Passing the burden: corporate tax incidence in open economies

Appendix A: Derivation of Mathematical Results

Three-Level Nested CES Production Function

Production function with 4 inputs:

в-

Y

b [aK^θ + (1 - a)L ]^θ + (1 - b)L^γ

+ (1 - c ) L^β_i >

Marginal productivity of labor skill-level 1:

∂ Q               _β1Γ O              л

— = (1 - a)bcL [ aK^θ + (1 - a)Lθ ] )

∂L

1

Y

b [ aK^θ + (1 - a ) L^θ_ι ]^θ

+ (1 - b ) l^y2

/

b [ aK^θ + (1 - a ) Lθ ]^θ + (1 - b ) L^Y2

У

+ (1 - c ) I

Marginal productivity of labor skill-level 2:

-^dQ- = (1 - b ) cL2Y ¹)

^dL 2

(1-в )

β

L

b [ aK^θ + (1 - a ) L^θθ ] ° + (1 - b ) L2

L

b [ aK^θ + (1 - a ) L^θ_i ]" + (1 - b ) L2

Marginal productivity of labor skill-level 3:

— = (1 - c ) L^-1)
∂L 3

(1-в )
в

+ (1 - c ) L^β₃ ^

c b [ aK^θ + (1 - a ) L^θθ ] ° + (1 - b ) L^y₂

(1-в )

в 1“

^Y + (1 - c ) /'■