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The price index change is just "rebasing". It happens all the time to make price index numbers readable (so indexes don't climb to like 5000). No information is loss. You can get pre-2010 data that is comparable with the new index by dividing the old series by the 2010 index number and combining it with the new series. E.g. if under the old series 2009=280, 2010=300, then under the new series 2009=93.3, 2010=100.
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Why can you not solve the non-random model? I'm not an economist, but a mathematician, and pretty much any system of differential equation can be solved numerically with well-known techniques. What about a numerical solution instead of a analytical solution?
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Dec 19, 2013