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Evaluation of the Australian Wage Subsidy Special Youth ...

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15<br />

Real wages are predetermined when firms consider employment. Incumbents get <strong>the</strong><br />

market wage w*. Entrants Le have no market power and no disutility <strong>of</strong> work, so <strong>the</strong><br />

wage received is equal to <strong>the</strong> exogenous unemployment benefit level (b). The subsidy<br />

amount (v) means <strong>the</strong> firms pay <strong>the</strong> entrant (b-v). The difference in marginal revenue and<br />

marginal costs for zero time discount factor is<br />

(9) (a-cL-w*) / σ<br />

The entrants are hired until <strong>the</strong> present value <strong>of</strong> <strong>the</strong> difference is zero<br />

(10) [(a-cL) – b +v] +(1-σ) (a-cL-w*) / σ = 0<br />

The incumbents’ market wage w* is set to <strong>the</strong> present value <strong>of</strong> <strong>the</strong>ir difference in<br />

marginal revenue and marginal costs plus <strong>the</strong> positive constant firing cost (f):<br />

(11) (a-cL-w*) / σ = - f<br />

The equilibrium level <strong>of</strong> employment is <strong>the</strong>n<br />

(12) L* = (1/c)(a-b+ v- (1-σ) f )<br />

The subsidy constraint is <strong>the</strong>n introduced to close <strong>the</strong> model, and it ensures that <strong>the</strong> value<br />

<strong>of</strong> <strong>the</strong> subsidy (v L* e ) is no greater than <strong>the</strong> saving on unemployment benefits, which are<br />

a function <strong>of</strong> <strong>the</strong> change in employment due to <strong>the</strong> subsidy (b∆L ) where ∆L is <strong>the</strong><br />

difference in equilibrium employment without <strong>the</strong> voucher L - and with <strong>the</strong> voucher L*<br />

( b∆L=L*- L - ):<br />

(13) subsidy constraint v L* e = vσL* ≤ b∆L<br />

Figure 1.2 shows <strong>the</strong> Snower (1994) subsidy constraint with <strong>the</strong> curve representing<br />

equilibrium employment (LE), in a model <strong>of</strong> <strong>the</strong> subsidy v and employment L. The<br />

employment gain <strong>of</strong> <strong>the</strong> subsidy (∆L) is maximized at v*, where L - < b/ c σ , that is<br />

where <strong>the</strong> subsidy constraint curve is steeper than equilibrium employment (LE).<br />

The (1994) model is <strong>the</strong>n expanded to incorporate deadweight and displacement effects,<br />

<strong>the</strong> replacement ratio <strong>of</strong> benefits to <strong>the</strong> average wage, and subsidies are restricted to <strong>the</strong><br />

long-term unemployed. There is <strong>the</strong>n a new subsidy constraint that only a fraction <strong>of</strong> <strong>the</strong><br />

unemployment benefits <strong>of</strong> <strong>the</strong> long-term unemployed should be reflected in <strong>the</strong> value <strong>of</strong><br />

<strong>the</strong> subsidy, and that <strong>the</strong> share depend inversely on <strong>the</strong> deadweight and displacement

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