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household aids, male participation in home labour and so on. As only familypriority
women leave the labour market when such a demand arises, women’s
labour force withdrawal probability is given by
p t =(1− q t ) µ,
where q t is the fraction of j-women at time t, with adult women’s population
normalized to 1. Thus, the withdrawal probability of women p t ,givenµ,
is increasing in the proportion of women with family preferences, (1 − q t ) .
It is assumed that firms know this probability p t , that is, they know the
probability, on average, that a woman leaves the labour market.
Because the labour market is competitive, firmsinthismodelwilldesign
jobs to maximize the expected lifetime incomes of the workers that will
occupy them.
Firms’ problem for women-workers. Since firms cannot distinguish between
the two types of women, they offer every women the same type of
job.
Formally, the problem for firms is to decide the on-the-job training
that maximizes the expected lifetime productivity of a worker:
max
C
[f(C) − C]+δ(1 − p t )f(C) (1)
subject to a zero-profit constraint,whereδ ∈ (0, 1) is the discount factor
of the firms. The optimal training to perform a job is characterized by the
following first-order condition:
f 0 (C) =
1
1+δ(1 − p t ) . (2)
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