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Antitrust agencies all over the world need to estimate the effects of a proposed merger of companies. What happens to prices and market shares after two or more companies merge? The OFT from the UK wanted an up-to-date and clear implementation of two popular models to simulate company mergers. The requirements read: “[...]We require a simple and straightforward implementation of the nested version of both models in separate Mathematica workbooks, but, where possible, with consistent naming and terminology. The clarity of the notebooks is far more important than their computational efficiency. We require the workbooks to be intuitive to use by a novice, and we would expect a slightly experienced Mathematica user to be able to fully understand the calculations with only a little help. We expect the notebooks to be well annotated and the functions to be well defined. [...] We require the notebooks to output all intermediate calculations about the market in a clearly readable format. In particular we wish to know, where possible, the model’s estimation of: pre and post-merger shares, quantities, prices, costs, elasticity’s, profits and consumer surplus on both a brand and a firm level. We are particularly interested in using the power of Mathematica to use the models to solve for any given value. For example, if we know more than one own-price elasticity of demand in the PCAIDS model, we would like to be able to solve for the industry elasticity of demand.” This talk gives a short review of the ALM [1] and PCAIDS [2] models and the quick implementation of their nested formulations in Mathematica, fulfilling the wish-list of the OFT. The software-challenges included good function design, handling of different Mathematica versions, understanding and translating some existing programs by Forni [4], written in MATLAB, and issues regarding different mathematical formulations especially of the ALM model. A comparison to an older but much more complicated Mathematica implementation of the ALM model by Luke Froeb [3] is sketched.
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