Thesis topic publishing network Thesis topic publishing network: Thesis topic recommendation is published for free, and thesis topic oriented writing is free; Baidu, you will know that the world's largest Chinese search engine has been devoted to listening, digging and satisfying China netizens ... Therefore, some methods of advanced mathematics such as function theory, calculus, matrix, probability, statistics and operational research have been widely used in economic management. It enables people to analyze relevant economic models in theory, thus giving a reasonable explanation and better guiding economic construction.

First, the application of function in economic analysis

In economic activities, producers and consumers exchange goods through the market, consumers buy goods to obtain their utility, producers provide goods to obtain profits, and the market is a bridge between producers and consumers. We know that the market demand for a commodity is a function of the commodity price, which generally decreases with the increase of the price, that is, the demand is a monotonic decreasing function of the market price, contrary to the demand function, the supply function increases with the increase of the market price. Income is the income after the goods produced by producers are sold. The total income of producers selling a commodity depends on the sales volume and price of the commodity, and the cost function is the fixed salary of factory equipment managers and the salary of raw material workers with variable cost. Profit is the surplus of producers after deducting costs, and it is also a function of output.

Example: It is known that the total cost (unit: 10,000 yuan) when producing Q pieces of a certain commodity is

C(q)= 10+5q+0.2q

If you earn 90 thousand yuan for every item you sell.

(1) Find the total profit when producing 10 pieces of this commodity. (2) Find the total profit when producing 20 pieces of this commodity.

The revenue function of this commodity is R(q)=9q (ten thousand yuan).

We also know that C(q)= 10+5q+0.2q (ten thousand yuan).

The profit function of this commodity is l (q) = r (q)-c (q) = 4q-10-0.2q (ten thousand yuan).

(1) The profit when producing 10 pieces of this commodity is L (10) =10 (ten thousand pieces).

(2) The total profit of producing 20 pieces of this commodity is (ten thousand yuan).

From the above example, it can be analyzed that the profit does not always increase with the increase of output. Sometimes the output increases, but the profit decreases, even causing losses. According to theoretical analysis, the profit function can be divided into three situations.

At this time, producers are profitable.

Producer loss.

At this point, the producer is neither profitable nor loss-making, that is, breakeven.

Profit and loss analysis is often used in various price or production decisions in enterprise management.

Second, the application of calculus in economic analysis

In economics, it is customary to use the concepts of average and margin to describe the change of one economic quantity to another, such as the economic significance of marginal cost when the output is the total cost of reproducing a unit product.

The average change rate of marginal profit and total profit is set as the profit function of selling a certain product is equal to the total income MINUS the total cost, which is known from the derivative algorithm. Therefore, the marginal profit is equal to the marginal income minus the marginal cost 129 cases 9.

As we all know, the total cost function of producing a color TV set is

Through market research, we can predict the annual demand of this kind of color TV, which is the sales price of color TV, not the demand, and strive to find the sales volume and sales price to maximize profits.

The solution is obtained from the demand, so when the sales volume is 0, the total revenue function is 0 and the profit function is 0.

According to practical problems, the only stagnation point is the maximum point of profit function and its maximum point, and the maximum profit is

When is the selling price of color TV set (RMB)?

Marginal demand is 0, and demand elasticity is 0.

Make the price of color TV the most profitable (yuan), then the demand elasticity is

That is, when the price of color TV is high, the demand elasticity is elastic. At this time, appropriate price reduction can not only increase the sales of color TV sets and expand their share in the sales market, but also reduce the inventory backlog of products, reduce inventory costs, increase the total sales revenue and bring economic benefits to enterprises.

Third, the application of linear equations in economic analysis

The national economy is a large system that is interrelated and restricted, and the change of any factor will have a series of direct and indirect effects. When the technical coefficient between industrial departments, that is, the direct consumption coefficient matrix A is determined, we can find out the close relationship between industrial departments in an economic system through the final demand Y.

For example, the following table lists the statistical results of intermediate products and final products in three industry, China during 1992.

Product Flow Table of 1992

Intermediate department final product

Total product

Primary industry, secondary industry and tertiary industry

Primary Industry 1265 2943 249 4628 9085

Secondary industry14242168447081459942415

Tertiary industry 543 5622 3380 7420 16965

Direct consumption function matrix of tertiary industry

If the price of the primary industry rises, it can be considered that the final product of the primary industry has a gap of 462.8 billion yuan, and the final products of the other two industries remain unchanged, namely

It can be seen that the total product volume of the primary industry actually increased by 55.536 billion yuan, with a growth rate of, that is, the total product volume of the primary industry only increased by 6. 1 1%, from which we can know that it is not how much you can earn.

In a word, through the mathematical analysis of the economic model, we can better manage the enterprise scientifically and provide scientific theoretical basis for the general thesis center.