Contenu connexe Similaire à ゲーム理論BASIC 演習68 -最適賃金設定2- (10) Plus de ssusere0a682 (20) ゲーム理論BASIC 演習68 -最適賃金設定2-3.
༻ޏओ ਓͷ࿑ಇऀͱܖΛ͠ ͋ΔλεΫͷ࣮ߦΛߟ͍͑ͯΔ
λεΫͷޭ֬ ࿑ಇऀ͕ྗͨ͠߹ Ͱ ྗ͠ͳ͍߹ Ͱ͋Δͱ͢Δ
ྗͨ͠߹ʹ ͷίετ͕࿑ಇऀʹ͔͔Δͱ͢Δ
λεΫ͕ޭͨ͠ͱ͖ ༻ޏओ ͷརӹΛಘͯ ࿑ಇऀۚ ΛಘΔࣦഊͷ߹ʹ͍ޓԿಘͳ͍ͱ͢Δ
·ͨ ͦͦܖΛ݁ͳ͍߹ʹ͍ޓԿಘͳ͍ͱ͢Δ
༻ޏओಘΒΕΔརӹʹରͯ͠ ϦεΫதཱతͳޮ༻ؔ Λͪ
࿑ಇऀใुʹରͯ͠ ϦεΫճආతͳޮ༻ؔ ΛͭͱԾఆ͢Δ
DG#4*$ԋशͰͲͪΒϦεΫதཱతͳޮ༻ؔΛͭͱԾఆͨ͠
ྗ͢Δ͜ͱΛ͖Ͱ੍ڧΔ߹ͷ࠷దͳۚ ΛٻΊΑ
ࢀՃ੍ͷΈߟ͑ͨ࠷దԽΛղ͚ྑ͍
ྗ͢Δ͜ͱΛ͍ͳ͖Ͱ੍ڧ߹ͷ࠷దͳۚ ΛٻΊΑ
ࢀՃ੍͓Αͼ༠Ҿཱ྆ੑ݅ ࿑ಇऀʹͱͬͯྗ͢Δํ͕ ྗ͠ͳ͍ΑΓಘ͢ΔͨΊͷ݅
Λߟ͑ͯ ࠷దԽΛղ͚ྑ͍ˎྗͤͨ͞ํ͕༻ޏओʹͱͬͯಘͰ͋Δͱͯ͠ྑ͍
#4*$ԋशࢀর
1
3
1
16
c 0
R 0 w
u(x) = x
u(x) = x
wF
wS
ेେ͖ͳ
R 0
4. ղ
λεΫͷޭ֬ ࿑ಇऀ͕ྗͨ͠߹ Ͱ ྗ͠ͳ͍߹ Ͱ͋Δͱ͢Δ
ྗͨ͠߹ʹ ͷίετ͕࿑ಇऀʹ͔͔Δͱ͢Δ
λεΫ͕ޭͨ͠ͱ͖ ༻ޏओ ͷརӹΛಘͯ ࿑ಇऀۚ ΛಘΔࣦഊͷ߹ʹ͍ޓԿಘͳ͍ͱ͢Δ
·ͨ ͦͦܖΛ݁ͳ͍߹ʹ͍ޓԿಘͳ͍ͱ͢Δ
༻ޏओಘΒΕΔརӹʹରͯ͠ ϦεΫதཱతͳޮ༻ؔ Λͪ
࿑ಇऀใुʹରͯ͠ ϦεΫճආతͳޮ༻ؔ ΛͭͱԾఆ͢Δ
ྗ͢Δ͜ͱΛ͖Ͱ੍ڧΔ߹ͷ࠷దͳۚ ΛٻΊΑࢀՃ੍ͷΈߟ͑ͨ࠷దԽΛղ͚ྑ͍
TU
੍݅ ΑΓ
త͕ؔ࠷େͱͳΔͷ
Ώ͑ʹ࠷దͳۚ ͱͳΔ
1
3
1
16
c 0
R 0 w
u(x) = x
u(x) = x
wF
max
w
1
3
(R − w)
1
3
( w − c) +
2
3
(0 − c) ≥ 0
1
3
( w − c) +
2
3
(0 − c) ≥ 0 ⇒ w ≥ 9c2
w = 9c2
wF
= 9c2
w ࢀՃ
ڋ൱
ྗ͢Δ
ྗ͠ͳ͍
ޭ
ࣦഊ
ޭ
ࣦഊ
༻ޏओ ࿑ಇऀ
ࣗવ
R − w w − c
D
ڋ൱
ڋ൱
5. ղ
λεΫͷޭ֬࿑ಇऀ͕ྗͨ͠߹ Ͱ ྗ͠ͳ͍߹ Ͱ͋Δͱ͢Δ
ྗͨ͠߹ʹ ͷίετ͕࿑ಇऀʹ͔͔Δͱ͢Δ
λεΫ͕ޭͨ͠ͱ͖ ༻ޏओ ͷརӹΛಘͯ ࿑ಇऀۚ ΛಘΔࣦഊͷ߹ʹ͍ޓԿಘͳ͍ͱ͢Δ
༻ޏओಘΒΕΔརӹʹରͯ͠ ϦεΫதཱతͳޮ༻ؔ Λͪ ࿑ಇऀใुʹରͯ͠ ϦεΫճආతͳޮ༻ؔ ΛͭͱԾఆ͢Δ
ྗ͢Δ͜ͱΛ͍ͳ͖Ͱ੍ڧ߹ͷ࠷దͳۚ ΛٻΊΑ
TU
੍݅ ͔ͭ
త͕ؔ࠷େͱͳΔͷ
Ώ͑ʹ࠷దͳۚ ͱͳΔ
1
3
1
16
c 0
R 0 w
u(x) = x u(x) = x
wS
max
w
1
3
(R − w)
1
3
( w − c) +
2
3
(−c) ≥ 0
1
3
( w − c) +
2
3
(−c) ≥
1
16
w +
15
16
0
1
3
( w − c) +
2
3
(0 − c) ≥ 0 ⇒ w ≥ (3c)2
1
3
( w − c) +
2
3
(−c) ≥
1
16
w +
15
16
0 ⇒ w ≥
(
48
13
c
)
2
w =
(
48
13
c
)
2
wS
=
(
48
13
c
)
2
( (3c)2
= wF
)
w ࢀՃ
ڋ൱
ྗ͢Δ
ྗ͠ͳ͍
ޭ
ࣦഊ
ޭ
ࣦഊ
༻ޏओ ࿑ಇऀ
ࣗવ
R − w w − c
D
R − w w
༠Ҿཱ྆ੑ݅
༠Ҿཱ྆ੑ݅ͷͱͰ
ྗ͢ΔΛબͤΔ࣌ͷظརಘ
6. ߟ
࿑ಇऀ͕ϦεΫճආత ༻ޏओ͕ϦεΫதཱతͷ߹
࿑ಇऀͷظޮ༻
ϑΝʔετϕετͷ߹
ηΧϯυϕετͷ߹
༻ޏओͷظޮ༻
ϑΝʔετϕετͷ߹
ϑΝʔετϕετͷ߹
wF
= (3c)2
wS
=
(
48
13
c
)
2
1
3
( (3c)2
− c) +
2
3
(−c) = 0
1
3
(
(
48
13
c
)
2
− c) +
2
3
(−c) =
3
13
c
1
3
(R − (3c)2
)
1
3(
R−
(
48
13
c
)
2
)
ͲͪΒϦεΫதཱతͳ߹DG#4*$ԋश
࿑ಇऀͷظޮ༻
ϑΝʔετϕετͷ߹
ηΧϯυϕετͷ߹
༻ޏओͷظޮ༻
ϑΝʔετϕετͷ߹
ϑΝʔετϕετͷ߹
wF
= 3c wS
=
48
13
c
1
3
(3c − c) +
2
3
(−c) = 0
1
3
(
48
13
c − c) +
2
3
(−c) =
3
13
c
1
3
(R − 3c)
1
3(
R −
48
13
c
)
͕ेେ͖͍ͱ͢Ε ༻ޏओͷෛ୲͕େ͖͘ͳΔ
ϦεΫΛऔΓͨ͘ͳ͍࿑ಇऀʹ ྗΠϯηϯςΟϒΛ༩͑ΔͨΊʹϦεΫΛෛΘͤΔඞཁ͕͋Γ
ϦεΫΛෛΘͤΔ͚ͩՃඅ༻͕͔͔Δ
c