读笔:BARRIERS TO ENTRY AND ECONOMIC GROWTH IN TRANSITION ECONOMIES

最近正在准备产业经济学pre,偶然发现了一篇有意思的论文Barriers to Entry and Economic Growth in Transition Economies
原文的摘要如下

Some believe that temporary governmental policies are likely to have no permanent consequences. In this paper, we develop a mathematical model of crime and corruption. We show that even temporary imposition of the barriers to entry to a competitive industry may lead to permanent extortion development and substantial slow-down in the economic growth. Entry restrictions, if binding, lead to the excess profits, which create an incentive to extort. Emergence of the extorters reduces the expected profit from production, making the producers expect to get extorted in the future. If, after this adaptation of expectations, the government removes the barriers to entry, only few new firms enter the market. Hence, the total number of firms on the market is lower that it would have been under no barriers to entry. The low number of firms on the market allows each producer to earn relatively high pre-extortion profits which reinforces the desire of racketeers to take part on their wealth. Consequently, the part of the population is permanently diverted from the production to rent-seeking activities, which is likely slow down economic growth even in the long run.

机翻:一些人认为,政府的临时政策可能不会产生永久性的后果。在本文中,我们建立了一个犯罪和腐败的数学模型。我们表明,即使是暂时实施进入竞争性行业的壁垒,也可能导致永久性敲诈勒索的发展和经济增长的大幅放缓。进入限制如果具有约束力,就会导致超额利润,从而产生敲诈的动机。敲诈者的出现降低了生产的预期利润,使生产者对未来被敲诈有了预期。如果在这种预期适应之后,政府取消了进入壁垒,只有少数新公司进入市场。因此,市场上的公司总数比没有进入壁垒的情况下要低。市场上的公司数量很少,这使得每个生产商在敲诈之前都能获得相对较高的利润,这加强了敲诈者分享他们财富的欲望。因此,部分人口被永久地从生产转移到寻租活动,这可能会减缓经济增长,即使从长远来看。

原文的介绍中有这样一段话:

At the times of the Soviet Union, the consume goods sector suffered from the neglect of the state planners, the demand for consumer goods was enormous. Those few people who were allowed to enter the market often became millionaires overnight. For example, there wasa group of people who started to make pantyhose. After approximately six months they became so rich that they closed down the production because they feared that nobody would believe that they had made their money honestly (see Goldman, 1996; or Gorodnichenko et al., 2014). Having been deprived of wealth of this magnitude for several decades, it was understandable that first-tier businessmen began to spend money. At the same time, criminal groups were being formed in the society, which realized that with little effort they can take a share on that wealth. In a matter of months, racketeers began to control 70-80% of the private sector. Before Gorbachov, Yeltsin, and Kravchuk removed the ban completely, the transition faced many obstacles

由此可见,原文的模型相对比较复杂,并且研究的是前苏联模式的改革,为了更加贴近当代中国经济,下面的阐述中笔者会对模型进行一定的修改,如有错误请见谅

1.基本设定

1.1 产业竞争

总人口为N,所有人有三种选择

  • 进入某个特定产业生产(原文中是open their own business,即private sector)
  • 在其他产业生产,我们认为收入是给定的市场均衡收入(原文是留在state sector)
  • 从事敲诈活动(engage in racketeering activity)

对于这个特定产业,市场价格和市场总产出的关系为: 当市场上的从业者(公司)数量为时,每个从业者产出为,总产出为: 从业者的成本为: 我们认为这些从业者遵循一个古诺竞争,因此最优化产量为: 此时企业的利润为:

如果不了解古诺均衡的结果,可以参考下面的解析
古诺竞争(Cournot Model)
对于个企业中的任意一个,收益函数为: F.O.C.: 考虑,对上述个式子求和,则有: 化简整理,我们有: 注意到这些企业完全对称,因此每家企业产量相同,最终结果为:

1.2 Extort

有两种观点:

  • 敲诈的公司越多,越熟练,越有经验,所以敲诈的边际成本逐渐降低
  • 敲诈的公司越多,这些公司越可能联合抵抗,因此敲诈的边际成本逐渐升高

似乎都有道理,所以作者直接把敲诈的单位成本设为了固定的,敲诈成本是个关于敲诈公司数量的线性函数(太草率啊啊啊啊啊啊): 敲诈者的能力和贪婪程度为,表示掠夺比例,越高说明越贪婪,同时

此外,敲诈者的数量取决于下面的等式:(是在产业生产,或留在state sector的收入/工资,也就是选择去敲诈付出的) 式中表示市场全部公司被敲诈时,敲诈者的总收益,上式的意义是在均衡时,敲诈者的收入和机会成本相当。

因为每个敲诈者能敲诈的公司数量有限,上式每个敲诈者敲诈的公司数量应当在范围内,即

2. 无壁垒和产业壁垒下的均衡发展

我们将产业发展分为三个阶段,初始阶段,发展阶段,最终均衡阶段。三个阶段用下标1,2,3来表示。

2.1 无壁垒(Basic Model)

先考虑初始阶段,由古诺均衡,最优化产量: 此时的利润应当满足和机会成本相同: 因此求解出初始阶段的公司数量: 再考虑发展阶段,公司的数量没有发生变化,但是敲诈者开始出现,敲诈者的数量为: 此时,每个公司的收益都低于机会成本,且由于敲诈者敲诈的公司数量有上限,此时的条件可能无法满足,因此,敲诈者会逐渐减少,最终均衡阶段和初始阶段相同。

2.2 初始时有壁垒,然后再取消(Restricted Model)

先考虑初始阶段,由于初始的进入壁垒(许可证等),公司的数量被限制为 再考虑发展阶段,进入壁垒被取消,短期来看公司的数量没有发生变化,但是敲诈者开始出现,敲诈者的数量为: 由于初始阶段的进入壁垒,公司数量少,超额利润大,此时的条件能够得到满足,随着产业壁垒的取消,新的公司进入,长期来看,最终会再次形成均衡(机会成本等于公司被敲诈后的利润): 因此求解出最终均衡阶段的公司数量: 敲诈者的数量

福利分析和产出效率

3.1 发展阶段的产出效率

对于该产业的产出: 由于,因此,上式恒大于0,也就是说,在发展阶段,产业壁垒必然会阻碍该产业的发展,该结论是显然的,因为此阶段厂商数量未达到竞争时的数量。

对于其他产业的产出,我们假设产率为 这个式子有些复杂,考虑求导 短期来看,可能为负,也可能为正,这主要取决于,这说明其他产业的产出可能提高,也可能减小,特别的,当机会成本很低时,其他产业的产出也会降低,这点在发展中国家是更加常见的情况。

3.2 最终均衡阶段的产出效率

同样,对于该产业的产出: 显然,该产业最终均衡阶段的产出下降。

同样考虑其他产业,此时:

这个式子的正负性很难直接判断,但是,当敲诈勒索的成本不高时,,也就是说,产出是下降的,具体的条件如下

如果考虑总损失,即,这同时取决于二者的相对生产率,这里引用一段原文的内容进行总结:

Less is produced in private sector (since there are fewer firms on the market), but possibly more people work in the state sector. Generally, if the case in the state sector gains from the extortion development, the conclusion upon the effect of barriers to entry on economic growth depends on the relative productivity of the state and private sector workers. As it was discussed above, in the countries of transition the private sector workers tend to be more productive than the state sector ones. Thus, even in the case if the state sector gains from the extortion development, temporary entry restrictions are likely to have negative long rune effect on economic growth.

In the case if the state sector loses, the conclusion is even more apparent. The whole economy loses from the entry restrictions.