労働需要 - 北海道大学abe/LE2018/labor_demand_201806.pdf労働需要 •...
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労働需要 • 労働力を雇う側の意思決定 • 労働力を雇うのは企業と仮定。企業は利潤を 最大化する。 • 利潤最大化する企業は、どのように労働力を 需要するか？ • まず、一定の生産量を生産する際の、費用最 小化問題から考察する。 © Yukiko Abe 2018 All rights reserved
Transcript of 労働需要 - 北海道大学abe/LE2018/labor_demand_201806.pdf労働需要 •...
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労働需要
• 労働力を雇う側の意思決定• 労働力を雇うのは企業と仮定。企業は利潤を最大化する。
• 利潤最大化する企業は、どのように労働力を需要するか？
• まず、一定の生産量を生産する際の、費用最小化問題から考察する。
© Yukiko Abe 2018 All rights reserved
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企業の費用最小化
• 複数の生産要素を用いて生産活動を行なう企業を想定。
費用関数
© Yukiko Abe 2018 All rights reserved
,min ( , ; )
L KC w r y wL rK= +
subject to ( , )F K L y≥
( , ; )C w r y
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生産関数と等量曲線
• 企業は、2生産要素を用いて生産活動を行なうとする。生産関数を以下であらわす：
• これから、等量曲線を導出：以下を満たすの組み合わせ
© Yukiko Abe 2018 All rights reserved
( , )F L K
( , )F L K y=( , )L K
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等量曲線
© Yukiko Abe 2018 All rights reserved
K
Graph3
0.50.5
0.60.6
0.70.7
0.80.8
0.90.9
11
1.11.1
1.21.2
1.31.3
1.41.4
1.51.5
1.61.6
1.71.7
1.81.8
1.91.9
22
2.12.1
2.22.2
2.32.3
2.42.4
2.52.5
2.62.6
2.72.7
2.82.8
2.92.9
33
3.13.1
3.23.2
3.33.3
3.43.4
L
2
3
1.6666666667
2.5
1.4285714286
2.1428571429
1.25
1.875
1.1111111111
1.6666666667
1
1.5
0.9090909091
1.3636363636
0.8333333333
1.25
0.7692307692
1.1538461538
0.7142857143
1.0714285714
0.6666666667
1
0.625
0.9375
0.5882352941
0.8823529412
0.5555555556
0.8333333333
0.5263157895
0.7894736842
0.5
0.75
0.4761904762
0.7142857143
0.4545454545
0.6818181818
0.4347826087
0.652173913
0.4166666667
0.625
0.4
0.6
0.3846153846
0.5769230769
0.3703703704
0.5555555556
0.3571428571
0.5357142857
0.3448275862
0.5172413793
0.3333333333
0.5
0.3225806452
0.4838709677
0.3125
0.46875
0.303030303
0.4545454545
0.2941176471
0.4411764706
Graph1
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
1
0.9090909091
0.8333333333
0.7692307692
0.7142857143
0.6666666667
0.625
0.5882352941
0.5555555556
0.5263157895
0.5
0.4761904762
0.4545454545
0.4347826087
0.4166666667
0.4
0.3846153846
0.3703703704
0.3571428571
0.3448275862
0.3333333333
0.3225806452
0.3125
0.303030303
0.2941176471
Graph2
0.50.5
0.60.6
0.70.7
0.80.8
0.90.9
11
1.11.1
1.21.2
1.31.3
1.41.4
1.51.5
1.61.6
1.71.7
1.81.8
1.91.9
22
2.12.1
2.22.2
2.32.3
2.42.4
2.52.5
2.62.6
2.72.7
2.82.8
2.92.9
33
3.13.1
3.23.2
3.33.3
3.43.4
2
3
1.6666666667
2.5
1.4285714286
2.1428571429
1.25
1.875
1.1111111111
1.6666666667
1
1.5
0.9090909091
1.3636363636
0.8333333333
1.25
0.7692307692
1.1538461538
0.7142857143
1.0714285714
0.6666666667
1
0.625
0.9375
0.5882352941
0.8823529412
0.5555555556
0.8333333333
0.5263157895
0.7894736842
0.5
0.75
0.4761904762
0.7142857143
0.4545454545
0.6818181818
0.4347826087
0.652173913
0.4166666667
0.625
0.4
0.6
0.3846153846
0.5769230769
0.3703703704
0.5555555556
0.3571428571
0.5357142857
0.3448275862
0.5172413793
0.3333333333
0.5
0.3225806452
0.4838709677
0.3125
0.46875
0.303030303
0.4545454545
0.2941176471
0.4411764706
Sheet1
0.11015
0.257.5
0.33.33333333335
0.42.53.75
0.523
0.61.66666666672.5
0.71.42857142862.1428571429
0.81.251.875
0.91.11111111111.6666666667
111.5
1.10.90909090911.3636363636
1.20.83333333331.25
1.30.76923076921.1538461538
1.40.71428571431.0714285714
1.50.66666666671
1.60.6250.9375
1.70.58823529410.8823529412
1.80.55555555560.8333333333
1.90.52631578950.7894736842
20.50.75
2.10.47619047620.7142857143
2.20.45454545450.6818181818
2.30.43478260870.652173913
2.40.41666666670.625
2.50.40.6
2.60.38461538460.5769230769
2.70.37037037040.5555555556
2.80.35714285710.5357142857
2.90.34482758620.5172413793
30.33333333330.5
3.10.32258064520.4838709677
3.20.31250.46875
3.30.3030303030.4545454545
3.40.29411764710.4411764706
Sheet1
Sheet2
Sheet3
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等量曲線の性質
• 右下がり• 2本の等量曲線は交わらない• 右上方に位置する等量曲線のほうが、生産量が多い。
• 等量曲線は原点に対して凸• 効用関数との相違点：生産関数は基数的概念
© Yukiko Abe 2018 All rights reserved
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生産要素投入と生産量
• 規模に関する収穫– 生産要素K,Lをα倍（(1)についてはα＞0、(2)と(3)についてはα＞1）したとき、yが
(1)α倍になる→規模に関する収穫一定(2)α倍より多くなる→規模に関する収穫逓増(3)α倍より少なくなる→規模に関する収穫逓減
© Yukiko Abe 2018 All rights reserved
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費用最小化
© Yukiko Abe 2018 All rights reserved
等費用曲線
Graph2
00
0.10.1
0.20.2
0.30.3
0.40.4
0.50.5
0.60.6
0.70.7
0.80.8
0.90.9
11
1.11.1
1.21.2
1.31.3
1.41.4
1.51.5
1.61.6
1.71.7
1.81.8
1.91.9
等量曲線
L
K
1/X_1
2*sqrt(1.5)-1.5*X_1
2.4494897428
2.2994897428
2.1494897428
3.3333333333
1.9994897428
2.5
1.8494897428
2
1.6994897428
1.6666666667
1.5494897428
1.4285714286
1.3994897428
1.25
1.2494897428
1.1111111111
1.0994897428
1
0.9494897428
0.9090909091
0.7994897428
0.8333333333
0.6494897428
0.7692307692
0.4994897428
0.7142857143
0.3494897428
0.6666666667
0.1994897428
0.625
0.0494897428
0.5882352941
0.5555555556
0.5263157895
Sheet1 (2)
2-x
0.110151.9
0.257.51.8
0.33.333333333351.7
0.42.53.751.6
0.5231.5
0.61.66666666672.51.4
0.71.42857142862.14285714291.3
0.81.251.8751.2
0.91.11111111111.66666666671.1
111.51
1.10.90909090911.36363636360.9
1.20.83333333331.250.8
1.30.76923076921.15384615380.7
1.40.71428571431.07142857140.6
1.50.666666666710.5
1.60.6250.93750.4
1.70.58823529410.88235294120.3
1.80.55555555560.83333333330.2
1.90.52631578950.78947368420.1
20.50.750
2.10.47619047620.7142857143-0.1
2.20.45454545450.6818181818-0.2
2.30.43478260870.652173913-0.3
2.40.41666666670.625-0.4
2.50.40.6-0.5
2.60.38461538460.5769230769-0.6
2.70.37037037040.5555555556-0.7
2.80.35714285710.5357142857-0.8
2.90.34482758620.5172413793-0.9
30.33333333330.5-1
3.10.32258064520.4838709677-1.1
3.20.31250.46875-1.2
3.30.3030303030.4545454545-1.3
3.40.29411764710.4411764706-1.4
Sheet1 (2)
Graph1
indiff_c
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
1
0.9090909091
0.8333333333
0.7692307692
0.7142857143
0.6666666667
0.625
0.5882352941
0.5555555556
0.5263157895
0.5
0.4761904762
0.4545454545
0.4347826087
0.4166666667
0.4
0.3846153846
0.3703703704
0.3571428571
0.3448275862
0.3333333333
0.3225806452
0.3125
0.303030303
0.2941176471
Graph3
0.50.5
0.60.6
0.70.7
0.80.8
0.90.9
11
1.11.1
1.21.2
1.31.3
1.41.4
1.51.5
1.61.6
1.71.7
1.81.8
1.91.9
22
2.12.1
2.22.2
2.32.3
2.42.4
2.52.5
2.62.6
2.72.7
2.82.8
2.92.9
33
3.13.1
3.23.2
3.33.3
3.43.4
2
3
1.6666666667
2.5
1.4285714286
2.1428571429
1.25
1.875
1.1111111111
1.6666666667
1
1.5
0.9090909091
1.3636363636
0.8333333333
1.25
0.7692307692
1.1538461538
0.7142857143
1.0714285714
0.6666666667
1
0.625
0.9375
0.5882352941
0.8823529412
0.5555555556
0.8333333333
0.5263157895
0.7894736842
0.5
0.75
0.4761904762
0.7142857143
0.4545454545
0.6818181818
0.4347826087
0.652173913
0.4166666667
0.625
0.4
0.6
0.3846153846
0.5769230769
0.3703703704
0.5555555556
0.3571428571
0.5357142857
0.3448275862
0.5172413793
0.3333333333
0.5
0.3225806452
0.4838709677
0.3125
0.46875
0.303030303
0.4545454545
0.2941176471
0.4411764706
income_eff
0.50.50.50.5
0.60.60.60.6
0.70.70.70.7
0.80.80.80.8
0.90.90.90.9
1111
1.11.11.11.1
1.21.21.21.2
1.31.31.31.3
1.41.41.41.4
1.51.51.51.5
1.61.61.61.6
1.71.71.71.7
1.81.81.81.8
2
3
1.5
1.9494897428
1.6666666667
2.5
1.4
1.8494897428
1.4285714286
2.1428571429
1.3
1.7494897428
1.25
1.875
1.2
1.6494897428
1.1111111111
1.6666666667
1.1
1.5494897428
1
1.5
1
1.4494897428
0.9090909091
1.3636363636
0.9
1.3494897428
0.8333333333
1.25
0.8
1.2494897428
0.7692307692
1.1538461538
0.7
1.1494897428
0.7142857143
1.0714285714
0.6
1.0494897428
0.6666666667
1
0.5
0.9494897428
0.625
0.9375
0.4
0.8494897428
0.5882352941
0.8823529412
0.3
0.7494897428
0.5555555556
0.8333333333
0.2
0.6494897428
計算
0.50.50.50.5
0.60.60.60.6
0.70.70.70.7
0.80.80.80.8
0.90.90.90.9
1111
1.11.11.11.1
1.21.21.21.2
1.31.31.31.3
1.41.41.41.4
1.51.51.51.5
1.61.61.61.6
1.71.71.71.7
1.81.81.81.8
1.91.91.91.9
2
3
1.5
1.9494897428
1.6666666667
2.5
1.4
1.8494897428
1.4285714286
2.1428571429
1.3
1.7494897428
1.25
1.875
1.2
1.6494897428
1.1111111111
1.6666666667
1.1
1.5494897428
1
1.5
1
1.4494897428
0.9090909091
1.3636363636
0.9
1.3494897428
0.8333333333
1.25
0.8
1.2494897428
0.7692307692
1.1538461538
0.7
1.1494897428
0.7142857143
1.0714285714
0.6
1.0494897428
0.6666666667
1
0.5
0.9494897428
0.625
0.9375
0.4
0.8494897428
0.5882352941
0.8823529412
0.3
0.7494897428
0.5555555556
0.8333333333
0.2
0.6494897428
0.5263157895
0.7894736842
0.1
0.5494897428
X_11/X_11.5/X_12-X_12*sqrt(1.5)-X_12*sqrt(1.5)-1.5*X_1
022.44948974282.4494897428
0.11.92.34948974282.2994897428
0.21.82.24948974282.1494897428
0.33.33333333331.72.14948974281.9994897428
0.42.51.62.04948974281.8494897428
0.5231.51.94948974281.6994897428
0.61.66666666672.51.41.84948974281.5494897428
0.71.42857142862.14285714291.31.74948974281.3994897428
0.81.251.8751.21.64948974281.2494897428
0.91.11111111111.66666666671.11.54948974281.0994897428
111.511.44948974280.9494897428
1.10.90909090911.36363636360.91.34948974280.7994897428
1.20.83333333331.250.81.24948974280.6494897428
1.30.76923076921.15384615380.71.14948974280.4994897428
1.40.71428571431.07142857140.61.04948974280.3494897428
1.50.666666666710.50.94948974280.1994897428
1.60.6250.93750.40.84948974280.0494897428
1.70.58823529410.88235294120.30.7494897428
1.80.55555555560.83333333330.20.6494897428
1.90.52631578950.78947368420.10.5494897428
20.50.7500.4494897428
2.10.47619047620.7142857143-0.10.3494897428
2.20.45454545450.6818181818-0.2
2.30.43478260870.652173913-0.3
2.40.41666666670.625-0.4
2.50.40.6-0.5
2.60.38461538460.5769230769-0.6
2.70.37037037040.5555555556-0.7
2.80.35714285710.5357142857-0.8
2.90.34482758620.5172413793-0.9
30.33333333330.5-1
3.10.32258064520.4838709677-1.1
3.20.31250.46875-1.2
3.30.3030303030.4545454545-1.3
3.40.29411764710.4411764706-1.4
1/X_1
2*sqrt(1.5)-1.5*X_1
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費用最小化の条件 （１）
• 技術的限界代替率と生産要素価格比率が一致する。• 技術的限界代替率と生産関数の関係
• 上記の条件は、支出１円あたりの限界生産物が労働と資本の間で均等化することを示す（練習問題：なぜそれが最適なのか？）
© Yukiko Abe 2018 All rights reserved
//
K F L wMRTSL F K r
∆ ∂ ∂= − = =
∆ ∂ ∂
-
費用最小化の条件 （２）
• また、等費用曲線の傾きは、市場の交換比率であり、客観的交換比率といえる。
• 限界代替率は個別企業の交換比率であるので、費用最小化の条件は、客観的交換比率と個別的交換比率が等しくなるところに要素投入量を設定することになる。
© Yukiko Abe 2018 All rights reserved
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限界費用と平均費用
• 限界費用（Marginal Cost）: 生産量(y)1単位の増加の際に、費用がどれだけ上昇するか？
• 平均費用（Average Cost）: 生産量(y)1単位あたりの費用
© Yukiko Abe 2018 All rights reserved
( , ; )( ) C w r yMC yy
∆=
∆
( )( ) C yAC yy
=
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長期と短期
• 長期にはすべての生産要素（KとL）の水準を調整できる。
• 短期にはLのみが調整可能なので、短期に生産量を増やす場合には、Lのみを増やすことで対応。
• LMC （長期限界費用）, LAC （長期平均費用）, SMC（短期限界費用）, SAC（短期平均費用）の表記を使う。
© Yukiko Abe 2018 All rights reserved
-
長期の総費用曲線（短期の総費用曲線の包絡線）
© Yukiko Abe 2018 All rights reserved
y
C
K=K1
K=K3
実線：長期の総費用
点線：それぞれの資本投入量に応じた、短期の総費用
Graph2
1111
1.21.21.21.2
1.41.41.41.4
1.61.61.61.6
1.81.81.81.8
2222
2.22.22.22.2
2.42.42.42.4
2.62.62.62.6
2.82.82.82.8
3333
3.23.23.23.2
3.43.43.43.4
3.63.63.63.6
3.83.83.83.8
4444
K=K2
2
3.7
7.3
2
2.44
4.008
7.432
2.44
2.96
4.372
7.588
2.96
3.56
4.792
7.768
3.56
4.24
5.268
7.972
4.24
5
5.8
8.2
5
5.84
6.388
8.452
5.84
6.76
7.032
8.728
6.76
7.76
7.732
9.028
7.732
8.84
8.488
9.352
8.488
10
9.3
9.7
9.3
11.24
10.168
10.072
10.072
12.56
11.092
10.468
10.468
13.96
12.072
10.888
10.888
15.44
13.108
11.332
11.332
17
14.2
11.8
11.8
Graph1
1111
1.21.21.21.2
1.41.41.41.4
1.61.61.61.6
1.81.81.81.8
2222
2.22.22.22.2
2.42.42.42.4
2.62.62.62.6
2.82.82.82.8
3333
3.23.23.23.2
3.43.43.43.4
3.63.63.63.6
3.83.83.83.8
4444
2
3.7
7.3
2
2.44
4.008
7.432
2.44
2.96
4.372
7.588
2.96
3.56
4.792
7.768
3.56
4.24
5.268
7.972
4.24
5
5.8
8.2
5
5.84
6.388
8.452
5.84
6.76
7.032
8.728
6.76
7.76
7.732
9.028
7.732
8.84
8.488
9.352
8.488
10
9.3
9.7
9.3
11.24
10.168
10.072
10.072
12.56
11.092
10.468
10.468
13.96
12.072
10.888
10.888
15.44
13.108
11.332
11.332
17
14.2
11.8
11.8
Sheet1
123.77.32
1.22.444.0087.4322.44
1.42.964.3727.5882.96
1.63.564.7927.7683.56
1.84.245.2687.9724.24
255.88.25
2.25.846.3888.4525.84
2.46.767.0328.7286.76
2.67.767.7329.0287.732
2.88.848.4889.3528.488
3109.39.79.3
3.211.2410.16810.07210.072
3.412.5611.09210.46810.468
3.613.9612.07210.88810.888
3.815.4413.10811.33211.332
41714.211.811.8
Sheet1
Sheet2
Sheet3
-
長期と短期：限界費用と平均費用
SMC2 (K=K2)
LMCLAC （包絡線）
SAC2 (K=K2)
SMC1(K=K1)SAC1 (K=K1)
y1 y2 y
MC, AC
© Yukiko Abe 2018 All rights reserved
-
短期の平均費用と長期の平均費用
• Kの水準が異なる総費用曲線の包絡線が、長期の総費用曲線になる。
• 同様の理由で、長期の平均費用は、短期の平均費用の包絡線となる。
• 長期の限界費用は、短期の限界費用の包絡線にはならない。
• 長期の限界費用は、短期の限界費用よりも、傾きが緩やかである。それは、資本の投入量を調整することができるためである。
© Yukiko Abe 2018 All rights reserved
-
長期と短期：限界費用と平均費用
SMC2 (K=K2)
LMCLAC （包絡線）
SAC2 (K=K2)
SMC1(K=K1)SAC1 (K=K1)
y1 y2 y
MC, AC
© Yukiko Abe 2018 All rights reserved
-
短期の平均費用と限界費用
• 短期には資本の投入量（Kの水準）が固定されている。生産量(y)の調整は、労働投入（L）を変えることによってのみ行われる。
• 長期において、生産量y1を生産するために最適な資本の投入量をK1であるとき（ y=y1における短期平均費用の水準が平均費用の包絡線に一致するとき）、K=K1であるような短期の限界費用がy=y1の生産量に対応する長期の限界費用になる。
© Yukiko Abe 2018 All rights reserved
-
平均費用と限界費用
• 平均費用が最小になる点で、平均費用と限界費用が一致する：
• 微分して求める方法（公式を用いる）
• 上昇率が等しい性質を使う方法（弾力性の時の考え方の応用）
© Yukiko Abe 2018 All rights reserved
( ) ( )[ ]AC y C yy y y
∂ ∂= =
∂ ∂
( ) ( )( )
C y MC y y y yC y y+ ∆ + ∆
=
-
企業の利潤最大化
• 利潤
• yが内生変数。最適解の条件は
© Yukiko Abe 2018 All rights reserved
( ) ( )y py C yπ = −
( )p MC y=
-
限界費用と生産量の決定
© Yukiko Abe 2018 All rights reservedy
MC, p
Graph3
00
11
1.21.2
1.41.4
1.61.6
1.81.8
22
2.22.2
2.42.4
2.62.6
2.82.8
33
3.23.2
3.43.4
3.63.6
3.83.8
44
4.24.2
4.44.4
4.64.6
4.84.8
55
5.25.2
5.45.4
5.65.6
5.85.8
66
6.26.2
6.46.4
6.66.6
6.86.8
77
7.27.2
7.47.4
7.67.6
7.87.8
8
8.2
8.4
8.6
8.8
9
9.2
9.4
9.6
9.8
限界費用、MC
P
2
6
2
6
2.0333333333
6
2.1142857143
6
2.225
6
2.3555555556
6
2.5
6
2.6545454545
6
2.8166666667
6
2.9846153846
6
3.1571428571
6
3.3333333333
6
3.5125
6
3.6941176471
6
3.8777777778
6
4.0631578947
6
4.25
6
4.4380952381
6
4.6272727273
6
4.8173913043
6
5.0083333333
6
5.2
6
5.3923076923
6
5.5851851852
6
5.7785714286
6
5.9724137931
6
6.1666666667
6
6.3612903226
6
6.55625
6
6.7515151515
6
6.9470588235
6
7.1428571429
6
7.3388888889
6
7.5351351351
6
7.7315789474
6
7.9282051282
6
6
6
6
6
6
6
6
6
6
6
Graph2
00
11
1.21.2
1.41.4
1.61.6
1.81.8
22
2.22.2
2.42.4
2.62.6
2.82.8
33
3.23.2
3.43.4
3.63.6
3.83.8
44
4.24.2
4.44.4
4.64.6
4.84.8
55
5.25.2
5.45.4
5.65.6
5.85.8
66
6.26.2
6.46.4
6.66.6
6.86.8
77
7.27.2
7.47.4
7.67.6
7.87.8
8
8.2
8.4
8.6
8.8
9
9.2
9.4
9.6
9.8
2
6
2
6
2.0333333333
6
2.1142857143
6
2.225
6
2.3555555556
6
2.5
6
2.6545454545
6
2.8166666667
6
2.9846153846
6
3.1571428571
6
3.3333333333
6
3.5125
6
3.6941176471
6
3.8777777778
6
4.0631578947
6
4.25
6
4.4380952381
6
4.6272727273
6
4.8173913043
6
5.0083333333
6
5.2
6
5.3923076923
6
5.5851851852
6
5.7785714286
6
5.9724137931
6
6.1666666667
6
6.3612903226
6
6.55625
6
6.7515151515
6
6.9470588235
6
7.1428571429
6
7.3388888889
6
7.5351351351
6
7.7315789474
6
7.9282051282
6
6
6
6
6
6
6
6
6
6
6
Sheet1 (2)
026
123.77.326
1.22.03333333333.346.19333333332.03333333336
1.42.11428571433.12285714295.422.11428571436
1.62.2252.9954.8552.2256
1.82.35555555562.92666666674.42888888892.35555555566
22.52.94.12.56
2.22.65454545452.90363636363.84181818182.65454545456
2.42.81666666672.933.63666666672.81666666676
2.62.98461538462.97384615383.47230769232.97384615386
2.83.15714285713.03142857143.343.03142857146
33.33333333333.13.23333333333.16
3.23.51253.17753.14753.14756
3.43.69411764713.26235294123.07882352943.07882352946
3.63.87777777783.35333333333.02444444443.02444444446
3.84.06315789473.44947368422.98210526322.98210526326
44.253.552.952.956
4.24.43809523813.65428571432.92666666676
4.44.62727272733.76181818182.91090909096
4.64.81739130433.8721739132.90173913046
4.85.00833333333.9852.89833333336
55.24.12.96
5.25.39230769234.21692307692.90615384626
5.45.58518518524.33555555562.91629629636
5.65.77857142864.45571428572.936
5.85.97241379314.57724137932.94689655176
66.16666666674.72.96666666676
6.26.36129032264.82387096772.98903225816
6.46.556254.948753.013756
6.66.75151515155.07454545453.04060606066
6.86.94705882355.20117647063.06941176476
77.14285714295.32857142863.16
7.27.33888888895.45666666673.13222222226
7.47.53513513515.58540540543.16594594596
7.67.73157894745.71473684213.20105263166
7.87.92820512825.84461538463.23743589746
86
8.26
8.46
8.66
8.86
96
9.26
9.46
9.66
9.86
Graph1
1111
1.21.21.21.2
1.41.41.41.4
1.61.61.61.6
1.81.81.81.8
2222
2.22.22.22.2
2.42.42.42.4
2.62.62.62.6
2.82.82.82.8
3333
3.23.23.23.2
3.43.43.43.4
3.63.63.63.6
3.83.83.83.8
4444
2
3.7
7.3
2
2.44
4.008
7.432
2.44
2.96
4.372
7.588
2.96
3.56
4.792
7.768
3.56
4.24
5.268
7.972
4.24
5
5.8
8.2
5
5.84
6.388
8.452
5.84
6.76
7.032
8.728
6.76
7.76
7.732
9.028
7.732
8.84
8.488
9.352
8.488
10
9.3
9.7
9.3
11.24
10.168
10.072
10.072
12.56
11.092
10.468
10.468
13.96
12.072
10.888
10.888
15.44
13.108
11.332
11.332
17
14.2
11.8
11.8
Sheet1
123.77.32
1.22.444.0087.4322.44
1.42.964.3727.5882.96
1.63.564.7927.7683.56
1.84.245.2687.9724.24
255.88.25
2.25.846.3888.4525.84
2.46.767.0328.7286.76
2.67.767.7329.0287.732
2.88.848.4889.3528.488
3109.39.79.3
3.211.2410.16810.07210.072
3.412.5611.09210.46810.468
3.613.9612.07210.88810.888
3.815.4413.10811.33211.332
41714.211.811.8
Sheet1
Sheet2
Sheet3
-
平均費用と限界費用：利潤最大化（長期の均衡）
© Yukiko Abe 2018 All rights reserved
y
MC, AC 限界費用、MC
長期に実現する価格
Graph3
000.2
0.20.20.4
0.40.40.6
0.60.60.8
0.80.81
111.2
1.21.21.4
1.41.41.6
1.61.61.8
1.81.82
222.2
2.22.22.4
2.42.42.6
2.62.62.8
2.82.83
333.2
3.23.23.4
3.43.43.6
3.63.63.8
3.83.84
444.2
4.24.24.4
4.44.44.6
4.64.64.8
4.84.85
555.2
5.25.25.4
5.45.45.6
5.65.65.8
5.85.86
666.2
6.26.26.4
6.46.46.6
6.66.66.8
6.86.87
777.2
7.27.27.4
7.47.47.6
7.67.67.8
7.87.88
15.888.2
16.28.28.4
16.68.48.6
178.68.8
17.48.89
17.899.2
18.29.2
18.69.4
199.6
19.49.8
平均費用、AC
0
2
5.2
0.2
2
2.9
0.6
2
2.2666666667
1
2
2.05
1.4
2
2
1.8
2
2.0333333333
2.2
2
2.1142857143
2.6
2
2.225
3
2
2.3555555556
3.4
2
2.5
3.8
2
2.6545454545
4.2
2
2.8166666667
4.6
2
2.9846153846
5
2
3.1571428571
5.4
2
3.3333333333
5.8
2
3.5125
6.2
2
3.6941176471
6.6
2
3.8777777778
7
2
4.0631578947
7.4
2
4.25
7.8
2
4.4380952381
8.2
2
4.6272727273
8.6
2
4.8173913043
9
2
5.0083333333
9.4
2
5.2
9.8
2
5.3923076923
10.2
2
5.5851851852
10.6
2
5.7785714286
11
2
5.9724137931
11.4
2
6.1666666667
11.8
2
6.3612903226
12.2
2
6.55625
12.6
2
6.7515151515
13
2
6.9470588235
13.4
2
7.1428571429
13.8
2
7.3388888889
14.2
2
7.5351351351
14.6
2
7.7315789474
15
2
7.9282051282
15.4
2
8.125
2
8.3219512195
2
8.519047619
2
8.7162790698
2
8.9136363636
2
9.1111111111
2
9.3086956522
2
2
2
2
Graph2
000.2
0.20.20.4
0.40.40.6
0.60.60.8
0.80.81
111.2
1.21.21.4
1.41.41.6
1.61.61.8
1.81.82
222.2
2.22.22.4
2.42.42.6
2.62.62.8
2.82.83
333.2
3.23.23.4
3.43.43.6
3.63.63.8
3.83.84
444.2
4.24.24.4
4.44.44.6
4.64.64.8
4.84.85
555.2
5.25.25.4
5.45.45.6
5.65.65.8
5.85.86
666.2
6.26.26.4
6.46.46.6
6.66.66.8
6.86.87
777.2
7.27.27.4
7.47.47.6
7.67.67.8
7.87.88
15.888.2
16.28.28.4
16.68.48.6
178.68.8
17.48.89
17.899.2
18.29.2
18.69.4
199.6
19.49.8
0
2
5.2
0.2
2
2.9
0.6
2
2.2666666667
1
2
2.05
1.4
2
2
1.8
2
2.0333333333
2.2
2
2.1142857143
2.6
2
2.225
3
2
2.3555555556
3.4
2
2.5
3.8
2
2.6545454545
4.2
2
2.8166666667
4.6
2
2.9846153846
5
2
3.1571428571
5.4
2
3.3333333333
5.8
2
3.5125
6.2
2
3.6941176471
6.6
2
3.8777777778
7
2
4.0631578947
7.4
2
4.25
7.8
2
4.4380952381
8.2
2
4.6272727273
8.6
2
4.8173913043
9
2
5.0083333333
9.4
2
5.2
9.8
2
5.3923076923
10.2
2
5.5851851852
10.6
2
5.7785714286
11
2
5.9724137931
11.4
2
6.1666666667
11.8
2
6.3612903226
12.2
2
6.55625
12.6
2
6.7515151515
13
2
6.9470588235
13.4
2
7.1428571429
13.8
2
7.3388888889
14.2
2
7.5351351351
14.6
2
7.7315789474
15
2
7.9282051282
15.4
2
8.125
2
8.3219512195
2
8.519047619
2
8.7162790698
2
8.9136363636
2
9.1111111111
2
9.3086956522
2
2
2
2
Sheet1 (2)
0022
0.20.25.22
0.40.62.92
0.612.26666666672
0.81.42.052
11.8223.77.322
1.22.22.03333333332.03333333333.346.19333333332.03333333332
1.42.62.11428571432.11428571433.12285714295.422.11428571432
1.632.2252.2252.9954.8552.2252
1.83.42.35555555562.35555555562.92666666674.42888888892.35555555562
23.82.52.52.94.12.52
2.24.22.65454545452.65454545452.90363636363.84181818182.65454545452
2.44.62.81666666672.81666666672.933.63666666672.81666666672
2.652.98461538462.98461538462.97384615383.47230769232.97384615382
2.85.43.15714285713.15714285713.03142857143.343.03142857142
35.83.33333333333.33333333333.13.23333333333.12
3.26.23.51253.51253.17753.14753.14752
3.46.63.69411764713.69411764713.26235294123.07882352943.07882352942
3.673.87777777783.87777777783.35333333333.02444444443.02444444442
3.87.44.06315789474.06315789473.44947368422.98210526322.98210526322
47.84.254.253.552.952.952
4.28.24.43809523814.43809523813.65428571432.92666666672
4.48.64.62727272734.62727272733.76181818182.91090909092
4.694.81739130434.81739130433.8721739132.90173913042
4.89.45.00833333335.00833333333.9852.89833333332
59.85.25.24.12.92
5.210.25.39230769235.39230769234.21692307692.90615384622
5.410.65.58518518525.58518518524.33555555562.91629629632
5.6115.77857142865.77857142864.45571428572.932
5.811.45.97241379315.97241379314.57724137932.94689655172
611.86.16666666676.16666666674.72.96666666672
6.212.26.36129032266.36129032264.82387096772.98903225812
6.412.66.556256.556254.948753.013752
6.6136.75151515156.75151515155.07454545453.04060606062
6.813.46.94705882356.94705882355.20117647063.06941176472
713.87.14285714297.14285714295.32857142863.12
7.214.27.33888888897.33888888895.45666666673.13222222222
7.414.67.53513513517.53513513515.58540540543.16594594592
7.6157.73157894747.73157894745.71473684213.20105263162
7.815.47.92820512827.92820512825.84461538463.23743589742
815.88.1252
8.216.28.32195121952
8.416.68.5190476192
8.6178.71627906982
8.817.48.91363636362
917.89.11111111112
9.218.29.30869565222
9.418.69.50638297872
9.6199.70416666672
9.819.49.90204081632
2
Graph1
1111
1.21.21.21.2
1.41.41.41.4
1.61.61.61.6
1.81.81.81.8
2222
2.22.22.22.2
2.42.42.42.4
2.62.62.62.6
2.82.82.82.8
3333
3.23.23.23.2
3.43.43.43.4
3.63.63.63.6
3.83.83.83.8
4444
2
3.7
7.3
2
2.44
4.008
7.432
2.44
2.96
4.372
7.588
2.96
3.56
4.792
7.768
3.56
4.24
5.268
7.972
4.24
5
5.8
8.2
5
5.84
6.388
8.452
5.84
6.76
7.032
8.728
6.76
7.76
7.732
9.028
7.732
8.84
8.488
9.352
8.488
10
9.3
9.7
9.3
11.24
10.168
10.072
10.072
12.56
11.092
10.468
10.468
13.96
12.072
10.888
10.888
15.44
13.108
11.332
11.332
17
14.2
11.8
11.8
Sheet1
123.77.32
1.22.444.0087.4322.44
1.42.964.3727.5882.96
1.63.564.7927.7683.56
1.84.245.2687.9724.24
255.88.25
2.25.846.3888.4525.84
2.46.767.0328.7286.76
2.67.767.7329.0287.732
2.88.848.4889.3528.488
3109.39.79.3
3.211.2410.16810.07210.072
3.412.5611.09210.46810.468
3.613.9612.07210.88810.888
3.815.4413.10811.33211.332
41714.211.811.8
Sheet1
Sheet2
Sheet3
-
可変費用
• 可変費用とは、生産量が変化するときに変化する費用である。
• 一方、生産量がゼロであってもかかる費用のことを、固定費用と呼ぶ。
© Yukiko Abe 2018 All rights reserved
-
損益分岐点と操業停止点
• 短期には、利潤がマイナスであっても操業したほうがよい場合がある。
• それは、収入が可変費用を上回る場合である。
• 操業しない場合の利潤：• 操業した場合の利潤：• であっても、 にできる範囲で、操業したほうがよい。
© Yukiko Abe 2018 All rights reserved
0rK− <py wL rK− −
0py wL− >0py wL rK− −
-
平均費用と限界費用：利潤最大化
© Yukiko Abe 2018 All rights reservedy
MC, AC, AVC
Graph3
00.80.8
0.211
0.41.21.2
0.61.41.4
0.81.61.6
11.81.8
1.222
1.42.22.2
1.62.42.4
1.82.62.6
22.82.8
2.233
2.43.23.2
2.63.43.4
2.83.63.6
33.83.8
3.244
3.44.24.2
3.64.44.4
3.84.64.6
44.84.8
4.255
4.45.25.2
4.65.45.4
4.85.65.6
55.85.8
5.266
5.46.26.2
5.66.46.4
5.86.66.6
66.86.8
6.277
6.47.27.2
6.67.47.4
6.87.67.6
77.87.8
7.288
7.48.28.2
7.68.48.4
7.88.68.6
198.88.8
19.499
19.89.29.2
20.29.4
20.69.6
219.8
21.4
21.8
22.2
22.6
平均費用
平均可変費用
限界費用
3
22.55
10.05
3.4
19
9
3.8
16.7
8.3666666667
4.2
15.1142857143
7.9714285714
4.6
13.975
7.725
5
13.1333333333
7.5777777778
5.4
12.5
7.5
5.8
12.0181818182
7.4727272727
6.2
11.65
7.4833333333
6.6
11.3692307692
7.5230769231
7
11.1571428571
7.5857142857
7.4
11
7.6666666667
7.8
10.8875
7.7625
8.2
10.8117647059
7.8705882353
8.6
10.7666666667
7.9888888889
9
10.7473684211
8.1157894737
9.4
10.75
8.25
9.8
10.7714285714
8.3904761905
10.2
10.8090909091
8.5363636364
10.6
10.8608695652
8.6869565217
11
10.925
8.8416666667
11.4
11
9
11.8
11.0846153846
9.1615384615
12.2
11.1777777778
9.3259259259
12.6
11.2785714286
9.4928571429
13
11.3862068966
9.6620689655
13.4
11.5
9.8333333333
13.8
11.6193548387
10.0064516129
14.2
11.74375
10.18125
14.6
11.8727272727
10.3575757576
15
12.0058823529
10.5352941176
15.4
12.1428571429
10.7142857143
15.8
12.2833333333
10.8944444444
16.2
12.427027027
11.0756756757
16.6
12.5736842105
11.2578947368
17
12.7230769231
11.441025641
17.4
12.875
11.625
17.8
13.0292682927
11.8097560976
18.2
13.1857142857
11.9952380952
18.6
13.3441860465
12.1813953488
13.5045454545
12.3681818182
13.6666666667
12.5555555556
13.8304347826
12.7434782609
12.9319148936
13.1208333333
13.3102040816
Graph2
00.80.8
0.211
0.41.21.2
0.61.41.4
0.81.61.6
11.81.8
1.222
1.42.22.2
1.62.42.4
1.82.62.6
22.82.8
2.233
2.43.23.2
2.63.43.4
2.83.63.6
33.83.8
3.244
3.44.24.2
3.64.44.4
3.84.64.6
44.84.8
4.255
4.45.25.2
4.65.45.4
4.85.65.6
55.85.8
5.266
5.46.26.2
5.66.46.4
5.86.66.6
66.86.8
6.277
6.47.27.2
6.67.47.4
6.87.67.6
77.87.8
7.288
7.48.28.2
7.68.48.4
7.88.68.6
198.88.8
19.499
19.89.29.2
20.29.4
20.69.6
219.8
21.4
21.8
22.2
22.6
平均費用
平均可変費用
限界費用
3
22.55
10.05
3.4
19
9
3.8
16.7
8.3666666667
4.2
15.1142857143
7.9714285714
4.6
13.975
7.725
5
13.1333333333
7.5777777778
5.4
12.5
7.5
5.8
12.0181818182
7.4727272727
6.2
11.65
7.4833333333
6.6
11.3692307692
7.5230769231
7
11.1571428571
7.5857142857
7.4
11
7.6666666667
7.8
10.8875
7.7625
8.2
10.8117647059
7.8705882353
8.6
10.7666666667
7.9888888889
9
10.7473684211
8.1157894737
9.4
10.75
8.25
9.8
10.7714285714
8.3904761905
10.2
10.8090909091
8.5363636364
10.6
10.8608695652
8.6869565217
11
10.925
8.8416666667
11.4
11
9
11.8
11.0846153846
9.1615384615
12.2
11.1777777778
9.3259259259
12.6
11.2785714286
9.4928571429
13
11.3862068966
9.6620689655
13.4
11.5
9.8333333333
13.8
11.6193548387
10.0064516129
14.2
11.74375
10.18125
14.6
11.8727272727
10.3575757576
15
12.0058823529
10.5352941176
15.4
12.1428571429
10.7142857143
15.8
12.2833333333
10.8944444444
16.2
12.427027027
11.0756756757
16.6
12.5736842105
11.2578947368
17
12.7230769231
11.441025641
17.4
12.875
11.625
17.8
13.0292682927
11.8097560976
18.2
13.1857142857
11.9952380952
18.6
13.3441860465
12.1813953488
13.5045454545
12.3681818182
13.6666666667
12.5555555556
13.8304347826
12.7434782609
12.9319148936
13.1208333333
13.3102040816
Sheet1 (2)
032
0.23.478.228.22
0.43.840.915.92
0.64.228.611.93333333332
0.84.622.5510.052
1519992
1.25.416.78.36666666678.36666666672
1.45.815.11428571437.97142857147.97142857142
1.66.213.9757.7257.7252
1.86.613.13333333337.57777777787.57777777782
2712.57.57.52
2.27.412.01818181827.47272727277.47272727272
2.47.811.657.48333333337.48333333332
2.68.211.36923076927.52307692317.52307692312
2.88.611.15714285717.58571428577.58571428572
39117.66666666677.66666666672
3.29.410.88757.76257.76252
3.49.810.81176470597.87058823537.87058823532
3.610.210.76666666677.98888888897.98888888892
3.810.610.74736842118.11578947378.11578947372
41110.758.258.252
4.211.410.77142857148.39047619052
4.411.810.80909090918.53636363642
4.612.210.86086956528.68695652172
4.812.610.9258.84166666672
5131192
5.213.411.08461538469.16153846152
5.413.811.17777777789.32592592592
5.614.211.27857142869.49285714292
5.814.611.38620689669.66206896552
61511.59.83333333332
6.215.411.619354838710.00645161292
6.415.811.7437510.181252
6.616.211.872727272710.35757575762
6.816.612.005882352910.53529411762
71712.142857142910.71428571432
7.217.412.283333333310.89444444442
7.417.812.42702702711.07567567572
7.618.212.573684210511.25789473682
7.818.612.723076923111.4410256412
81912.87511.6252
8.219.413.029268292711.80975609762
8.419.813.185714285711.99523809522
8.620.213.344186046512.18139534882
8.820.613.504545454512.36818181822
92113.666666666712.55555555562
9.221.413.830434782612.74347826092
9.421.813.995744680912.93191489362
9.622.214.162513.12083333332
9.822.614.330612244913.31020408162
2
Graph1
1111
1.21.21.21.2
1.41.41.41.4
1.61.61.61.6
1.81.81.81.8
2222
2.22.22.22.2
2.42.42.42.4
2.62.62.62.6
2.82.82.82.8
3333
3.23.23.23.2
3.43.43.43.4
3.63.63.63.6
3.83.83.83.8
4444
2
3.7
7.3
2
2.44
4.008
7.432
2.44
2.96
4.372
7.588
2.96
3.56
4.792
7.768
3.56
4.24
5.268
7.972
4.24
5
5.8
8.2
5
5.84
6.388
8.452
5.84
6.76
7.032
8.728
6.76
7.76
7.732
9.028
7.732
8.84
8.488
9.352
8.488
10
9.3
9.7
9.3
11.24
10.168
10.072
10.072
12.56
11.092
10.468
10.468
13.96
12.072
10.888
10.888
15.44
13.108
11.332
11.332
17
14.2
11.8
11.8
Sheet1
123.77.32
1.22.444.0087.4322.44
1.42.964.3727.5882.96
1.63.564.7927.7683.56
1.84.245.2687.9724.24
255.88.25
2.25.846.3888.4525.84
2.46.767.0328.7286.76
2.67.767.7329.0287.732
2.88.848.4889.3528.488
3109.39.79.3
3.211.2410.16810.07210.072
3.412.5611.09210.46810.468
3.613.9612.07210.88810.888
3.815.4413.10811.33211.332
41714.211.811.8
Sheet1
Sheet2
Sheet3
-
平均費用と限界費用：供給曲線
© Yukiko Abe 2018 All rights reservedy
供給曲線
P
Graph3
00.80.8
0.211
0.41.21.2
0.61.41.4
0.81.61.6
11.81.8
1.222
1.42.22.2
1.62.42.4
1.82.62.6
22.82.8
2.233
2.43.23.2
2.63.43.4
2.83.63.6
33.83.8
3.244
3.44.24.2
3.64.44.4
3.84.64.6
44.84.8
4.255
4.45.25.2
4.65.45.4
4.85.65.6
55.85.8
5.266
5.46.26.2
5.66.46.4
5.86.66.6
66.86.8
6.277
6.47.27.2
6.67.47.4
6.87.67.6
77.87.8
7.288
7.48.28.2
7.68.48.4
7.88.68.6
198.88.8
19.499
19.89.29.2
20.29.4
20.69.6
219.8
21.4
21.8
22.2
22.6
平均費用
平均可変費用
限界費用
3
22.55
10.05
3.4
19
9
3.8
16.7
8.3666666667
4.2
15.1142857143
7.9714285714
4.6
13.975
7.725
5
13.1333333333
7.5777777778
5.4
12.5
7.5
5.8
12.0181818182
7.4727272727
6.2
11.65
7.4833333333
6.6
11.3692307692
7.5230769231
7
11.1571428571
7.5857142857
7.4
11
7.6666666667
7.8
10.8875
7.7625
8.2
10.8117647059
7.8705882353
8.6
10.7666666667
7.9888888889
9
10.7473684211
8.1157894737
9.4
10.75
8.25
9.8
10.7714285714
8.3904761905
10.2
10.8090909091
8.5363636364
10.6
10.8608695652
8.6869565217
11
10.925
8.8416666667
11.4
11
9
11.8
11.0846153846
9.1615384615
12.2
11.1777777778
9.3259259259
12.6
11.2785714286
9.4928571429
13
11.3862068966
9.6620689655
13.4
11.5
9.8333333333
13.8
11.6193548387
10.0064516129
14.2
11.74375
10.18125
14.6
11.8727272727
10.3575757576
15
12.0058823529
10.5352941176
15.4
12.1428571429
10.7142857143
15.8
12.2833333333
10.8944444444
16.2
12.427027027
11.0756756757
16.6
12.5736842105
11.2578947368
17
12.7230769231
11.441025641
17.4
12.875
11.625
17.8
13.0292682927
11.8097560976
18.2
13.1857142857
11.9952380952
18.6
13.3441860465
12.1813953488
13.5045454545
12.3681818182
13.6666666667
12.5555555556
13.8304347826
12.7434782609
12.9319148936
13.1208333333
13.3102040816
Graph2
00.80.8
0.211
0.41.21.2
0.61.41.4
0.81.61.6
11.81.8
1.222
1.42.22.2
1.62.42.4
1.82.62.6
22.82.8
2.233
2.43.23.2
2.63.43.4
2.83.63.6
33.83.8
3.244
3.44.24.2
3.64.44.4
3.84.64.6
44.84.8
4.255
4.45.25.2
4.65.45.4
4.85.65.6
55.85.8
5.266
5.46.26.2
5.66.46.4
5.86.66.6
66.86.8
6.277
6.47.27.2
6.67.47.4
6.87.67.6
77.87.8
7.288
7.48.28.2
7.68.48.4
7.88.68.6
198.88.8
19.499
19.89.29.2
20.29.4
20.69.6
219.8
21.4
21.8
22.2
22.6
平均費用
平均可変費用
限界費用
3
22.55
10.05
3.4
19
9
3.8
16.7
8.3666666667
4.2
15.1142857143
7.9714285714
4.6
13.975
7.725
5
13.1333333333
7.5777777778
5.4
12.5
7.5
5.8
12.0181818182
7.4727272727
6.2
11.65
7.4833333333
6.6
11.3692307692
7.5230769231
7
11.1571428571
7.5857142857
7.4
11
7.6666666667
7.8
10.8875
7.7625
8.2
10.8117647059
7.8705882353
8.6
10.7666666667
7.9888888889
9
10.7473684211
8.1157894737
9.4
10.75
8.25
9.8
10.7714285714
8.3904761905
10.2
10.8090909091
8.5363636364
10.6
10.8608695652
8.6869565217
11
10.925
8.8416666667
11.4
11
9
11.8
11.0846153846
9.1615384615
12.2
11.1777777778
9.3259259259
12.6
11.2785714286
9.4928571429
13
11.3862068966
9.6620689655
13.4
11.5
9.8333333333
13.8
11.6193548387
10.0064516129
14.2
11.74375
10.18125
14.6
11.8727272727
10.3575757576
15
12.0058823529
10.5352941176
15.4
12.1428571429
10.7142857143
15.8
12.2833333333
10.8944444444
16.2
12.427027027
11.0756756757
16.6
12.5736842105
11.2578947368
17
12.7230769231
11.441025641
17.4
12.875
11.625
17.8
13.0292682927
11.8097560976
18.2
13.1857142857
11.9952380952
18.6
13.3441860465
12.1813953488
13.5045454545
12.3681818182
13.6666666667
12.5555555556
13.8304347826
12.7434782609
12.9319148936
13.1208333333
13.3102040816
Sheet1 (2)
032
0.23.478.228.22
0.43.840.915.92
0.64.228.611.93333333332
0.84.622.5510.052
1519992
1.25.416.78.36666666678.36666666672
1.45.815.11428571437.97142857147.97142857142
1.66.213.9757.7257.7252
1.86.613.13333333337.57777777787.57777777782
2712.57.57.52
2.27.412.01818181827.47272727277.47272727272
2.47.811.657.48333333337.48333333332
2.68.211.36923076927.52307692317.52307692312
2.88.611.15714285717.58571428577.58571428572
39117.66666666677.66666666672
3.29.410.88757.76257.76252
3.49.810.81176470597.87058823537.87058823532
3.610.210.76666666677.98888888897.98888888892
3.810.610.74736842118.11578947378.11578947372
41110.758.258.252
4.211.410.77142857148.39047619052
4.411.810.80909090918.53636363642
4.612.210.86086956528.68695652172
4.812.610.9258.84166666672
5131192
5.213.411.08461538469.16153846152
5.413.811.17777777789.32592592592
5.614.211.27857142869.49285714292
5.814.611.38620689669.66206896552
61511.59.83333333332
6.215.411.619354838710.00645161292
6.415.811.7437510.181252
6.616.211.872727272710.35757575762
6.816.612.005882352910.53529411762
71712.142857142910.71428571432
7.217.412.283333333310.89444444442
7.417.812.42702702711.07567567572
7.618.212.573684210511.25789473682
7.818.612.723076923111.4410256412
81912.87511.6252
8.219.413.029268292711.80975609762
8.419.813.185714285711.99523809522
8.620.213.344186046512.18139534882
8.820.613.504545454512.36818181822
92113.666666666712.55555555562
9.221.413.830434782612.74347826092
9.421.813.995744680912.93191489362
9.622.214.162513.12083333332
9.822.614.330612244913.31020408162
2
Graph1
1111
1.21.21.21.2
1.41.41.41.4
1.61.61.61.6
1.81.81.81.8
2222
2.22.22.22.2
2.42.42.42.4
2.62.62.62.6
2.82.82.82.8
3333
3.23.23.23.2
3.43.43.43.4
3.63.63.63.6
3.83.83.83.8
4444
2
3.7
7.3
2
2.44
4.008
7.432
2.44
2.96
4.372
7.588
2.96
3.56
4.792
7.768
3.56
4.24
5.268
7.972
4.24
5
5.8
8.2
5
5.84
6.388
8.452
5.84
6.76
7.032
8.728
6.76
7.76
7.732
9.028
7.732
8.84
8.488
9.352
8.488
10
9.3
9.7
9.3
11.24
10.168
10.072
10.072
12.56
11.092
10.468
10.468
13.96
12.072
10.888
10.888
15.44
13.108
11.332
11.332
17
14.2
11.8
11.8
Sheet1
123.77.32
1.22.444.0087.4322.44
1.42.964.3727.5882.96
1.63.564.7927.7683.56
1.84.245.2687.9724.24
255.88.25
2.25.846.3888.4525.84
2.46.767.0328.7286.76
2.67.767.7329.0287.732
2.88.848.4889.3528.488
3109.39.79.3
3.211.2410.16810.07210.072
3.412.5611.09210.46810.468
3.613.9612.07210.88810.888
3.815.4413.10811.33211.332
41714.211.811.8
Sheet1
Sheet2
Sheet3
-
短期の労働需要
• 短期の労働需要量の決定
• 書き直して
© Yukiko Abe 2018 All rights reserved
,max ( )
L ypy wL rK− +
subject to ( , )F K L y≥
max ( , ) ( )L
pF K L wL rK− +
-
利潤最大化の一階条件（短期）
• Ｌで微分してゼロと置くと、短期の最適な労働需要量Ｌ*は以下で表すことができる：
© Yukiko Abe 2018 All rights reserved
*( , ) 0LpF L K w− =
-
操業停止条件
• 以下の比較をし、もし後者のほうが大きければ操業
• その条件は、
• 書き換えて、
© Yukiko Abe 2018 All rights reserved
( 0)rK− <py wL rK− −
0py wL− >
/p wL y>
-
操業停止条件（続き）
• 平均可変費用（労働への費用）が生産物価格を下回れば操業する。
• 同じ条件を書き換えて、
（実質賃金が平均生産性より低い）
© Yukiko Abe 2018 All rights reserved
/p wL y>
/ /y L w p>
-
労働の限界生産性、平均生産性
© Yukiko Abe 2018 All rights reserved
90
92
94
96
98
100
102
104
106
1 2 3 4 5 6 7 8
Ｌ
ＡＰＬ
MPL
MPL, APL
-
労働の限界生産性、平均生産性
© Yukiko Abe 2018 All rights reserved
ＡＰＬ
MPL
90
100
110
0 2 4 6L
APL MPL LD
w/p
-
市場均衡と効率性
• 競争市場均衡は効率的• 労働市場の場合に、この点を確認（余剰分析を用いる）
• 政府の規制や税金がある場合、市場均衡はどのような影響を受けるか？
© Yukiko Abe 2018 All rights reserved
-
© Yukiko Abe 2018 All rights reserved
労働需要と供給、均衡
w
Graph4
0.20.2
0.210.21
0.220.22
0.230.23
0.240.24
0.250.25
0.260.26
0.270.27
0.280.28
0.290.29
0.30.3
0.310.31
0.320.32
0.330.33
0.340.34
0.350.35
0.360.36
0.370.37
0.380.38
0.390.39
0.40.4
0.410.41
0.420.42
0.430.43
0.440.44
0.450.45
0.460.46
0.470.47
0.480.48
0.490.49
0.50.5
0.510.51
0.520.52
0.530.53
0.540.54
0.550.55
0.560.56
0.570.57
0.580.58
0.590.59
0.60.6
0.610.61
0.620.62
0.630.63
0.640.64
0.650.65
0.660.66
0.670.67
0.680.68
0.690.69
0.70.7
0.710.71
0.720.72
0.730.73
0.740.74
0.750.75
0.760.76
0.770.77
0.780.78
0.790.79
0.80.8
0.810.81
0.820.82
0.830.83
0.840.84
0.850.85
0.860.86
0.870.87
0.880.88
0.890.89
0.90.9
0.910.91
0.920.92
0.930.93
0.940.94
0.950.95
0.960.96
0.970.97
0.980.98
0.990.99
11
1.011.01
1.021.02
1.031.03
1.041.04
1.051.05
1.061.06
1.071.07
1.081.08
1.091.09
1.11.1
1.111.11
1.121.12
1.131.13
1.141.14
1.151.15
1.161.16
1.171.17
1.181.18
1.191.19
1.21.2
1.211.21
1.221.22
1.231.23
1.241.24
1.251.25
1.261.26
1.271.27
1.281.28
1.291.29
1.31.3
1.311.31
1.321.32
1.331.33
1.341.34
1.351.35
1.361.36
1.371.37
1.381.38
1.391.39
1.41.4
1.411.41
1.421.42
1.431.43
1.441.44
1.451.45
1.461.46
1.471.47
1.481.48
1.491.49
1.51.5
1.511.51
1.521.52
1.531.53
1.541.54
1.551.55
1.561.56
1.571.57
1.581.58
1.591.59
1.61.6
1.611.61
1.621.62
1.631.63
1.641.64
1.651.65
1.661.66
1.671.67
1.681.68
1.691.69
1.71.7
1.711.71
1.721.72
1.731.73
1.741.74
1.751.75
1.761.76
1.771.77
1.781.78
1.791.79
1.81.8
1.811.81
1.821.82
1.831.83
1.841.84
1.851.85
1.861.86
1.871.87
1.881.88
1.891.89
1.91.9
1.911.91
1.921.92
1.931.93
1.941.94
1.951.95
1.961.96
1.971.97
1.981.98
1.991.99
均衡
需要曲線
供給曲線
需要量、供給量
賃金
需要曲線と供給曲線
5.2
0.9
5.16
0.92
5.12
0.94
5.08
0.96
5.04
0.98
5
1
4.96
1.02
4.92
1.04
4.88
1.06
4.84
1.08
4.8
1.1
4.76
1.12
4.72
1.14
4.68
1.16
4.64
1.18
4.6
1.2
4.56
1.22
4.52
1.24
4.48
1.26
4.44
1.28
4.4
1.3
4.36
1.32
4.32
1.34
4.28
1.36
4.24
1.38
4.2
1.4
4.16
1.42
4.12
1.44
4.08
1.46
4.04
1.48
4
1.5
3.96
1.52
3.92
1.54
3.88
1.56
3.84
1.58
3.8
1.6
3.76
1.62
3.72
1.64
3.68
1.66
3.64
1.68
3.6
1.7
3.56
1.72
3.52
1.74
3.48
1.76
3.44
1.78
3.4
1.8
3.36
1.82
3.32
1.84
3.28
1.86
3.24
1.88
3.2
1.9
3.16
1.92
3.12
1.94
3.08
1.96
3.04
1.98
3
2
2.96
2.02
2.92
2.04
2.88
2.06
2.84
2.08
2.8
2.1
2.76
2.12
2.72
2.14
2.68
2.16
2.64
2.18
2.6
2.2
2.56
2.22
2.52
2.24
2.48
2.26
2.44
2.28
2.4
2.3
2.36
2.32
2.32
2.34
2.28
2.36
2.24
2.38
2.2
2.4
2.16
2.42
2.12
2.44
2.08
2.46
2.04
2.48
2
2.5
1.96
2.52
1.92
2.54
1.88
2.56
1.84
2.58
1.8
2.6
1.76
2.62
1.72
2.64
1.68
2.66
1.64
2.68
1.6
2.7
1.56
2.72
1.52
2.74
1.48
2.76
1.44
2.78
1.4
2.8
1.36
2.82
1.32
2.84
1.28
2.86
1.24
2.88
1.2
2.9
1.16
2.92
1.12
2.94
1.08
2.96
1.04
2.98
1
3
0.96
3.02
0.92
3.04
0.88
3.06
0.84
3.08
0.8
3.1
0.76
3.12
0.72
3.14
0.68
3.16
0.64
3.18
0.6
3.2
0.56
3.22
0.52
3.24
0.48
3.26
0.44
3.28
0.4
3.3
0.36
3.32
0.32
3.34
0.28
3.36
0.24
3.38
0.2
3.4
0.16
3.42
0.12
3.44
0.08
3.46
0.04
3.48
0
3.5
3.52
3.54
3.56
3.58
3.6
3.62
3.64
3.66
3.68
3.7
3.72
3.74
3.76
3.78
3.8
3.82
3.84
3.86
3.88
3.9
3.92
3.94
3.96
3.98
4
4.02
4.04
4.06
4.08
4.1
4.12
4.14
4.16
4.18
4.2
4.22
4.24
4.26
4.28
4.3
4.32
4.34
4.36
4.38
4.4
4.42
4.44
4.46
4.48
供給曲線
0.20.2
0.210.21
0.220.22
0.230.23
0.240.24
0.250.25
0.260.26
0.270.27
0.280.28
0.290.29
0.30.3
0.310.31
0.320.32
0.330.33
0.340.34
0.350.35
0.360.36
0.370.37
0.380.38
0.390.39
0.40.4
0.410.41
0.420.42
0.430.43
0.440.44
0.450.45
0.460.46
0.470.47
0.480.48
0.490.49
0.50.5
0.510.51
0.520.52
0.530.53
0.540.54
0.550.55
0.560.56
0.570.57
0.580.58
0.590.59
0.60.6
0.610.61
0.620.62
0.630.63
0.640.64
0.650.65
0.660.66
0.670.67
0.680.68
0.690.69
0.70.7
0.710.71
0.720.72
0.730.73
0.740.74
0.750.75
0.760.76
0.770.77
0.780.78
0.790.79
0.80.8
0.810.81
0.820.82
0.830.83
0.840.84
0.850.85
0.860.86
0.870.87
0.880.88
0.890.89
0.90.9
0.910.91
0.920.92
0.930.93
0.940.94
0.950.95
0.960.96
0.970.97
0.980.98
0.990.99
11
1.011.01
1.021.02
1.031.03
1.041.04
1.051.05
1.061.06
1.071.07
1.081.08
1.091.09
1.11.1
1.111.11
1.121.12
1.131.13
1.141.14
1.151.15
1.161.16
1.171.17
1.181.18
1.191.19
1.21.2
1.211.21
1.221.22
1.231.23
1.241.24
1.251.25
1.261.26
1.271.27
1.281.28
1.291.29
1.31.3
1.311.31
1.321.32
1.331.33
1.341.34
1.351.35
1.361.36
1.371.37
1.381.38
1.391.39
1.41.4
1.411.41
1.421.42
1.431.43
1.441.44
1.451.45
1.461.46
1.471.47
1.481.48
1.491.49
1.51.5
1.511.51
1.521.52
1.531.53
1.541.54
1.551.55
1.561.56
1.571.57
1.581.58
1.591.59
1.61.6
1.611.61
1.621.62
1.631.63
1.641.64
1.651.65
1.661.66
1.671.67
1.681.68
1.691.69
1.71.7
1.711.71
1.721.72
1.731.73
1.741.74
1.751.75
1.761.76
1.771.77
1.781.78
1.791.79
1.81.8
1.811.81
1.821.82
1.831.83
1.841.84
1.851.85
1.861.86
1.871.87
1.881.88
1.891.89
1.91.9
1.911.91
1.921.92
1.931.93
1.941.94
1.951.95
1.961.96
1.971.97
1.981.98
1.991.99
均衡
需要曲線
供給曲線
需要量、供給量
価格
需要曲線と供給曲線
5.2
0.9
5.16
0.92
5.12
0.94
5.08
0.96
5.04
0.98
5
1
4.96
1.02
4.92
1.04
4.88
1.06
4.84
1.08
4.8
1.1
4.76
1.12
4.72
1.14
4.68
1.16
4.64
1.18
4.6
1.2
4.56
1.22
4.52
1.24
4.48
1.26
4.44
1.28
4.4
1.3
4.36
1.32
4.32
1.34
4.28
1.36
4.24
1.38
4.2
1.4
4.16
1.42
4.12
1.44
4.08
1.46
4.04
1.48
4
1.5
3.96
1.52
3.92
1.54
3.88
1.56
3.84
1.58
3.8
1.6
3.76
1.62
3.72
1.64
3.68
1.66
3.64
1.68
3.6
1.7
3.56
1.72
3.52
1.74
3.48
1.76
3.44
1.78
3.4
1.8
3.36
1.82
3.32
1.84
3.28
1.86
3.24
1.88
3.2
1.9
3.16
1.92
3.12
1.94
3.08
1.96
3.04
1.98
3
2
2.96
2.02
2.92
2.04
2.88
2.06
2.84
2.08
2.8
2.1
2.76
2.12
2.72
2.14
2.68
2.16
2.64
2.18
2.6
2.2
2.56
2.22
2.52
2.24
2.48
2.26
2.44
2.28
2.4
2.3
2.36
2.32
2.32
2.34
2.28
2.36
2.24
2.38
2.2
2.4
2.16
2.42
2.12
2.44
2.08
2.46
2.04
2.48
2
2.5
1.96
2.52
1.92
2.54
1.88
2.56
1.84
2.58
1.8
2.6
1.76
2.62
1.72
2.64
1.68
2.66
1.64
2.68
1.6
2.7
1.56
2.72
1.52
2.74
1.48
2.76
1.44
2.78
1.4
2.8
1.36
2.82
1.32
2.84
1.28
2.86
1.24
2.88
1.2
2.9
1.16
2.92
1.12
2.94
1.08
2.96
1.04
2.98
1
3
0.96
3.02
0.92
3.04
0.88
3.06
0.84
3.08
0.8
3.1
0.76
3.12
0.72
3.14
0.68
3.16
0.64
3.18
0.6
3.2
0.56
3.22
0.52
3.24
0.48
3.26
0.44
3.28
0.4
3.3
0.36
3.32
0.32
3.34
0.28
3.36
0.24
3.38
0.2
3.4
0.16
3.42
0.12
3.44
0.08
3.46
0.04
3.48
0
3.5
3.52
3.54
3.56
3.58
3.6
3.62
3.64
3.66
3.68
3.7
3.72
3.74
3.76
3.78
3.8
3.82
3.84
3.86
3.88
3.9
3.92
3.94
3.96
3.98
4
4.02
4.04
4.06
4.08
4.1
4.12
4.14
4.16
4.18
4.2
4.22
4.24
4.26
4.28
4.3
4.32
4.34
4.36
4.38
4.4
4.42
4.44
4.46
4.48
需要曲線
0.2
0.21
0.22
0.23
0.24
0.25
0.26
0.27
0.28
0.29
0.3
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.4
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.5
0.51
0.52
0.53
0.54
0.55
0.56
0.57
0.58
0.59
0.6
0.61
0.62
0.63
0.64
0.65
0.66
0.67
0.68
0.69
0.7
0.71
0.72
0.73
0.74
0.75
0.76
0.77
0.78
0.79
0.8
0.81
0.82
0.83
0.84
0.85
0.86
0.87
0.88
0.89
0.9
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.1
1.11
1.12
1.13
1.14
1.15
1.16
1.17
1.18
1.19
1.2
1.21
1.22
1.23
1.24
1.25
1.26
1.27
1.28
1.29
1.3
1.31
1.32
1.33
1.34
1.35
1.36
1.37
1.38
1.39
1.4
1.41
1.42
1.43
1.44
1.45
1.46
1.47
1.48
1.49
1.5
1.51
1.52
1.53
1.54
1.55
1.56
1.57
1.58
1.59
1.6
1.61
1.62
1.63
1.64
1.65
1.66
1.67
1.68
1.69
1.7
1.71
1.72
1.73
1.74
1.75
1.76
1.77
1.78
1.79
1.8
1.81
1.82
1.83
1.84
1.85
1.86
1.87
1.88
1.89
1.9
1.91
1.92
1.93
1.94
1.95
1.96
1.97
1.98
1.99
需要曲線
需要量、供給量
価格
5.2
5.16
5.12
5.08
5.04
5
4.96
4.92
4.88
4.84
4.8
4.76
4.72
4.68
4.64
4.6
4.56
4.52
4.48
4.44
4.4
4.36
4.32
4.28
4.24
4.2
4.16
4.12
4.08
4.04
4
3.96
3.92
3.88
3.84
3.8
3.76
3.72
3.68
3.64
3.6
3.56
3.52
3.48
3.44
3.4
3.36
3.32
3.28
3.24
3.2
3.16
3.12
3.08
3.04
3
2.96
2.92
2.88
2.84
2.8
2.76
2.72
2.68
2.64
2.6
2.56
2.52
2.48
2.44
2.4
2.36
2.32
2.28
2.24
2.2
2.16
2.12
2.08
2.04
2
1.96
1.92
1.88
1.84
1.8
1.76
1.72
1.68
1.64
1.6
1.56
1.52
1.48
1.44
1.4
1.36
1.32
1.28
1.24
1.2
1.16
1.12
1.08
1.04
1
0.96
0.92
0.88
0.84
0.8
0.76
0.72
0.68
0.64
0.6
0.56
0.52
0.48
0.44
0.4
0.36
0.32
0.28
0.24
0.2
0.16
0.12
0.08
0.04
0
Graph1
0.20.2
0.210.21
0.220.22
0.230.23
0.240.24
0.250.25
0.260.26
0.270.27
0.280.28
0.290.29
0.30.3
0.310.31
0.320.32
0.330.33
0.340.34
0.350.35
0.360.36
0.370.37
0.380.38
0.390.39
0.40.4
0.410.41
0.420.42
0.430.43
0.440.44
0.450.45
0.460.46
0.470.47
0.480.48
0.490.49
0.50.5
0.510.51
0.520.52
0.530.53
0.540.54
0.550.55
0.560.56
0.570.57
0.580.58
0.590.59
0.60.6
0.610.61
0.620.62
0.630.63
0.640.64
0.650.65
0.660.66
0.670.67
0.680.68
0.690.69
0.70.7
0.710.71
0.720.72
0.730.73
0.740.74
0.750.75
0.760.76
0.770.77
0.780.78
0.790.79
0.80.8
0.810.81
0.820.82
0.830.83
0.840.84
0.850.85
0.860.86
0.870.87
0.880.88
0.890.89
0.90.9
0.910.91
0.920.92
0.930.93
0.940.94
0.950.95
0.960.96
0.970.97
0.980.98
0.990.99
11
1.011.01
1.021.02
1.031.03
1.041.04
1.051.05
1.061.06
1.071.07
1.081.08
1.091.09
1.11.1
1.111.11
1.121.12
1.131.13
1.141.14
1.151.15
1.161.16
1.171.17
1.181.18
1.191.19
1.21.2
1.211.21
1.221.22
1.231.23
1.241.24
1.251.25
1.261.26
1.271.27
1.281.28
1.291.29
1.31.3
1.311.31
1.321.32
1.331.33
1.341.34
1.351.35
1.361.36
1.371.37
1.381.38
1.391.39
1.41.4
1.411.41
1.421.42
1.431.43
1.441.44
1.451.45
1.461.46
1.471.47
1.481.48
1.491.49
1.51.5
1.511.51
1.521.52
1.531.53
1.541.54
1.551.55
1.561.56
1.571.57
1.581.58
1.591.59
1.61.6
1.611.61
1.621.62
1.631.63
1.641.64
1.651.65
1.661.66
1.671.67
1.681.68
1.691.69
1.71.7
1.711.71
1.721.72
1.731.73
1.741.74
1.751.75
1.761.76
1.771.77
1.781.78
1.791.79
1.81.8
1.811.81
1.821.82
1.831.83
1.841.84
1.851.85
1.861.86
1.871.87
1.881.88
1.891.89
1.91.9
1.911.91
1.921.92
1.931.93
1.941.94
1.951.95
1.961.96
1.971.97
1.981.98
1.991.99
均衡
需要曲線
供給曲線
需要量、供給量
価格
需要曲線と供給曲線
5.2
0.9
5.16
0.92
5.12
0.94
5.08
0.96
5.04
0.98
5
1
4.96
1.02
4.92
1.04
4.88
1.06
4.84
1.08
4.8
1.1
4.76
1.12
4.72
1.14
4.68
1.16
4.64
1.18
4.6
1.2
4.56
1.22
4.52
1.24
4.48
1.26
4.44
1.28
4.4
1.3
4.36
1.32
4.32
1.34
4.28
1.36
4.24
1.38
4.2
1.4
4.16
1.42
4.12
1.44
4.08
1.46
4.04
1.48
4
1.5
3.96
1.52
3.92
1.54
3.88
1.56
3.84
1.58
3.8
1.6
3.76
1.62
3.72
1.64
3.68
1.66
3.64
1.68
3.6
1.7
3.56
1.72
3.52
1.74
3.48
1.76
3.44
1.78
3.4
1.8
3.36
1.82
3.32
1.84
3.28
1.86
3.24
1.88
3.2
1.9
3.16
1.92
3.12
1.94
3.08
1.96
3.04
1.98
3
2
2.96
2.02
2.92
2.04
2.88
2.06
2.84
2.08
2.8
2.1
2.76
2.12
2.72
2.14
2.68
2.16
2.64
2.18
2.6
2.2
2.56
2.22
2.52
2.24
2.48
2.26
2.44
2.28
2.4
2.3
2.36
2.32
2.32
2.34
2.28
2.36
2.24
2.38
2.2
2.4
2.16
2.42
2.12
2.44
2.08
2.46
2.04
2.48
2
2.5
1.96
2.52
1.92
2.54
1.88
2.56
1.84
2.58
1.8
2.6
1.76
2.62
1.72
2.64
1.68
2.66
1.64
2.68
1.6
2.7
1.56
2.72
1.52
2.74
1.48
2.76
1.44
2.78
1.4
2.8
1.36
2.82
1.32
2.84
1.28
2.86
1.24
2.88
1.2
2.9
1.16
2.92
1.12
2.94
1.08
2.96
1.04
2.98
1
3
0.96
3.02
0.92
3.04
0.88
3.06
0.84
3.08
0.8
3.1
0.76
3.12
0.72
3.14
0.68
3.16
0.64
3.18
0.6
3.2
0.56
3.22
0.52
3.24
0.48
3.26
0.44
3.28
0.4
3.3
0.36
3.32
0.32
3.34
0.28
3.36
0.24
3.38
0.2
3.4
0.16
3.42
0.12
3.44
0.08
3.46
0.04
3.48
0
3.5
3.52
3.54
3.56
3.58
3.6
3.62
3.64
3.66
3.68
3.7
3.72
3.74
3.76
3.78
3.8
3.82
3.84
3.86
3.88
3.9
3.92
3.94
3.96
3.98
4
4.02
4.04
4.06
4.08
4.1
4.12
4.14
4.16
4.18
4.2
4.22
4.24
4.26
4.28
4.3
4.32
4.34
4.36
4.38
4.4
4.42
4.44
4.46
4.48
補助線2
5.9605.960
5.920.025.920.02
5.880.045.880.04
5.840.065.840.06
5.80.085.80.08
5.760.15.760.1
5.720.125.720.12
5.680.145.680.14
5.640.165.640.16
5.60.185.60.18
5.560.25.560.2
5.520.225.520.22
5.480.245.480.24
5.440.265.440.26
5.40.285.40.28
5.360.35.360.3
5.320.325.320.32
5.280.345.280.34
5.240.365.240.36
5.20.385.20.38
5.160.45.160.4
5.120.425.120.42
5.080.445.080.44
5.040.465.040.46
50.4850.48
4.960.54.960.5
4.920.524.920.52
4.880.544.880.54
4.840.564.840.56
4.80.584.80.58
4.760.64.760.6
4.720.624.720.62
4.680.644.680.64
4.640.664.640.66
4.60.684.60.68
4.560.74.560.7
4.520.724.520.72
4.480.744.480.74
4.440.764.440.76
4.40.784.40.78
4.360.84.360.8
4.320.824.320.82
4.280.844.280.84
4.240.864.240.86
4.20.884.20.88
4.160.94.160.9
4.120.924.120.92
4.080.944.080.94
4.040.964.040.96
40.9840.98
3.9613.961
3.921.023.921.02
3.881.043.881.04
3.841.063.841.06
3.81.083.81.08
3.761.13.761.1
3.721.123.721.12
3.681.143.681.14
3.641.163.641.16
3.61.183.61.18
3.561.23.561.2
3.521.223.521.22
3.481.243.481.24
3.441.263.441.26
3.41.283.41.28
3.361.33.361.3
3.321.323.321.32
3.281.343.281.34
3.241.363.241.36
3.21.383.21.38
3.161.43.161.4
3.121.423.121.42
3.081.443.081.44
3.041.463.041.46
31.4831.48
2.961.52.961.5
2.921.522.921.52
2.881.542.881.54
2.841.562.841.56
2.81.582.81.58
2.761.62.761.6
2.721.622.721.62
2.681.642.681.64
2.641.662.641.66
2.61.682.61.68
2.561.72.561.7
2.521.722.521.72
2.481.742.481.74
2.441.762.441.76
2.41.782.41.78
2.361.82.361.8
2.321.822.321.82
2.281.842.281.84
2.241.862.241.86
2.21.882.21.88
2.161.92.161.9
2.121.922.121.92
2.081.942.081.94
2.041.962.041.96
21.9821.98
1.9621.962
1.922.021.922.02
1.882.041.882.04
1.842.061.842.06
1.82.081.82.08
1.762.11.762.1
1.722.121.722.12
1.682.141.682.14
1.642.161.642.16
1.62.181.62.18
1.562.21.562.2
1.522.221.522.22
1.482.241.482.24
1.442.261.442.26
1.42.281.42.28
1.362.31.362.3
1.322.321.322.32
1.282.341.282.34
1.242.361.242.36
1.22.381.22.38
1.162.41.162.4
1.122.421.122.42
1.082.441.082.44
1.042.461.042.46
12.4812.48
0.962.50.962.5
0.922.520.922.52
0.882.540.882.54
0.842.560.842.56
0.82.580.82.58
0.762.60.762.6
0.722.620.722.62
0.682.640.682.64
0.642.660.642.66
0.62.680.62.68
0.562.70.562.7
0.522.720.522.72
0.482.740.482.74
0.442.760.442.76
0.42.780.42.78
0.362.80.362.8
0.322.820.322.82
0.282.840.282.84
0.242.860.242.86
0.22.880.22.88
0.162.90.162.9
0.122.920.12
0.082.940.08
0.042.960.04
02.980
3
3.02
3.04
3.06
3.08
3.1
3.12
3.14
3.16
3.18
3.2
3.22
3.24
3.26
3.28
3.3
3.32
3.34
3.36
3.38
3.4
3.42
3.44
3.46
3.48
供給曲線の補助線
需要曲線の補助線
供給曲線
需要曲線
需要曲線
供給曲線
需要曲線補助線
供給曲線補助線
数量
価格
2本の補助線を引く場合
0.01
0.25
0.0090909091
0.2777777778
0.02
0.26
0.0181818182
0.2888888889
0.03
0.27
0.0272727273
0.3
0.04
0.28
0.0363636364
0.3111111111
0.05
0.29
0.0454545455
0.3222222222
0.06
0.3
0.0545454545
0.3333333333
0.07
0.31
0.0636363636
0.3444444444
0.08
0.32
0.0727272727
0.3555555556
0.09
0.33
0.0818181818
0.3666666667
0.1
0.34
0.0909090909
0.3777777778
0.11
0.35
0.1
0.3888888889
0.12
0.36
0.1090909091
0.4
0.13
0.37
0.1181818182
0.4111111111
0.14
0.38
0.1272727273
0.4222222222
0.15
0.39
0.1363636364
0.4333333333
0.16
0.4
0.1454545455
0.4444444444
0.17
0.41
0.1545454545
0.4555555556
0.18
0.42
0.1636363636
0.4666666667
0.19
0.43
0.1727272727
0.4777777778
0.2
0.44
0.1818181818
0.4888888889
0.21
0.45
0.1909090909
0.5
0.22
0.46
0.2
0.5111111111
0.23
0.47
0.2090909091
0.5222222222
0.24
0.48
0.2181818182
0.5333333333
0.25
0.49
0.2272727273
0.5444444444
0.26
0.5
0.2363636364
0.5555555556
0.27
0.51
0.2454545455
0.5666666667
0.28
0.52
0.2545454545
0.5777777778
0.29
0.53
0.2636363636
0.5888888889
0.3
0.54
0.2727272727
0.6
0.31
0.55
0.2818181818
0.6111111111
0.32
0.56
0.2909090909
0.6222222222
0.33
0.57
0.3
0.6333333333
0.34
0.58
0.3090909091
0.6444444444
0.35
0.59
0.3181818182
0.6555555556
0.36
0.6
0.3272727273
0.6666666667
0.37
0.61
0.3363636364
0.6777777778
0.38
0.62
0.3454545455
0.6888888889
0.39
0.63
0.3545454545
0.7
0.4
0.64
0.3636363636
0.7111111111
0.41
0.65
0.3727272727
0.7222222222
0.42
0.66
0.3818181818
0.7333333333
0.43
0.67
0.3909090909
0.7444444444
0.44
0.68
0.4
0.7555555556
0.45
0.69
0.4090909091
0.7666666667
0.46
0.7
0.4181818182
0.7777777778
0.47
0.71
0.4272727273
0.7888888889
0.48
0.72
0.4363636364
0.8
0.49
0.73
0.4454545455
0.8111111111
0.5
0.74
0.4545454545
0.8222222222
0.51
0.75
0.4636363636
0.8333333333
0.52
0.76
0.4727272727
0.8444444444
0.53
0.77
0.4818181818
0.8555555556
0.54
0.78
0.4909090909
0.8666666667
0.55
0.79
0.5
0.8777777778
0.56
0.8
0.5090909091
0.8888888889
0.57
0.81
0.5181818182
0.9
0.58
0.82
0.5272727273
0.9111111111
0.59
0.83
0.5363636364
0.9222222222
0.6
0.84
0.5454545455
0.9333333333
0.61
0.85
0.5545454545
0.9444444444
0.62
0.86
0.5636363636
0.9555555556
0.63
0.87
0.5727272727
0.9666666667
0.64
0.88
0.5818181818
0.9777777778
0.65
0.89
0.5909090909
0.9888888889
0.66
0.9
0.6
1
0.67
0.91
0.6090909091
1.0111111111
0.68
0.92
0.6181818182
1.0222222222
0.69
0.93
0.6272727273
1.0333333333
0.7
0.94
0.6363636364
1.0444444444
0.71
0.95
0.6454545455
1.0555555556
0.72
0.96
0.6545454545
1.0666666667
0.73
0.97
0.6636363636
1.0777777778
0.74
0.98
0.6727272727
1.0888888889
0.75
0.99
0.6818181818
1.1
0.76
1
0.6909090909
1.1111111111
0.77
1.01
0.7
1.1222222222
0.78
1.02
0.7090909091
1.1333333333
0.79
1.03
0.7181818182
1.1444444444
0.8
1.04
0.7272727273
1.1555555556
0.81
1.05
0.7363636364
1.1666666667
0.82
1.06
0.7454545455
1.1777777778
0.83
1.07
0.7545454545
1.1888888889
0.84
1.08
0.7636363636
1.2
0.85
1.09
0.7727272727
1.2111111111
0.86
1.1
0.7818181818
1.2222222222
0.87
1.11
0.7909090909
1.2333333333
0.88
1.12
0.8
1.2444444444
0.89
1.13
0.8090909091
1.2555555556
0.9
1.14
0.8181818182
1.2666666667
0.91
1.15
0.8272727273
1.2777777778
0.92
1.16
0.8363636364
1.2888888889
0.93
1.17
0.8454545455
1.3
0.94
1.18
0.8545454545
1.3111111111
0.95
1.19
0.8636363636
1.3222222222
0.96
1.2
0.8727272727
1.3333333333
0.97
1.21
0.8818181818
1.3444444444
0.98
1.22
0.8909090909
1.3555555556
0.99
1.23
0.9
1.3666666667
1
1.24
0.9090909091
1.3777777778
1.01
1.25
0.9181818182
1.3888888889
1.02
1.26
0.9272727273
1.4
1.03
1.27
0.9363636364
1.4111111111
1.04
1.28
0.9454545455
1.4222222222
1.05
1.29
0.9545454545
1.4333333333
1.06
1.3
0.9636363636
1.4444444444
1.07
1.31
0.9727272727
1.4555555556
1.08
1.32
0.9818181818
1.4666666667
1.09
1.33
0.9909090909
1.4777777778
1.1
1.34
1
1.4888888889
1.11
1.35
1.0090909091
1.5
1.12
1.36
1.0181818182
1.5111111111
1.13
1.37
1.0272727273
1.5222222222
1.14
1.38
1.0363636364
1.5333333333
1.15
1.39
1.0454545455
1.5444444444
1.16
1.4
1.0545454545
1.5555555556
1.17
1.41
1.0636363636
1.5666666667
1.18
1.42
1.0727272727
1.5777777778
1.19
1.43
1.0818181818
1.5888888889
1.2
