胡一鳴

【Abstract】In this essay,I address the problem of inefficiency in the state-owned enterprises in China.The main question, arising from this problem,is that what government should do to make the enterprises more efficient and that whether the privatization is a good way to solve the problem.My central thesis is that selling the small size enterprises to the managers is the best way to raise the efficiency and increase the total welfare, compared with its alternatives.I start from some basic assumptions and use game theory analysis to conclude that it is right for Chinese government to privatize the state-owned enterprises.

【Key words】Privatization；State-owned enterprises；game theory

0.Introduction

In the process of economic reform, Chinese government set up a policy that the government only continued to own few state-owned companies that are crucial to national economy and sold other relatively small companies to the their managers.Afterwards,the original state-owned enterprises which are not crucial to national economy became private.

This reform was strongly criticized by some journalists and experts, who argues that government lost many assets and resources in this process.But why did government still decide to privatize them?Is it right for government to sell them?This can be illustrated by game theory.My discussion will limit to small enterprises which are not crucial for national economy,and I agree that keeping big companies like Petro China state-owned is good for the safety of Chinese economy.

1.Basic Assumptions

Let us assume that every state-owned enterprise has a manager,who pursues his own economic benefit only.Here,I hold rational person hypothesis,and do not consider the morality in the game process. Government pays the manager a fixed amount of salary,but can choose between high salary and low salary.Suppose the high salary is 5 and low salary is 2.If the manager works hard, the enterprise will have a profit of 30, but the cost of working hard for the manager is 5.If the manager works lazily,the enterprise will only have a profit of 20,and the cost for the manager is only 1.The reason for cost difference between hard-working and lazy-working is that the latter one gives manager more leisure time and less workload,apparently more preferable than long working hours and high workload,given the fixed salary.Government and the manager make the decision of high or low salary and working hard or lazily simultaneously.We only need to analyze the game in one period, because the manager is national staff,he only has one term of office.

2.Initial Game

According to the basic assumptions,when manager works hard and government pays a high salary,the managers net benefit is high salary minus the cost of working hard,i.e.5-5=0.Government enjoys high profit 30,and pays manager 5,so the net benefit of government is 25.

By the same method,when manager works hard and government pays a low salary, the managers net benefit is 2-5=-3,and governments net benefit is 30-2=28.When manager works lazily and government pays a high salary,manager will get 4 and government will get 15.When manager works lazily and government pays a low salary,manager and government will get 1 and 18 respectively.

The payoff table (Table One) is as follows:

Because the manager knows his own salary,and his own cost of working hard or lazily,the manager always gets a better payoff if he chooses to work lazily, given his salary,so working lazily is the managers dominant strategy.

Knowing the manager has strong incentive to work lazily,government will be better off if it pays manager a low salary.So the equilibrium of this game is (work lazily,pay low salary).The manager will get 1 and government will get 18,totaling 19,which is not the social optimum.

3.Introducing Bonus

Government knows that it will get 10 more if the manager works hard.One common way to induce the manager to work hard is giving bonus,which can change the payoff of the manager.As the above payoff table indicates,government should at least give the manager a bonus more than 4;otherwise the dominant strategy of manager is still working lazily.

Suppose the government decides to change its policy by giving a bonus of 5 to compensate the managers hard work,the payoff table (Table Two) will change to the following one:

The dominant strategy for the manager becomes working hard and the new equilibrium is (work hard, low salary). The government will get 23 (28 minus bonus) and the manager will get 2 (a salary of 2 plus bonus and minus the cost of hardworking).The total payoff is 25,which is more than 19 before,indicating an increase in total welfare.

4.Problems with Bonus

In the real world,it is unlikely that government spend 5 to increase gross profit by 10. In China, the manager of state-owned enterprise is usually government officers, so the salary and bonus are linked to these of the government officials.Suppose the enterprise earns a profit of 10 million Yuan, it is impossible for the manager to earn a bonus of 5 million, which will break the whole salary structure in government system.

The second problem is very similar to agent problem of big corporations in western world. It is very hard for government to judge whether the manager is hardworking or not. Since it costs to work hard,the manager have the incentive to pretend to be hardworking while perform lazily indeed,which will yield 4 more.(Manager earns the salary and bonus as before, but switch from hardworking to lazy working, yielding 5-1=4 more).

One common method of monitoring the manager is hiring a supervisor. But how much can government pay the supervisor? From the Table Two,if the supervisor can ensure the hardworking of the manager,government will get 5 more,so government can pay a fraction of 5 to the supervisor. Suppose the payment to the supervisor is 2.

But will the supervisor act responsibly and closely supervise the manager? Because the manager can bribe the supervisor, the effectiveness of hiring a supervisor needs to be examined. Suppose the manager is able to use 2 out of an extra benefit of 5 to bribe the supervisor. If the supervisor takes the bride and acts irresponsibly, the manger will get extra benefit of 3 (5-2=3) and the supervisor will get 2+2=4.If the supervisor does not take the bride, the manager will have no extra benefit and the supervisor will get 2. Hence, both the manager and the supervisor will be better off if the supervisor takes the bribe. The final outcome is as follows:

The manager: works lazily but pretends to work hard, get low salary 2+bonus 5cost of working lazily 1 bribe to the supervisor 2=4

The supervisor: takes the bribe and acts irresponsibly, get salary 2+bribe 2=4

Government: get low profit 20-salary to manager 2-bonus to manager 5-salary to supervisor 2=11.

Government will be even worse than the initial situation, and the total payoff is 19, not the social optimum either.

By the same argument, it is very difficult for government to judge whether the supervisor is acting responsibly or irresponsibly. If government hires another supervisor to monitor the previous supervisor, it will face a vicious cycle.

5.Final Solution: Privatization

The payoff table is as follows:

Some experts criticize that the government should sell the enterprise to all the workers rather than the managers, because this will increase the motivation of all workers. This kind of criticism can be easily refuted by following analysis:

Suppose the total number of the workers is N and the number of worker who works hard is n. The profit depends on the proportion of the hard workers, say 30*(n/N).All profits are shared equally between workers.It costs 2 for a worker to work hard and 0 to work lazily (shirk). If n other workers are working, then an individual workers payoff from choosing to work hard is H=30*(n+1)/N2-2 and his payoff from working lazily is L=30*n/N2.L is larger than H when N>3.87 for every n.Hence, if the total number of workers is more than 4,every worker will choose to work lazily,and the worker-owned enterprise will get zero profit.This result is even worse than the initial situation.

6.Conclusion

I have shown that the game between government and the manager in the small state-owned enterprises will result in an inefficient outcome, making welfare loss of the whole economy.Government can use bonus to induce the manager to work hard, and hire a supervisor to monitor the manager, but this turns out to be useless and results in more loss of the government.The final solution of selling the enterprise to the manager can change the payoff structure substantially,which successfully induces the manager to work hard and increase the total welfare in the society. And moreover, I have rejected the opinion of selling the enterprises to all the workers.Therefore,it is right for the government to sell the state-owned enterprises to the managers.[科]