted the value a=1, i.e. the maximum volume of the supply of goods the (Preal= Pmax).
The following theorem facilitates the determination of intensity of the supply goods
It shows that this value has the property of ergodicity, which is that
Average at the time is equal to the average of the ensemble.
In this case, monitoring the arrival of shipments on time can be replaced by monitoring the number of simultaneously incoming groups of consumers.
The theorem on the quantification of the intensity incoming supply of goods:
The intensity of incoming supply of goods, which is expressed in units o relative consumption, quantitatively equal to the average number of simultaneously busy consumer groups serving this load.
Suppose that during the T hours continuously recorded the number of simultaneously busy groups of consumers market, which receives steady flow of supplies for consumer groups. Let the result of the observations was that during the time t1 was busy υ1 consumer groups, during the time t2. was busy v2 consumer groups, etc. (Fig.1.1). In General can imagine that during the time ti was busy υi consumer groups,
Σni=1 ti= T
and where n is the number, the value of v which is taken, within T hours.
Total time, when busy all consumers of the market at time ti expressed by the product of υit. In the time interval T total time when all users busy of the market will be expressed by amount. This amount, it is supplies of goods all consumers of the market at the time T.
The supplies of goods what, all consumers acquired of the market per unit time are equal to:
Aserv = (1/T) Σni=1vi ⋅ ti
On the other hand, the average number of simultaneously consumer groups occupied during the time T can be defined as a weighted average of ti:
v‘= (v1t1 + v2t2 +•••+ vntn) / (t1 + t2 + ⋯ tn) =
= (1/T) Σ ni=1 (vi ⋅ti)
therefore Aserv= v’
A theorem about the quantitative assessment of the intensity of the incoming floe supplies of goods.
To quantify the intensity of the incoming flow supply of goods you can use the following theorem:
The intensity of the incoming flow supplies of goods, which expressed in terms of relative consumption, creates a simplest flow of goods, which quantitatively equal to the mathematical expectation of the number of goods (c’), received for a time equal to the average СКАЧАТЬ