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Consider price-taking firms and assume for simplicity that real wages and output per employed
worker are constant and independent of the type of contract. The value functions pertaining to vacant and
occupied jobs take the form:
rVj =-ky+qj(Jj -Vj), j = T, P
rJT =y-w+λ(VT -JT)
rJP = y-w+φ(VP -JP -C)
where V j is the expected present value of a type j vacancy and J j the value of an occupied job of type j.
Worker productivity (real revenue) is denoted y and w is the real wage. It is costly to hold a vacancy open
so k>0. Temporary contracts expire at the exogenous rate λ and permanent contracts at the rate φ , where
λ> φ . Moreover, if a worker is separated from a permanent contract the firm has to pay a firing cost, C.
This cost is of the “red tape” type and does not involve any transfer to the worker.
There are thus two key differences between temporary and permanent contracts. First, permanent
contracts carry firing costs whereas temporary contracts don’t. Second, temporary contracts expire at a
higher rate than permanent ones. These differences have implications for the firms’ choices between the
contract types. Operating firms need to maintain a positive surplus from employed workers, i.e., y-w>0,
because of hiring and firing costs. The surplus needs to be higher the tighter the labour market is since it
is more costly to recruit in a tight labour market when it takes a longer time to fill vacancies. The surplus
must also be higher for jobs (contracts) that are destroyed at a faster rate, all else equal. The reason is that
a high destruction (separation) rate forces firms to engage more frequently in costly hiring. Moreover, the
surplus must be higher for permanent jobs since they carry separation costs. These claims are immediately
confirmed by imposing the standard free entry conditions for vacancies, i.e., V j = 0 , in the value
functions above. We then get two equations that describe how the firms’ supplies of vacancies depend on
profitability, y/w, and other factors:
(A1) w/y = 1 - (r +φ)k(θP)η -φc
(A2) w / y = 1 -( r + λ)k (θT П
where c ≡ C/y . These two “zero-profit conditions” can be thought of as labour demand equations and
capture firms’ supply of vacancies as functions of wages and productivity. The equations are illustrated in
TP
Figure 1. As θT goes to zero, w/y approaches unity since recruitment costs vanish. As θ goes to zero,
w/y approaches 1 - φc < 1 because of the need to maintain a surplus to cover firing costs. Moreover, the P-
curve is flatter than the T-curve since φ< λ ; an increase in θT is more costly to the firms than an