A Theoretical Growth Model for Ireland

A THEORETICAL GROWTH MODEL FOR IRELAND

home or abroad depends on preferences and the relative wage available in the
two locations.¹⁰ Thus labour supply and employment can be written as:

L = €(D; w/w*) with €1, €2 > 0.                       (1)

where w is the domestic wage, w^* the foreign wage and D is a shock term
representing a reduction in labour-market distortions. The distorted labour
supply schedule lies to the left of the undistorted schedule.

Imperfect capital mobility means that the cost of domestic borrowing is
related to the total stock of borrowing. This equals the capital stock, which is
owned in its entirety by foreign investors. Thus the required rate of return on
capital is:

r = r^* + Φ(S; K)                              (2)

where r^* is the foreign interest rate and S represents the beneficial capital-
market shocks discussed earlier, with Φ₁ < 0 and Φ₂ > 0.

Output is given by the CRS production function:

Y = AF(K,L)                           (3)

which yields

AF_L (K/L) = w                          (4)

and

p = c(w,r)/A                                (5)

With output prices exogenous (given the small open economy assumption),
these five equations then determine the five endogenous variables Y, K, L, w
and r.¹¹

¹⁰Technically, each individual allocates part of his or her working life to the two locations so that
the population with whose income per head we are concerned remains static. There is no
unemployment in the formal model. Unemployment could be taken into account by introducing it
as another state over which individuals have preferences. If social welfare payments remained
constant throughout the analysis (as we assume the foreign wage does), the unemployment rate
would then rise or fall in line with emigration, which is broadly consistent with the Irish
experience.

¹¹The cost function in Equation (5) is linearly homogenous. For the Cobb-Douglas production
function Y=AK^α L^1-α , for example, the price-cost equation is p=c(r^αw^1-α)∕A.

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