Mathematics of the market. Problem book. Alexander Berlin

system of consumption operates as follows.

      The system consists of n groups (or individual) consumers.

      Each group receiving a certain amount of goods and after out some time (time of consumption – t_consum) and may be free for further consumption.

      For example, a consumer who bought a vehicle, uses it (consumes) for about 3 years, and then begins to look for a new one.

      Not to be confused with the time of consumption and time of possession. User has

      the old car, but as soon as he begins to look for a new one car – this point is the end point of consumption.

      If satisfied demands one of a group of consumption then the number of groups decreases by one, i.e., for consumption remains n-1 group.

      At high intensity can be that there will come a time when all n groups of customers will busy.

      Whereupon, the received goods will not be sold. Unsold merchandise we will call a LOSSES.

      The probability of losses of the goods with a certain number of receipts and number of groups consumption, can give answer one or more questions.

      For example,

      1. At what size supply, losses will exceed a given norm?

      2. What number of goods can processing the market in a given time?

      3. How much should be consumer groups to ensure that given quantities of goods were sold with losses less than or equal to the specified norm?

      4. What happens to losses if we increase the supply at a certain value? The appearance on the market of new suppliers or an increase in the supply of production.

      The answers to these questions can be found by applying the formula of Erlang.

      2.2. The first Erlang formula for the calculation of market indicators

      The first Erlang formula has the form.

      The first Erlang formula

      where A is the value proposal, expressed in relative units (see further explanations)

      E_1,n (A) – value of loss for the consumer system of n groups (the number one indicates that this is the first Erlang formula, then will the area of application of the second formula Erlang).

      Chapter 3. Examples of application of the first formula of erlang for solving problems of the market

      3.1. Define the initial data

      3.1.1 Example 1. Determination of the intensity of consumption

      Problem: Structural composition of consumers of products offered on the market is divided into 5 categories n₁=50; n₂=40; n₃=30; n₄=20; n₅