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2015 〈商品不可分割性與最適所得稅〉，《經濟論文叢刊》，即將出版。(Lu, Chun-hui and K. L. Glen Ueng, 2015, “Consumption Indivisibility and Optimal Income Taxation,” Tai-wan Economic Review (forthcoming).)
顏志達
2009 〈員工分紅與最適所得稅〉，國立政治大學財政學系博士論文。(Yen, Chih-ta, 2009,
“Pay for Performance and Optimal Income Taxation,” Ph.D. Dissertation, Department of Public Finance, National Chengchi University.)
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數學附錄1：
將（ 13 ）、（ 14 ）兩不等式左右兩邊相加並進一步整理為如下：
1 β~H2(ωH2−ωL2)≥ 1 β~L2(ωH2−ωL2). （ A1 ）
2 2
將不等式兩邊同時消去 12(ωH2−ωL2)可得：
β~H2≥ β~L2, （ A2 ） (β~H+ β~L)(β~H− β~L)≥0. （ A3 ）
即為所求。 □
數學附錄2：
當（ 13 ）、（ 14 ）兩式的等號皆成立時，即 VHH=VHL、VLL=VLH，將此二等式左右 兩邊相加如下：
VHH+VLL=VHL+VLH, （ A4 ）
整理可得：
β~H2(ωH2−ωL2)= β~L2(ωH2−ωL2), （ A5 ） β~H= β~L. （ A6 ） 則此時TH+α~H=TL+α~L，因而兩類型的人將混合在一起，這表示工資契約為
混合工資契約，而非分離均衡。 □
數學附錄3：
當勞動市場中雇主與員工間為訊息充分，但是存在道德冒險的問題時，
政府的最適租稅政策問題如下：
SWF=λU(VHc)+(1−λ)U(VLc), （ A7 ）
{TH, TmaxL, tH, tL}
s.t. λtHE(yHc)+(1−λ)tLE(yLc)=−λTH−(1−λ)TL=0, （ A8 ）
其中，（ A8 ）式為政府的預算限制式；Vic=Ti+(1−ti)2 ωi4
2(ωi2+rσ2)、E(yic)= β~icωi2= (1−ti) ωi4
2(ωi2+rσ2) , i=H, L。為求解上述問題，建立政府決策問題的拉氏函數 如下：
Γ=λU(VHc)+(1−λ)U(VLc)+ϕ[λtHE(yHc)+(1−λ)tLE(yLc)−λTH−(1−λ)TL], （ A9 ）
其中，ϕ 為拉氏乘數。求解其一階條件如下：
∂Γ =λU′(VHc)−ϕλ=0, （ A10 ）
∂TH
∂Γ =(1−λ)U′(VLc)−ϕ(1−λ)=0, （ A11 ）
∂TL
∂Γ =−λU′(VHc) (1−tH)ωH4
+ϕλ (1−2tH)ωH4
=0, （ A12 ）
∂tH (ωH2+rσ2) (ωH2+rσ2)
∂Γ =−(1−λ)U′(VLc) (1−tL)ωL4
+ϕ(1−λ) (1−2tL)ωL4
=0. （ A13 ）
∂tL (ωL2+rσ2) (ωL2+rσ2)
由（ A10 ）、（ A11 ）兩式可知：
ϕ=U′(VHc)=U′(VLc), （ A14 ） 將此一結果分別代入（ A12 ）、（ A13 ）兩式整理可得 tH=tL=0。 □