Abstract
General Motors or a local business, which one is it better to be stimulated in postcrisis recessions, when government stimulation is meant to overcome recessions? Due to the budget constraints, it is quite relevant to ask how government can increase the chance of economic recovery. One of the key elements to answer this question is to understand metastable features of crises in economic networks and their related hysteresis. The Ising model has been suggested for studying such features. In the homogeneous networks, one needs at least a minimum budget, to force the network to switch its local equilibria, where such a minimum is independent of the network characteristics such as the average degree. In the scale free networks however, when the government aims to push the network to switch to another equilibrium, one may wonder which nodes are to be preferably stimulated in order to minimize the cost. In this paper, it is shown that stimulation of high degree nodes costs less in general. It is also found that in scale free networks, the stimulation cost depends on the networks features such as its assortativity. Although we confine our study to the Ising model in order to tackle a problem in economics, our analysis shines lights on many other problems concerning stimulations of socio-economic systems where dynamical hysteresis appears.
Highlights
In the aftermath of the 2007-2008 economic crisis, while the US government was going to stimulate the economy, some controversial issues had risen
Similar to the ferromagnet systems, the positive correlation can result in a dynamical hysteresis for the economic networks when in deep recessions one faces a global reduction in the activities of firms
Huge studies have been devoted to the occurrence of crises and spread of shocks in economics
Summary
In the aftermath of the 2007-2008 economic crisis, while the US government was going to stimulate the economy, some controversial issues had risen. The debate about a recovery plan for the General Motors (GM) and Chrysler went up to the level of the US Senate. Some experts favored helping the big companies such as GM and Chrysler while others favored small local businesses, see Stiglitz (2010) [1] and references therein. To explain the problem more rigorously, we should recall that firms purchase products from their "neighbors" in the trade networks. Such a trade results in positive correlations between activities of both firms. Similar to the ferromagnet systems, the positive correlation can result in a dynamical hysteresis for the economic networks when in deep recessions one faces a global reduction in the activities of firms. Managers have no choice but keeping steps with their part-
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