# 数学代写|最优化理论作业代写optimization theory代考|EECE506

## 数学代写|最优化理论作业代写optimization theory代考|Mathematical model operation of market structures

A market structure is understood as a set of elements that determine the functioning of the market. Here we enter the number of companies operating in the market and competing with each other, the relative size of these companies (concentration), technological and cost indexes, the conditions of demand, the offer conditions, and the degree of market openness for the emergence of new companies or for the removal of former participants [15].
The concept of market structure provides an opportunity to estimate demand volumes and offers, and to define lines of company conduct for the consumer over a period of time.

The structure of the market depends on a number of structural characteristics and factors of size and value which, in many respects, management decisions depend on: the size of companies; the number of the sellers acting in a particular commodity market; the share occupied by sellers in a particular market; the concentration in the industry; technology; and the conditions of demand and other market conditions. According to changes to the above factors, market structures are subdivided into perfect and imperfect competition.

To analyse the formulated market structures, we consider a mathematical model (9.6.6)-(9.6.10) to be the simplest situation when two producers and two consumers operate in the market with one type of product. The closest such model is the duopoly developed by Kurno, Shtakelberg, Bertrand and Edgeworth [95], in which the relationship between just two firms is considered. We will call such a model “basic”.

## 数学代写|最优化理论作业代写optimization theory代考|Constructing a basic mathematical model of the market

A market with one product in which two producers and two consumers of this product participate [96 and 97].

Let us enter the following designations:
$x_1$ and $x_2$ are volumes of a product sold by the first manufacturer; $x_3$ and $x_4$ are the same for the second manufacturer as the first, and the second consumer accordingly;
$p_1=p_2=p_3=p_4$ is the price of a product;
$a_1=a_2=a_3=a_4$ are the costs of production for both manufacturers;
$\pi_q=p_q-a_q, q=\overline{1, Q}$ is the profit made from the production and sale of a product for both manufacturers.
$b_i^{\min }, b_i^{\max }, l=1,2$ are minimal and maximal volumes of financial assets which the first and second consumer can allocate to buy the product from different firms.
$b_q$ are a firm’s financial opportunities to manufacture the product, $q=$ $1,2$.

The entered designations indicate that each firm can make no more than $x_q^{\max }=b_q / a_q, q=1,2$ product units.

Let us solve the vector problem (9.7.1)-(9.7.4) on the basis of the normalization of criteria and the principle of a guaranteed result, with equivalent criteria and a prioritized criterion.

The mathematical model of the market (9.7.1) – (9.7.4) can be used for various market structures by changing the relevant parameters, and is therefore known as “basic”. Similarly, basic models with higher dimensions can be constructed.

# 最优化理论代考

## 数学代写|最优化理论作业代写optimization theory代考|Constructing a basic mathematical model of the market

X1和X2是第一个制造商销售的产品的数量；X3和X4第二个制造商与第一个制造商相同，第二个消费者相应地；
p1=p2=p3=p4是产品的价格；

b一世分钟,b一世最大限度,l=1,2是第一和第二消费者可以分配以从不同公司购买产品的最小和最大金融资产量。
bq是公司制造产品的财务机会，q= 1,2.

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