In a perfectly competitive market economy, the quantity of a certain consumer product such as pork on the market during a period is far greater than the demand. Due to poor sales, the price drops. Producers find that raising pigs is losing money, so they turn to other agricultural and sideline products. After a period of time, the amount of pork on the market will decrease. At this time, the supply exceeds demand, causing prices to rise. Producers see profits and return to large-scale pig raising. From this point on, the supply of pork will exceed demand again in the next period, and prices will drop. Without outside intervention, this market phenomenon will continue in cycles.
[Model Assumptions]
(1) The price of a commodity during a certain period depends on the supply of the commodity;
(2) The supply of the commodity in the next period depends on the price of the commodity in the previous period;
(3) For conventional commodities, the demand function is a decreasing function; the supply function is an increasing function.
【Symbol settings】
k: time period, which is also the production and consumption cycle of commodities, k=1,2,…;
xk: The quantity of goods in the kth period, k=1,2,…;
yk: The price of the commodity in the kth period, k=1,2,…;
【Modeling】
In the kth period, according to assumption (1), there are 
It is called the demand function. The more goods are supplied, the lower the price. Yk is the decreasing function of xk.
In the k+1th period, according to assumption (2), there is 
[15]
Here h and g are inverse functions of each other, indicating the supply function, which is an increasing function.
That is, the supply and price model of this commodity is
【16】
【Model Analysis】
1. Analysis of stationary and non-stationary phenomena
Taking supply as the abscissa and price as the ordinate, draw the demand function and supply function in the same coordinate system, as shown in Figure 1 and Figure 2.
Among them, the equilibrium point p0(x0,y0) 
is obtained by the system of equations
As the period k increases, xk and yk continue to fluctuate and change, and p1, p2,...,pk do not converge with p0.
That is to say, the market price and supply of products will fluctuate greatly, which is not conducive to people's livelihood.
The model used to analyze market stability using the curves in Figures 1 and 2 is called the spider web model. Among them, f depends on the consumer's demand and consumption level for the commodity, and g depends on the producer's production capacity, operating level, etc. When the level of water consumption increases, the curve f moves upward; when the production capacity increases, g moves to the right.
2. Analysis of stationary conditions
Once the demand function and supply function are determined through survey data, whether the quantity and price of the commodity are stable will be completely determined by the shape of these two curves near the equilibrium point p0.
Near the equilibrium point p0, both f and g can be approximated by straight lines as 
[17]
Eliminating yk in the system of equations [17], the difference equation can be obtained
【18】
[18] is a first-order linear constant coefficient difference equation, and its special solution is 
[19]
When k→+∞, the necessary and sufficient conditions for xk→x0 (p0 is stable) are 
[20]
3. Explanation of model parameters
【17】
α represents the increase in price when the supply of the commodity decreases by one unit; β represents the increase in the supply of the commodity when the price increases by one unit. α reflects the sensitivity of consumers to commodity demand, and β reflects the sensitivity of producers and operators to commodity prices. When β is fixed, the smaller α is, the flatter the demand curve is, and the market is easier to stabilize; when α is fixed, the smaller β is, that is, the steeper the supply curve is, indicating that producers are less sensitive to price, and the market is easier to stabilize. . When both α and β are large, it indicates that consumers are overly sensitive to commodities, producers are overly dependent on prices, and the economy is unstable.
4. Model application
When the market economy becomes unstable, the government has two methods of intervention:
- To make α as small as possible, we might as well examine the extreme situation, let α = 0, which is the level of the demand curve. No matter what the supply curve is, [20] the condition is always true, that is, the market is always stable. This method is for the government to control prices and command prices not to change regardless of the quantity of goods.
- Make β as small as possible. The extreme case is β=0, that is, the supply curve is vertical, so no matter what the demand curve is, it is always stable. In fact, this is equivalent to controlling the quantity of goods in the market. When the supply is less than the demand, it is purchased or allocated from other places and put into the market; when the supply exceeds demand, the remaining part is purchased to keep the quantity of goods in the mall unchanged. This approach requires the government to have considerable economic strength.
5. Model promotion
If the quality of the production manager is higher, when determining the product output xk+1, not only yk but also yk-1 will be considered, [15] becomes
When linearized, the second equation of [17] becomes
Then bring it into the system of equations [17] to get the second-order linear constant coefficient difference equation, and you can also get the stability condition as 
[21]