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By T. Asada, T. Ishikawa

In August 2005, a small yet very important convention came about at Chuo college in Tokyo, Japan. The Chuo assembly on Economics of Time and house 2005 (Chuo METS 05) aimed to complement the respective disciplines of the economics of time (dynamic economics) and the economics of house (spatial economics) and to extend their applicability within the actual international. The chapters contained herein are according to the papers provided at that convention.

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If we proceed in this way and simplify the rest by neglecting ∆yt in Eq. 23 and denoting the composed coefficient on yt as by, our Phillips curve Eq. 23 becomes ∞ π t = α c ∑ (1 − α c )k[γπ *+ (1 − γ )(π t − k −1 + α y yt − k −1 + α g ∆yt − k −1 )] + β y yt k=0 Since the infinite series Σ ∞k=0(1 − a c)k has limit 1/a c, the equation can be rewritten as ∞ π t = γπ *+ (1 − γ )∑ α c (1 − α c )k π t − k −1 k=0 ∞ + β y yt + α c (1 − γ ) ∑ (1 − α c )k (α y yt − k −1 + α g ∆yt − k −1 ) (27) k=0 which includes the inflation terms in the same form as Eq.

D 2π WG ′xn uG ′′ =− ε+ du 2 u G′ ) so that we impose the restriction given below. (15) H. Yoshida 34 Assumption 1: e + uG″/G′ > 0 (16) From the implicit function theorem, Eq. 14 can be rewritten as u = u(k, xn) (17) This equation means that the optimal choice of u depends on k and xn. The functional relationships above can be summarized as follows: Lemma 1: The partial derivatives of the function, u = u(k, xn), are given by uk = ∂u u ε =− <0 ∂k k ε + uG ′′ (u) / G ′ (u) (18) ux = ∂u u 1 − θ (1 − ε ) =− <0 ∂xn x ε + uG ′′ (u) / G ′ (u) (19) Proof of Lemma 1: Substituting Eq.

This completes the proof. ᭿ Proposition 1 assures us of the stability of the warranted growth path. The local stability can be ensured in the case of 0 < w < 1 and F(u) > 0. What happens in the case where f u < 0? We can obtain the following: Proposition 2: Suppose that 0 < w < 1 and that max{−[1 − q(1 − e)], −q(e + G″/G′)} < [1 − q(1 − e)]F(u) < −we. Then there exists a positive critical value bH. The steady state is locally stable if b < bH, while it is unstable if b > bH. Furthermore, the system undergoes a Hopf bifurcation at b = bH.

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