Download The Complex Networks of Economic Interactions: Essays in by Akira Namatame, Taisei Kaizouji, Yuuji Aruka PDF
By Akira Namatame, Taisei Kaizouji, Yuuji Aruka
This booklet includes high quality multi-disciplinary examine contributions addressing theoretical and computational points of interplay and coordination of monetary brokers. It makes a speciality of emergent phenomena and collective habit in financial actions in addition to at the improvement of analytical and computational instruments in types with heterogeneous brokers. The contributions will not be limited to any specific tuition of concept, yet are in keeping with rigorous theoretical types and supported through experimental validation.
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Additional info for The Complex Networks of Economic Interactions: Essays in Agent-Based Economics and Econophysics
Example text
If we relax this assumption, the measurement of GRV of a country can become complex. Let Yt be aggregate output in period t, that is: Nt i Yt = Σi=1 yt . Therefore the aggregate growth rate is given by: µt = i where αt−1 = 1 + gti εit Σ Nt y i Yt − Yt−1 Nt i = i=1 t−1 − 1 = Σi=1 αt−1 gti εit , N t i Yt−1 Σi=1 yt−1 i yt−1 N (1) is the share of output of sector i with respect to total t yi Σi=1 t−1 Nt i that Σi=1 αt−1 output, so = 1, ∀t. From definition (1) we have that the expected value and variance of µt are given by: Nt i µ ¯t = Et [µt ] = Σi=1 αt−1 gti (2) Nt i Σi=1 αt−1 gti ηti σ ¯t2 = Et 2 , (3) where ηti = εit −1.
It has eigenvalues 0 and -4q, the latter with multiplicity 3. We can similarly aggregate the first two sites and the second two sites separately to produce a two node tree. The eigenvalue are still 0 and -4q. In other words, after the lapse of time of the order 1/q, the one-level tree has approximately reached its equilibrium state, while dynamics of the two-level tree has not. This fact remains true when one-level trees of K sites is compared with k level trees with K = 2k . Suppose that we group l of K sites into one cluster, Why Macroeconomic Price Indices are Sluggish in Large Economies ?
The eigenvalues are 0 and −Kq, repeated K − 1 times, while those of k level tree are 0 and −(2q)k . We can show that the larger the number of hierarchies the slower the process of disturbance propagation, and response of macro-price index to shocks to one of the sectors. Ogielski and Stein (1985),10 among several others, have shown that in the limit of the number of hierarchy going to infinity, the response becomes power-law, not exponential decay. See also Paladin et al. 3 Inflexible Macroeconomic Prices: An Example We present an example of slow adjustments of some macroeconomic price (index) composed of prices of goods of several sectors of economy.