Workforce or Workfare?

Appendix

Proof of Proposition 1. As in Diamond (1980), the Lagrangian associated with the opti-
mal tax problem is

L(c(n), b, λ; r) =

The first-order condition with respect to c (n) yields:

Using (5) and (6), and dividing both sides by F(m*,n), (A.2) can be rewritten as

1 „М -WW^dm* ⁽c^{(n) ,b,r}) ^f (^m*^,n)

^{1 - g(n)} = ^{τ (n)}      ■         Fm ■

From (A.3) we see that τ(n) takes the sign of 1 - g(n) as stated in Proposition 1.

The first-order condition with respect to r is

≤0 ≤ 0, r ≥ 0 and r-τf- = 0.
∂r                ∂r

Differentiating (A.1) yields:

By the Envelope Theorem, (A.5) provides the dW/dr that we display in (8).

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