Agent-based asset exchange models serve as an interesting and tractable means by which to study the emergence of an economy's wealth distribution. Although asset exchange models have reproduced certain features of real-world wealth distributions, previous research has largely neglected the effects of economic growth and network connectivity between agents. In this work, we study the effects of globalization on wealth inequality in the Growth, Exchange, and Distribution (GED) model [Liu et al, Klein et al] on a network or lattice that connects potential trading partners. We find that increasing the number of trading partners per agent results in higher levels of wealth inequality as measured by the Gini coefficient and the variance of the agent wealth distribution. However, if globalization is accompanied by a proportionate increase in the economic growth rate, the level of inequality can be held constant. We present a mean-field theory to describe the GED model based on the Fokker-Planck equation and derive the stationary wealth distributions of the network GED model. For large Ginzburg parameter for which mean-field theory is applicable, the wealth distributions for the fully connected model are found to be Gaussian; however, for sparse trade networks, a non-Gaussian "hyperequal" phase is found even for large Ginzburg parameter. It is shown that several networks (Erdos-Renyi, Barabsi-Albert, one-dimensional and two-dimensional lattices) display mean-field critical exponents when the Ginzburg parameter is large and held constant and the system parameters are scaled properly.