A Theoretical Growth Model for Ireland

THE ECONOMIC AND SOCIAL REVIEW

of capital captured by the function I = g(q), which satisfies the conditions
g'(q) > 0, and g(1) = δK. The aggregate capital stock then adjusts according to:

K = g ( q ) - δK                          (11)

Foreign Investors

Foreign investors are modelled through the simple assumption that the
return on direct investment in the home economy must equal r. Following
recent literature (e.g., Turnovsky, 2002), we assume that there are frictions in
international capital markets which lead the cost of domestic borrowing to be
related to the total stock of borrowing (which, in our simplified modelling,
equals the capital stock). Thus, we assume that:

r = r* + Φ(K)                             (12)

where Φ'(K) > 0.

Equilibrium

Equations (8)-(12), in combination with the labour market clearing
equation fɪ = L give the full equilibrium for the economy. We can then solve
for w₁, q, r, K and L. We simplify the system by putting Equations (7) and (8)
together to obtain the implicit function L = L(K, Θ, A). This function satisfies
L₁ > 0, L₂ >0 and L₃ > 0. Using this in Equation (9), and combining Equations
(10) and (11), gives us a dynamic system in q and K which satisfies:

q = (r* + Φ(K) + δ)q - AFk(K, L(K, Θ, A)),               (13)

KC= g ( q ) - δK.                             (14)

The behaviour of the economy is illustrated in Figure 2. The q = 0 schedule
represents the arbitrage equation determining the optimal capital stock, and
is downward sloping. The K= 0 schedule is upward sloping. If the economy
begins with a relatively low capital stock, the price of capital is above its
steady state. This leads to positive net investment, and the economy converges
along the saddle path SS towards its steady state, characterised by

q= 1                                   (15)

(r* + Φ(K) + δ) = AF_κ(K, L(K, Θ, A))                 (16)

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