Economies of Scale in Elementary School in Taiwan –the application of the school

optimal scale measurement

Tien-Tsai Kuo12.15-16 2015

Singapore

ICMPR 2015

INTRODUCTION

As the number of educational faculties increases rapidly over these years, the whole world faces a deep financial pressure on investing in educational infrastructure.

Adjustment to make the school meets its most suitable scale of operation helps to bring effects of complementary resourcing, reduce educational cost, enhance efficiency of creating educational output and give a full play of economies of scale in education field.

The fact is, around the world there were already many relevant researches about scale of operation among schools and relation between student’s cost and output.

Relevant researches in Taiwan's academy had come out relatively late.

Objective of the study

Concerning the objective of the study, it aims at investigating the optimal scale of elementary education in Taiwan.

LITERATURE REVIEW 1/2

Economies of Scale in Education Economies of scale for a primary school means the size of an education will affect the number of changes that happen during a long-run average cost (LAC). Most researchers adopted three models such as liner, U-shaped curve and L-shaped curve as models in their hypothesis of cost theory. The results of researches show that expanding scale of education can effectively reduce the cost per student.

LITERATURE REVIEW 2/2

The optimal scale of education If the result of the U-shaped curve is the optimal LAC model, then compute the optimal scale of elementary education in Taiwan value.

RESEARCH MODEL

Figure 1: Research Model

RESEARCH QUESTIONS

1. Is there economies of scale in the procedure of management of elementary education in Taiwan?

2. Which is the optimal cost model of elementary education in Taiwan?

3. How many students is the optimal scale in an elementary school in Taiwan?

DATA ANALYSIS 1/5

Variable

S X1 X2 X3 X4 X5 X6 X7 X8 Y

S  1.0000

 .1500

✽✽✽.6290

✽✽✽.6498

✽✽-.2969

✽✽✽.5059

 -.0910

✽✽✽.8132

 -.5347

✽✽✽-.3826

X1    1.0000

✽.1795

 .2230

 -.0072

 .0719

 .1425

 .0839

 -.1750

 -.1507

X2     ✽✽✽1.0000

 .9622

 -.0271

 .1716

 -.1538

✽✽✽.4526

✽✽✽-.7006

✽✽✽-.7697

X3        1.0000

 -.0236

 .1723

 -.1182

 .4652

 -.6820

 -.7717

X4          1.0000

✽✽✽-.4820

 .6690

✽✽✽-.3492

 .1737

 -.0330

X5            1.0000

 -.0001

✽✽✽.4976

 -.1938

 -.0685

X6              1.0000

 -.0238

 .0564

 .0808

X7                1.0000

✽✽✽-.4711

 -.2896

X8                  1.0000

✽✽✽.5560

Y                   ✽✽✽1.0000

Table 1. Factors related to the correlation matrix of the unit cost

per-student of elementary education in Taiwan

✽✽p<.01 ✽✽✽p<.001

DATA ANALYSIS 2/5

pattern constant S X1 X2 X3 X4 X5 X6 X7 X8 F R2

1 181396.7 

16.16(2.32)

569.28(.173)

-1618.17(-1.474)

-4027.46(-2.349)

-7724.37(-.218)

-21395.47(-.229)

-1188.65(-.277)

-318.424(-.830)

4590.512(.596)

✽✽✽

18.838

.62

2 194143.09 

13.264(1.851)

-695.28(-.331)

-3947.30(-8.204)

  -11964.96(-.331)

-5042.98(-.053)

-2065.22(-.473)

-284.547(-.726)

4702.18(.597)

✽✽✽

19.6006

.61

3 58808.22 

-11.866(-1.418)

-2429.86(-.569)

    -70337.4(-1.534)

53867.88(.438)

2902.24(.519)

161.704(.322)

41567.88(4.973)

✽✽✽

7.658.35

4 154148.26 

-24.0112(-2.712)

-5190.02(-1.111)

    -57109.8(-1.127)

134778.9(.999)

3836.89(.621)

-76.009(-.137)

   3.921

.19

5 175077.73

  -7138.29(-1.500)

    -64399.73(-.1235)

59700.80(.439)

-6344.02(-1.000)

-1205.80(-3.218)

  ✽

3.044.13

6 174336.41 

-16.520(-2.467)

  -1607.04(-1.524)

-4025.57(-2.457)

      -329.87(-.894)

4352.35(-586)

✽✽✽

35.21.63

Table 2. Multiple regression reduction analysis of Taiwan elementary school representative optimal cost liner

pattern assumption

✽p<.05 ✽✽p<.01 ✽✽✽p<.001

DATA ANALYSIS 3/5

pattern constant

S S2 X1 X2 X3 X4 X5 X6 X7 X8 F R2

1 181420.15 

16.11(.946)

0.000146(.032)

566.75(.172)

-1616.97(-1.465)

-4011.88(-2.329)

-7820.49(-.219)

-25605.95(-.157)

-1184.25(-.275)

-321.63(-.801)

4592.39(.593)

✽✽✽

16.780

.66

2 193616.81 

3.482(.211)

.00298(.657)

-647.218(-.195)

-3739.86(-6.486)

  -13585.48(-.373)

-91926.78(-.563)

-1906.85(-.435)

-352.47(-.867)

4731.63(.599)

✽✽✽

17.369

.62

3 100972.21 

-66.042(-4.406)

.019087(4.221)

-1538.74(-.389)

    -61072.93(-1.439)

-52220.93(-2.939)

2274.81(.434)

-423.34(-.874)

29350.94(3.557)

✽✽

10.065

.45

4 57741.12 

  .00702(.796)

-3336.93(-.779)

    -75958.02(-1.678)

-67881.74(-.431)

4406.71(.790)

-625.88(-1.192)

45432.09(5.636)

✽7.3609

.34

5 177192.8 

  .00115(.400)

-7291.41(-1.521)

    -65018.93(-.1241)

13748.28(.077)

6613.31(1.041)

-1380.62(-2.394)

  ✽

2.542.13

6 32741.43 

  .0040(2.119)

-7040.43(-1.436)

    -50160.201(-.943)

37533.34(.787)

5705.31(.879)

    ✽

1.89.09

7 174607.76 

-15.7607(-1.454)

.0038(.221)

  -1507.84(1.518)

-4072.87(-2.408)

      -318.07(-.830)

4359.28(.584)

✽✽✽

29.058

.67

Table 3. Multiple regression reduction analysis of Taiwan elementary school representative optimal cost U-shaped curve

pattern assumption

✽p<.05 ✽✽p<.01 ✽✽✽p<.001

DATA ANALYSIS 4/5

pattern constant S-1 X1 X2 X3 X4 X5 X6 X7 X8 F R2

1 3695.60 

7674029.41(9.606)

4034.25(1.656)

496.58(.539)

-846.34(-.671)

-2725.46(-.105)

20961.76(.315)

-1952.87(-.621)

111.12(.527)

-4575.01(-.796)

✽✽✽

43.96

.65

2 172311.10 

  860.24(.256)

-1619.55(-1.444)

-3233.35(-1.883)

-10442.92(-.288)

33592.57(.363)

-1965.55(-.450)

  5069.15(.644)

✽✽✽

19.64

.62

3 188338.70 

  -246.01(-.074)

-3566.59(-8.101)

  -13530.22(-.369)

37999.45(.405)

-2551.79(-.581)

249.14(.919)

5324.64(.673)

✽✽✽

25.13

.60

4 55077.26 

  -3104.78(-.728)

    -74786.86(-1.627)

12971.47(.108)

3976.53(.715)

  45044.47(5.608)

✽✽✽

8.51.34

5 175077.73 

  -7138.29(-1.500)

    -64399.74(-1.235)

59700.81(.439)

6344.02(1.008)

-1205.80(-3.218)

  ✽

3.04.13

6 31241.16 

7513439.46(9.545)

  -342.59(-.422)

-614.32(-.498)

      142.34(.777)

-4885.85(-.867)

✽✽✽

79.21

.66

Table 4. Multiple regression reduction analysis of Taiwan elementary school representative optimal cost L-shaped curve

pattern assumption

✽p<.05 ✽✽p<.01 ✽✽✽p<.001

DATA ANALYSIS 5/5

With the comparison of R2 among the three above tables ( Table2, Table3, Table4) , the model of U-shaped curve serves as the most optimal curve. 

DISCUSSION1. Economies of scale in the procedure of management

of elementary schools do exist in Taiwan. 2. The optimal cost curve is U-shaped curve. 3. The quality factors could be defined as follows in the

study: school size, percentage of officially qualified teachers, average number of students among per class, teacher-student ratio, percentage of personnel expense in all regular expenses, percentage of teaching affairs in all regular expenses, average number of subjects taught per teacher, number of activities held by clubs, and location can explain the variance of average student’s regular expense in the school sufficiently.

4. The number of economies of school scale is 2,073 students within an elementary school in Taiwan.

CONCLUSION

The average size of operation among primary schools in Taiwan should be gradually adjusted around 2,000 people per school to reduce costs, enhance operational efficiency, and bring up effects of economies of scale.

The EndThanks