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1 ,, 43 ( ) ( ) sasaki@econ.kyoto-u.ac.jp 1 / 39
2 1. 2. (Rowthorn, 2014) / 39 1
3 ( 1). ( 2). = g. r. r > g ( 3).. 3 / 39 2
4 50% Figure I.1. Income inequality in the United States, Share of top decile in national income 45% 40% 35% 30% 25% The top decile share in U.S. national income dropped from 45-50% in the 1910s-1920s to less than 35% in the 1950s (this is the fall documented by Kuznets); it then rose from less than 35% in the 1970s to 45-50% in the 2000s-2010s. Sources and series: see piketty.pse.ens.fr/capital21c. 4 / 39
5 800% Figure I.2. The capital/income ratio in Europe, vate capital (% national income) 700% 600% 500% 400% Germany France United Kingdom Market value of pri 300% 200% 100% Aggregate private wealth was worth about 6-7 years of national income in Europe in 1910, between 2 and 3 years in 1950, and between 4 and 6 years in Sources and series: see piketty.pse.ens.fr/capital21c. 5 / 39
6 6% Figure Rate of return vs. growth rate at the world level, from Antiquity until 2100 rate of return or rate of growth Annual 5% 4% 3% 2% Pure rate of return to capital r (pre-tax) Growth rate of world output g 1% 0% The rate of return to capital (pre-tax) has always been higher than the world growth rate, but the gap was reduced during the 20th century, and might widen again in the 21st century. Sources and series: see piketty.pse.ens.fr/capital21c 6 / 39
7 国民所得 賃金 利潤 賃金 利潤 資本分配率 = 利潤 国民所得 の上昇 7 / 39
8 2. (Rowthorn, 2014) β: (K/Y) ( 2). α: (rk/y). β α ( 4)., σ 1, β α., α β, σ / 39 3
9 40% Figure 6.5. The capital share in rich countries, % al income (% national income) Capit 30% 25% 20% U.S. Germany Japan France 15% U.K. Italy Canada Australia 10% Capital income absorbs between 15% and 25% of national income in rich countries in 1970, and between 25% and 30% in Sources and series: see piketty.pse.ens.fr/capital21c 9 / 39
10 . Y = [δk σ 1 σ + (1 δ)e σ 1 σ ] σ σ 1. (1) Y:, K:, E:, σ:, δ:. r, α g α. g α = ( ) σ 1 g K/Y. (2) σ, g K/Y. σ > 1, g α g K/Y. 10 / 39 4
11 理論的には? 資本所得比率の上昇 かつ 1 より大きい代替の弾力性 資本分配率の上昇 資本所得比率の低下 かつ 1 より小さい代替の弾力性 資本分配率の上昇 11 / 39
12 , K/Y, W/Y., β = W Y = vk Y, v W K. (3), v ( Q ). β. g β = g K/Y + g v. (4) g v = 0, g β = g K/Y. 12 / 39 5
13 , K/Y, ( 5)., g v > 0 ( 6)., g K/Y 0 g v > 0, g v > g K/Y, g β > 0., σ 1, g α > 0. σ < / 39 6
14 500% Figure A133: Simulated private wealth / national income ratios in the absence of capital gains, % 400% 350% 300% 250% 200% USA Europe (weighted) 150% 100% / 39
15 160% Figure 5.6. Market value and book value of corporations Ratio between marke et value and book value of corporations 140% U.S. Japan 120% Germany France 100% U.K. Canada 80% 60% 40% 20% 0% Tobin's Q (i.e. the ratio between market value and book value of corporations) has risen in rich countries since the 1970s-1980s. Sources and series: see piketty.pse.ens.fr/capital21c. 15 / 39
16 , g β > 0 g β = g K/Y > 0 g α > 0 with σ > 1. (5), g β > 0 g β = g K/Y /0 + g v + > 0 g α > 0 with σ < 1. (6), g α > 0,,. 16 / 39 7
17 ピケティの観察した事実 資産 所得比率の上昇 ピケティの解釈 1 資本 所得比率の上昇 21 より大きい代替の弾力性 3 評価比率は一定 より正しい解釈 1 資本 所得比率の低下 21 より小さい代替の弾力性 いずれにしても資本分配率は上昇 3 評価比率の上昇 17 / 39
18 3...,,.,,.,,.,. 18 / 39 8
19 生産関数が CES 型のとき因果関係あり 新古典派成長モデルにおける因果関係 生産関数がコブ = ダグラス型だと因果関係なし 経済成長 所得分配 古典派成長モデルとカレツキ派成長モデルにおける因果関係 所得分配 経済成長 19 / 39
20 4. ( ),,,.. Y = min{ae, bk}. (7), a = Y/E, b = Y/K.. w:, r:. Y = we + rk. (8) 20 / 39 9
21 α. α = rk Y = Y we Y = 1 w a. (9), w a,,.. r = Y we K = ( 1 w ) b = αb. (10) a,. 21 / 39 10
22 : s c.,. S = s c rk, 0 < s c < 1. (11) S = I.,. g s c r = s c bα. (12) 22 / 39 11
23 ,., ( ).,. (= ) 23 / 39 12
24 : s w. S = s w we + s c rk, 0 < s w < 1. (13). g = [s w (1 α) + s c α]b. (14) 24 / 39 13
25 . dg dα = b(s c s w ). (15) s c > s w,. s c = s w,. 25 / 39 14
26 s w s c Table 1: (Storm and Naastepad, 2012) 26 / 39 15
27 5. ( ),,,.. Y = min{ae, ubk}, (16) = min{ae, uk}. (17) : b = Y /K = 1. u = Y/Y = Y/K:. r = Y we K = u ( 1 w ) a = αu. (18) 27 / 39 16
28 . p = (1 + µ) ω a. (19) µ:, ω: (ω = pw).,,, 1 α = w a = µ. (20) α = 1 w a = µ = µ 1 + µ. (21) 28 / 39 17
29 . g d = γ + ϕu, γ > 0, ϕ > 0. (22).. g s = s c r = s c αu. (23).. g d = g s = γ + ϕu = s c αu. (24) 29 / 39 18
30 . u = g = γ s c α ϕ, (25) γs cα s c α ϕ (26) α,.,. ( ) ( ) 30 / 39 19
31 s w. g s = [s w (1 α) + s c α]u (27), u = g = γ [s w (1 α) + s c α] ϕ, (28) [s w(1 α) + s c α]γ [s w (1 α) + s c α] ϕ. (29) 31 / 39 20
32 s c > s w,. s c = s w = s, u = g = γ s ϕ, (30) sγ s ϕ. (31) α. 32 / 39 21
33 . g d = γ + ϕu + ψα, γ > 0, ϕ > 0, ψ > 0. (32),,,.,. 33 / 39 22
34 古典派とカレツキ派の違い 古典派 資本分配率の上昇 経済成長率の上昇 カレツキ派 資本分配率の上昇 経済成長率の低下 あるいは 経済成長率の上昇 34 / 39
35 .,,.,,,.,. α = 1 w a. (33) w, a, α. 35 / 39 23
36 36 / 39 24
37 労使交渉 国際価格競争 市場占有度 金融政策 経済成長 所得分配率 経済成長 フィードバック効果 37 / 39
38 / 39 25
39 7. (2014) 21,. Rowthorn, R. (2014) A Note on Piketty s Capital in the Twenty-First Century, Cambridge Journal of Economics 38, pp Sasaki, H. (2014) Growth, Cycles, and Distribution: Approach, Kyoto: Kyoto University Press. A Kaleckian Storm, S. and Naastepad, C. W. M. (2012) Macroeconomics Beyond the NAIRU, Cambridge MA: Harvard Univeristy Press. 39 / 39 26
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