本文建立一個二社區（two communities），二財貨（two goods）的模型，探討實施教育券前後對不同社區公立學校的教育品質和居住其中的家庭效用水準的變化，是否有柏拉圖改進（Pareto improvement）的可能；以及每生平均教育資本財和教師數量的變化和教育品質的關係。本文的研究結果顯示，在有學區限制之下時，富裕學區裡的學生數比較少，學校的教育品質也較好；相反的，貧窮學區的學生人數較多，但是學校的教育品質卻較低。當沒有學區限制的時候，雖然隨著貧富差距的擴大，居住在富裕社區的家庭愈來愈少，稅率也愈來愈低，但是使用教育券來富裕學區學校就讀的學生也愈來愈多；對於居住在貧窮社區的家庭而言，和學區限制時的結果不同的是，貧窮學區的教育品質也獲得提昇，同時家庭的效用水準也增加了。換言之，使用教育券之後有柏拉圖改進的機會。且教育品質的高低和平均每生的教育資本財和教師數量之間沒有必然的關係。

This paper involves a model of two communities and two goods. It explores the possibility of Pareto improvement on the quality of education in the public schools of different communities and the changes of the utility level in the families living here before and after the implementation of education vouchers. It also explores the relationships among the average education capital per student spends, the changes in the number of
teachers and the quality of education.
This study suggests that the number of the students in the affluent district is small and the quality of school education is better under the constraints of a school district. On the contrary, the number of the students in the poverty district is large, but the quality of school education is relatively low. When there is no restrictions on school district, although the gap between the rich and the poor is large, the families living in affluent communities are less and less, the rate of tax is getting lower, those who use education vouchers to study in
schools of affluent school district are more and more. For those families who live in poverty communities, the difference is that the quality of education in poverty district is enhanced and the utility level in the families living here is increased. In other words, the possibility of Pareto improvement after the implementation of education vouchers is positive. And it’s not necessarily related among the average education capital per student spends, the changes in the number of teachers and the quality of education.