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By Masanao Aoki (auth.), Prof. Mauro Gallegati, Prof. Alan P. Kirman, Dr. Matteo Marsili (eds.)

This quantity encompasses a collection of contributions provided on the WEHIA02 (Workshop on Economies with Heterogeneous Interacting Agents), which was once held on the Abdus Salam foreign Centre for Physics of Trieste, Italy, on could 29- 31, below the auspices of Exystence, complicated method community of excellence . WEHIA02 is the seventh variation of a workshop, which used to be held for the 1st time on the college of Ancona, Italy , on 1996 (1), as a one-week sequence of seminars for the Italian PhD software . Ancona hosted the development within the years 1997 and 1998 (2) , sooner than it moved to Genoa 1999 (3), Marseille 2000 (4) , Maastricht 2001 (5), and eventually to Trieste 2002. The 2003 workshop was once held in child , Germany, whereas the subsequent variants can be in Kyoto, Japan (2004) and Essex, united kingdom (2005). the whole record of members, titles of the invited lectures, papers and posters of WEHIA are available in http ://econ . dea. it/wehia2. The workshop has been continuously very casual aiming to place jointly sch- ars of alternative disciplines engaged on interplay of heterogeneous "so- factor " (economists, physicists, biologists) . To facilitate participation there has no longer been convention expense . It aimed to be a locus for speak and trade effects and studies . a number of collaborations begun with the Workshop and it's not with out satisfaction that the organizers declare this type of outcome. The WEHIA has had pars: a pars desiruens and a pars adestruens.

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The paper is organized as follows. Section 2 sets up the Model, Section 3 solves the model by using Pontryagin 's maximum principle. Section 4 studies th e implied out-of-steady dynamics and section 5 provides some simulations . Section 6 concludes the paper. 2 The Model Let us define the present value of the dominant firm as follows 1 =1 w= 00 {(Pt - c)(D t - Xt) - tp(9t )K t} e- pt dt (1) 00 { (Pt - c)( E t - Yt) - tp(gt)}Kte-ptdt where Pt , price of the goods, c, average cost of the dominant firm which is assumed to be fixed (c > 0) , Ds, real market demand of the goods, Xt, real out put of th e fringe firm, K t , real capital stock of the dominant firm , gt , growth rat e of capit al stock of th e dominant firm (gt = Kti K t), p, discount rate of the dominant firm which is assumed to be fixed (p > 0).

Real output t herefore is yt = w + bit and yft = e ; + bit for the unskilled and the skilled worker respectively. Preferences are as before : U = (Cit+ d l' (bit+ d I - i' . Therefore the you ng do not consume. T hey exch an ge their output (income and beq uest) for mon ey: PtYit = 1\IJit . The old receive money tran sfers (T it + 1 = /-lh t ) and spe nd t heir money to consume and leave a bequest . J;;) are real money balances of t he old . Sin ce, given the pr eferences, indirect utili ty is 29 or U = hr (1 - , /-,.

Let's assume that efficiency is distributed as a uniform random variable with support (0,1). " . This share is constant and independent of money growth. The income of the skilled worker falls in the interval (e,l) where 1 is the maximum efficiency of the skilled (by the assumption above). But w == e so that average income of the skilled is - 8 e 1+e 1+ w = -2- = 2 (37) Therefore, average income is w = we + e , 8 ( 2 w -+-1 1 - e' ) = 2 Let 's define now the laws of motion. L whose steady state is 14 By assumption therefore w < 1.

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