A Theoretical Growth Model for Ireland



252


THE ECONOMIC AND SOCIAL REVIEW

the given wage rate, or emigrating abroad to work. Households are not
indifferent between labour supplied in the domestic economy and working
abroad - we assume that they have well defined preferences over the two
alternatives.

The Household and Labour Supply

The household in the model has preferences over consumption C and
labour supply
1 and 2 in the two locations 1 and 2, (where the wages in each
location are
w1 and w2, respectively) given by:

1 - φ

1 - -1            1 - -1 1 1

U = Cφ ^1 θ + μ2^2 θ J θ.

The household maximises utility subject to the budget constraint
C = w 11 + w 2^2, and a fixed total labour supply which must satisfy ι + 2 = 1.
The idea behind this specification is that the household receives some non-
pecuniary benefit from the time spent working in a given location besides the
direct wage income earned. The household has a fixed total amount of labour
supply it can offer, which we normalise at unity.

The first order condition for the household’s choice of location is given by:

w 1 - w2 = - - -  ---1---fμιf 1 θ - ,μ2'2 θ J

(6)


φ    μltl' ’’ + μ2<√'θk               '

Together with the constraint that 1 + 2 = 1, this describes a labour supply
schedule relating
1 positively to w 1 and negatively to w 2. Taking location 1 as
the home location, we thus have labour mobility such that households move
back into the home labour market as the home wage gap rises. But since
workers are not indifferent between locations, wages are not equalised
between them.

In addition to capturing the idea that home and foreign labour markets
are linked, we also wish to analyse the consequences of labour market reform.
One way to model this process is to imagine that, preceding the growth take-
off, labour markets were dominated by monopoly unions. In this case, instead
of Equation (6) characterising the labour supply relationship, we have a
condition that is implied by the monopoly union choosing to maximise utility,
taking an aggregate labour demand equation as given. This gives

w 1 - w 2 = 1


~ d1 I-1 (1 - φ)


------------ (μ 1 1 θ - μ2⅞ θJ.     (7)
μ1,' 1    θ +2 θ



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