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GABRIELA MUNDACA
than remittances. Otherwise the economy might experience formation of asset bubbles and excessive consumption of final goods.
Equilibrium Conditions In equilibrium, k t +2 = k t +2 =
⎡⎛ R ⎞(n w + rem ) + ρrem ⎤ . t t +1 ⎢⎣⎝ π ⎠ t t ⎥⎦
(4.18)
Equation (4.18) indicates that working capital at t+2 depends on the returns (R) on the long-run investments made using wages (wt) and remittances received at time t (remt), the returns on the remittances received at time t+1 (remt+1), whether they are invested in human capital (ρ > 1) or simply to alleviate liquidity needs (ρ = 1), and the probability that individuals will become late consumers. This should be so because capital formation takes two periods. _ Inserting equations (4.5) and (4.16) into equation (4.18) and dividing it b kt yields θ
γ
R(1 − θ)π (1 − π)Γ 1 Γ 2 (R − 1) + R remt = + × (1 − π) (1 − π) γ γ kt kt π 1+ π 1+ Γ 1Γ 2 Γ 1Γ 2 π π
k t +2
(
) (
)
⎛ Γ2 ⎞ − 1⎟ + ρ ⎝ π ⎠ remt +1 γ −1
+
Γ 1 Γ 2 ρ(1 − π) ⎜
(
1+
(1 − π) π
γ
Γ 1Γ 2
)
×
(4.19)
kt
or k t +2 kt
⎡ remt ⎤ ⎡ remt +1 ⎤ + β2 ⎢ ⎥ ⎥, ⎣ kt ⎦ ⎣ kt ⎦
= α + β1 ⎢
where θ
R(1 − θ)π , α= (1 − π) γ π 1+ Γ 1Γ 2 π
(
γ
)
(1 − π)Γ 1 Γ 2 (R − 1) + R β1 = , (1 − π) γ π 1+ Γ 1Γ 2 π
(
)
(3.20)