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Daniel_Burfoot comments on Open thread, Feb. 9 - Feb. 15, 2015 - Less Wrong Discussion
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The key idea to use here is linearization: even if a function is substantially non-linear overall, it is usually going to be linear in the small region around a point. Since the meal price is small compared to income, utility is just a linear function in that region.
If you haven't done the math in a while, it's a good exercise to see that when you do the Taylor approximations for the two functions, they are equal to first order.
Right, it was by using the Taylor series around the mean I got the approximation based on the variance. Paul pointed out to me you could do this and presumably did this calculation himself already