Mathematics ofВ the market. Service random flow
Alexandr Berlin
The book offers a new approach to the calculation of economic processes. This approach allows to obtain very interesting data: – to define a generic mathematical description of the goods. In book gives a mathematical market model, it is shown that calculations of the parameters of the market can be carried out according to the formulas of the Queuing theory, in particular according to the formulas of erlang, Engset, etc; to define formulas that reflect the relationship between supply and demand
Mathematics ofВ the market
Service random flow
Alexandr Berlin
© Alexandr Berlin, 2017
ISBNВ 978-5-4485-9239-3
Created with Ridero smart publishing system
AВ (P
). – relative consumption. The proposed load;
A
(t
, t
) – the difference between the incoming supply of goods and serviced supplies of goods;
A
. (t
, t
) – incoming supply of goods over a period of time (t
,В t
);
A
. (t
, t
) – the sum of the quantities of goods handled by consumer group during the period (t
, t
.;
AВ
. – the demand value for time of greatest demand;
A
. – the demand value during the observation;
a – the load intensity coming from a single source;
c�
s the number ofВ received requests;
c�
– the number of serviced requests;
c�
 – the number of lost requests;
c�– average length of queue or average numbers delays batches of goods;
P
– maximum consumption;
PВ
. – losses of volume of goods;
PВ
. – losses in the number of requests for suggestion of goods;
PВ
. – losses of volume of goods;
PВ t- losses ofВ implementation time;
p (γ> 0) the probability that the waiting time is greater than zero – that is, the probability of queue;
p (γ> t) – the probability of waiting for any incoming product over time t;
p (R> r) – the probability that the queue length exceeds the specified value r);
(γ) – the average waiting time in relation all requests received;
ОіВ
В the average waiting time ofВ only aВ delayed requests;
О› (t
, t
) -the mathematical expectation ofВ the number ofВ supplies placed on the market inВ the time interval [t
,В t
);
Ој (t
.t
). – the instantaneous flow rate;
Chapter 1. What are the REELECTION CONSUMPTION. unit ofВ measure ofВ supply and demand
1.1. So what is the goods?
Let’s start with a quote of Keynes [The General Theory of Employment, Interest, and Money by John Maynard Keynes. Book II: Definitions and Ideas]
“The perplexities which most impeded my progress in writing this book, so that I could not express myself conveniently until I had found some solution for them, are:
firstly, the choice ofВ the units ofВ quantity appropriate toВ the problems ofВ the economic system as aВ whole;..
“That the units, in terms of which economists commonly work, are unsatisfactory can be illustrated by the concepts of the national dividend, the stock of real capital and the general price-level:”
“The community’s output of goods and services is a non-homogeneous complex which cannot be measured, strictly speaking, except in certain special cases, as for example when all the items of one output are included in the same proportions in another output.”
InВ order toВ take the definition ofВ the unit ofВ goods we use the obvious statement.
We define the goods the market, as something that you want to sell or that you want to buy. Let’s try to express this in numbers
Do you love cakes? I will sell them to you. You will buy and will want again. Finally, you can eat 10 cakes a day. And I offer you still. You say, “Enough!” I suggest to you free of charge 12 cakes a day, and you ungrateful say me “No!”. Moreover, buying cakes, you have some time to consume them, and not buy a new one
What is it? It is the overproduction!
I repeat the question: How much can you eat on the day cakes – 10, 12, 15? It doesn’t matter for math, but in principle there is
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