The name is absent

αu⁰

w (r (α, τ) + τ) + r (α, τ) k) - (α +

δ) u⁰ (—
α

+ r (α, τ

) k)

=0,

(A.14)

α²g⁰ (α)(1+δ)+α²

μ τk

α

+ r (α, τ

) k)

- u (w (r (α, τ) + τ) + r (α, τ) k)

- (α + δ) τku⁰

μ τk

α

+ r (α, τ

) k)

=0,

(A.15)

where the derivatives of the function r (α, τ) are given by (2.13) and (2.14). Taking
total differentials of (A.14) and (A.15), evaluating the derivatives in an initial
equilibrium where δ =0(so that W = w, u_g = u_p and u⁰_g = u⁰_p initially), and
defining b ≡ -τk⁰∕k, we get (using (2.13) and (2.14) with n = 1 plus the facts
that τk = αw and g⁰ = u⁰w in the initial undistorted equilibrium):

^wu" [¹ + * ( T=S Γ
.«/ - ^wu⁰ ( 1⅛)2 + w⅛⁰ £1 + = (ɪ)]

-ku⁰⁰       dα

- wu⁰⁰k (1 - α)   ^dτ

u⁰ ∙ dδ

wu⁰ (1 - α) ∙ dδ

Applying Cramer’s rule to this system, we find that

∂α

Ы =0,
∂δ

(A.16)

∂τ = - (    )2 - αu⁰ .. + w²u⁰⁰) > 0

∂δ       u⁰⁰k £a (g⁰⁰ + w²u⁰⁰) - ^g0]

(A.17)

Thus the introduction of a small political distortion will drive up the tax rate but
leave public sector employment unchanged, as reported in section 3.1.

¹⁹A detailed derivation of (3.1) and (3.2) from (A.11) through (A.13) is provided in a supple-
mentary appendix available from the authors.

34