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The focus of my PhD research has been on the acquisition of computational modeling and simulation methods used in both theoretical and applied Economics. My first chapter provides an interactive review of finite-difference methods for solving systems of ordinary differential equations (ODEs) commonly encountered in economic applications using Python. The methods surveyed in this chapter, as well as the accompanying code and IPython lab notebooks should be of interest to any researcher interested in applying finite-difference methods for solving ODEs to economic problems. My second chapter is an empirical analysis of the evolution of the distribution of bank size in the U.S. This paper assesses the statistical support for Zipf's Law (i.e., a power law, or Pareto, distribution with a scaling exponent of α = 2) as an appropriate model for the upper tail of the distribution of U.S. banks. Using detailed balance sheet data for all FDIC regulated banks for the years 1992 through 2011, I find significant departures from Zipf's Law for most measures of bank size inmost years. Although Zipf's Law can be statistically rejected, a power law distribution with α of roughly 1.9 statistically outperforms other plausible heavy-tailed alternative distributions. In my final chapter, which is based on joint work with Dr. David Comerford, I apply computational methods to model the relationship between per capita income and city size. A well-known result from the urban economics literature is that a monopolistically competitive market structure combined with internal increasing returns to scale can be used to generate log-linear relations between income and population. I extend this theoretical framework to allow for a variable elasticity of substitution between factors of production in a manner similar to Zhelobodko et al. (2012). Using data on Metropolitan Statistical Areas (MSAs) in the U.S. I find evidence that supports what Zhelobodko et al. (2012) refer to as "increasing relative love for variety (RLV)." Increasing RLV generates procompetitive effects as market size increases which means that IRS, whilst important for small to medium sized cities, are exhausted as cities become large. This has important policy implications as it suggests that focusing intervention on creating scale for small populations is potentially much more valuable than further investments to increase market size in the largest population centers.