Software industry is an important industry in China, but since its development, there has been a problem of piracy. Because most pirated software is the products of foreign software manufacturers, there is often a debate about whether intellectual property protection is transitional. Supporters cite social welfare as a reason, while opponents insist that intellectual property protection is conducive to technological progress.

1 basic facts

Software piracy has recognized facts, which are the starting point of our analysis. First of all, software piracy is technically insurmountable, that is, no matter what anti-piracy technology genuine software manufacturers adopt, they cannot prevent their own software from being pirated; Secondly, it is very important that there is not much difference in practicality between pirated software and genuine software. Because this means that there is little difference between genuine software and pirated software products; Thirdly, the investment required to implement piracy is much lower than that of genuine software, because pirated manufacturers do not have to pay R&D fees; Finally, the marginal cost of software production is very low, close to zero, so it can be considered that the marginal cost of genuine and pirated software is equal and unchanged.

2 pricing strategy of genuine software when there is no pirated manufacturer

If we implement extremely strict intellectual property protection, there will be no pirated software in the market. At this time, genuine manufacturers are the only producers in the market, and the whole market structure is a standard complete monopoly market. The correlation function is as follows: reverse function: p1= a-bq1; Demand function: q1= a/b-p1/b; Cost function: c1= f+CQ1; Profit function:: μ 60. B-f p 1 is the price of genuine software, q 1 is the demand of genuine software, F is the fixed cost, mainly compared with the R&D expenditure of pirated manufacturers, and C is the constant marginal cost and the average variable cost.

Therefore, the first derivative of profit function p 1 can get its optimal pricing: p 1=c+(a-c)/2.

Based on the economic analysis of the market structure of genuine manufacturers and pirated manufacturers

3. 1 Anti-demand function and demand function of software market

Because there is little difference between genuine software and pirated software, it is quite replaceable for ordinary individual users. We use the following set of anti-demand functions to express this relationship:

p 1 = a-b(q 1+θQ2)p2 = a-b(θq 1+Q2)

Where A and B are positive, and 0≤θ≤ 1. When θ is negative, the model becomes a demand model of complementary goods. If θ=0, the price of a commodity is only related to the output of this commodity, but not to another commodity, and the two commodities are irreplaceable. The closer θ is to 1, the stronger the substitution between the two variables; When θ= 1, the two commodities are completely replaced, that is, for consumers, product 1 is exactly the same as product 2. Obviously, on the issue of piracy, 0 < θ < 1, that is, the two commodities are neither completely replaced nor completely unrelated, and θ is closer to 1.

By transforming the inverse demand function equation, we can get the demand function equation implied in the model: q1= [(1-θ) a-p1+θ p2]/(1-θ 2) bq2 = (1-θ).

3.2 Cost function and profit function of software enterprises

The cost function of genuine software can be expressed as:

C 1=f+c q 1, where f stands for fixed cost, which is mainly R&D expenditure compared with pirated manufacturers. C stands for constant marginal cost and average variable cost. Combined with Bowery's linear demand model, the profit function of genuine enterprises can be obtained as follows:

μ1= (p1-c) [(1-θ) (a-c)-(p1-c)+θ (p2-c)]/(1-θ 2)

Its profit function is:

μ2 =(p2-c)[( 1-θ)(a-c)-(p2-c)+θ(p 1-c)]/( 1-θ2)b

The first-order condition of p 1 which maximizes μ 1 gives the optimal price reflection function of genuine manufacturers relative to pirated manufacturers: 2 (p1-c)-θ (P2-c) = (1-θ) (a-c). Similarly, the optimal price reflection function of pirated manufacturers is: 2 (.

Economic analysis based on the market structure of a genuine manufacturer and several pirated manufacturers

4. 1 Bertrand model and the competition between pirated manufacturers

When there are many pirated manufacturers (this is a realistic assumption), there is fierce competition among pirated manufacturers, that is, the game objects of pirated manufacturers are no longer genuine manufacturers but other pirated manufacturers. There is no difference between pirated software, and the competition between them is completely price competition. The classic Bertrand model holds that when products are homogeneous, the final price will drop to marginal cost.

The classic Bertrand model is based on two manufacturers who produce homogeneous products, and these two manufacturers can only use price as a decision variable. At the same time, it is assumed that the average cost and marginal cost of the two manufacturers are the same, and the average cost is equal to the marginal cost. In figure 1, when the price of firm 2 is lower than the marginal cost (average cost), firm 1 chooses the marginal cost as its price; When the price of firm 2 is higher than the marginal cost (average cost) and lower than the monopoly price Pm (average cost), firm 1 chooses the price slightly lower than P2 as its price to occupy the whole market. When P2>；; The price of Pm, manufacturer 1 is set at Pm.

Fig. 2 includes the optimal response curves of firm 2 and firm 1, and their intersection point is the equilibrium point p 1=p2=mc. At this point, both manufacturers have reached the average cost, and no one has the motivation to leave the equilibrium point.

Obviously, the conclusion of Bertrand model is also valid for many manufacturers, so the price of pirated manufacturers will be reduced to marginal cost, which can also be proved by the fact that almost every provincial capital city in China has its own unified price for pirated software.

4.2 Response Function of Genuine Manufacturers Based on the Market Environment of Multiple Pirate Manufacturers

When the price of pirated software drops to marginal cost MC=c, the optimal price response function of genuine software manufacturers:

2(p 1-c)-θ(p2-c)=( 1-θ)(a-c)

The best pricing of genuine software that is easy to release is:

p 1=c+( 1-θ)(a-c)/2

5 Static efficiency and dynamic efficiency

Compare the optimal pricing adopted by genuine manufacturers to pirated manufacturers and the optimal pricing faced by multiple manufacturers;

p 1 = p2 = c+( 1-θ)(a-c)/(2-θ)p 1 = c+( 1-θ)(a-c)/2

We find that when there are multiple pirated vendors, the optimal pricing of genuine software should be lower. If compared with the optimal pricing of enterprises in a completely monopolized market, we find that with the participation of pirated manufacturers, the optimal pricing of genuine manufacturers will continue to decline and get closer to the standard of static social welfare, p=mc. So there is reason to believe that piracy is conducive to increasing social welfare. But this is only static efficiency, including configuration efficiency and production efficiency.

Social welfare includes dynamic efficiency besides static efficiency, which is related to knowledge diffusion, which is a function of innovation and intellectual property protection, so dynamic efficiency is a function of innovation and protection. If we don't pay attention to the protection of intellectual property, no one wants to invest in innovation. If there is excessive protection, such as extending the copyright of software indefinitely, knowledge will not spread, technology will not progress, and the economy will hardly grow. Some scholars use the following figure 3 to illustrate the relationship between social welfare and intellectual property rights:

In Figure 3, social welfare (strictly speaking, dynamic social welfare, that is, dynamic efficiency) is not linearly related to the level of intellectual property protection, and reaches the maximum at P* (where p is the level of protection, not the price), and greater or less than P* will cause the loss of dynamic efficiency.

6 main conclusions

Therefore, the view that piracy should be allowed for the progress of social welfare has no solid economic foundation. Because there is no need to protect intellectual property rights to maximize static efficiency, everyone can pirate, and the price of software will definitely drop to marginal cost. But dynamic efficiency needs a certain degree of intellectual property protection (P* cannot be zero), so it is impossible to maximize both at the same time.

Although there is no optimal quantitative value, some valuable conclusions can be drawn. We can make some strategic adjustments in software protection, such as shortening the copyright period of software protection, so as to improve the static efficiency and the speed of knowledge dissemination, and at the same time crack down on piracy during the protection period, protect the innovative spirit of enterprises and protect the long-term competitiveness of industries.

refer to

1 Zhang Man. On the Enlightenment of Digital Industry to Traditional Anti-monopoly Theory and Practice [J].2002 Economic Review (4)

2 Yuan Ke. Economic analysis of intellectual property rights in China [J]. Nankai Economic Research, 2003(2)

3 Stephen Martin. Advanced industrial economics [M]. Shanghai: Shanghai University of Finance and Economics Press, 2003.

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