1.1 Motivation and Objectives
Schools in Taiwan often screen students by ability. This might be unfair and causes potential pressure on students. The pressure is derived from the competition among themselves to get in better classes or better schools. After all, one takes the behavior of one's company, so parents try to cram kids in the best class, and students receive a lot of pressure from both the teacher and their parents. In some sense, parents are trying to purchase “peer effects”. One might see better students separated from those who perform worse relatively to those who are known as elite, which is pretty common here in Taiwan. However, this causes both a gain and loss in utility.
The gain comes from the elite students taking advantage of each other, while the loss part comes from the deprivation of good students who stimulates the relatively poor performing students. Furthermore, not only does the educational input such as facilities and faculties matters, but also the proportion of students of different ability alters. What motivates me most is the problem that why students spend more money on attending cram schools so often when the teachers in cram school actually teach the same thing as teachers in public school does. Therefore, I would like to find out the answer to this question in this thesis. Education has become a very important issue in the last few decades. Economists have attempted to analyze from many aspects of the issue and the most common way is to view education as one kind of industry or business, where the school is the firm, as mentioned in Rothschild and White (1995), which tries to maximize output, subject to several technological constraints. The main problem for the central planner to solve here of course is to choose the optimal amount of inputs subject to technological constraints in order to achieve the first best
solution. Conversely we can view the education industry as a decentralized market and compare the outcomes to that of the central planner’s problem, as mentioned in de Bartolome (1990). The comparison between the two enables us to know whether the central planner outcome can be achieved in a decentralized market, which means that we are trying to know if the solution is efficient, or generates more welfare in total.
However, sometimes first best solutions are very hard to find or impossible to achieve due to some constraints, so finding for a second best alternative becomes the solution to the problem we are facing.
When we talk about the production function of human capital, education is always an indispensable element that we have to focus on, but what kind of inputs and how should it be invested and how does the agents interact with the inputs has been the main problems of educational economics. Several issues have been discussed about, such as, voucher programs that allows students with low socioeconomic status to attend private schools or schools that are not near their residence, as mentioned in Epple and Romano (1998). There are also topics on subsidies, as mentioned in Winston (1999), in which the government tries to give aid to those who can not afford but are eager to study. Hierarchy has also been discussed before since it talks about the distribution of students are related to their income. One of the most popular topics that have been talked about is peer effect. The reason that it is important is that people cannot live alone. As long as they have interpersonal relationships they get influenced by their peers, more or less, even if they do not want to get affected.
What is peer effect then, if it is so important an issue? Peer effect is when the behavior or background of your peer influences your utility, education outcome to be specific, whether the effect is good or bad. The reason there is peer effect is because there exists externality in the production of education due to the presence of peers.
Some authors view education as a kind of club good, which means that the consumers
gain more than what they intended to obtain. For example in a ball game, fans get more than just the excitement of enjoying the game but also the experience as being part of the crowd. The price cannot be directly charged for the experience they share and the consumers simply have to pay only for the ticket fare. So, apparently peer effect causes a market failure if there is the effect of peers is not considered. Therefore, how to deal with this peer effect differs from model to model. Our model follows the model of de Bartolome (1990), which used a community model to find out the proportion of families with more able children and rent premium and also discussed the existence of equilibrium. Although in de Bartolome (1990) it was mentioned that Stiglitz (1974) did a research on private schools and conclude that private schools are a minority in education and thus assumed that private schools does not exist, this assumption can be further revised in order to focus on our model. Therefore, the objective of this thesis is to extend the community model of de Bartolome (1990) and find out how proportion of families with more-able children and the rent premium will be affected when adding private school to the model. We also attempt to find the conditions that enables private school to exist. Moreover, we want to see if voucher programs increase aggregate educational output under different policies of private school.
1.2 Contributions
The contribution of this thesis is based on the improvements we made on the theoretical model in the field of educational economics that deals with the problem of peer effect with public schools, private schools, vouchers. Epple and Romano (1998) discussed about the same issue with a similar structure and assumptions on income endowments, however in that paper public schools were treated in a much simplified method. In our model, public school is incorporated in a community model. We hope that this thesis is able to be a reference for the government before they make educational policies.
1.3 Outline
In the following, the second chapter will be the literature review, providing an overlook on what researchers have done in the past. In chapter three we will introduce the model in this paper, and notify the difference between other models. The fourth chapter will be the analysis and results of the model. Chapter five will be the conclusion.