Urn model with $b=2$ for product share kinetics {#sec:modelb2}
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The phase diagram in Fig. \[fig:model\] (b) indicates that $b=2$ is a critical value: Condensate emerges for finite particle density only when $b$ is larger than $2$. Given that the kinetics of product share in international trade is described by the model with $b=2$, one can expect that there will be no condensation in international trade. However in reality $N$ is large but finite and then a bump may appear in $p_\infty(m)$ even with $b\leq 2$ for $\rho$ sufficiently large, which is called pseudo-condensate [@Evans:2006uq]. In this section, we bring the urn model with $b=2$ as close as possible to the real trade by fitting the model parameters, mainly the particle density $\rho$ and the time scale, to address the model’s power of explaining the international trade in the past and predicting its future.

Time scale corresponding to one year
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Let $\Delta \tilde{t}$ denote the time interval in the model corresponding to one year in the real world. For the time interval $\Delta \tilde{t}$, a site $p$ is selected $2m_p^2 \Delta \tilde{t}$ times for gaining or losing a particle with the rate in Eq. (\[eq:u\]) and $b=2$, which either 