In approximately descending order of interestingness:
I proved that if you have a population with logarithmic utility in income and linear in leisure time, and you want to maximize utility with a flat tax rate funding a universal basic income, you want to set the tax rate to 1 - harmonic mean of wages / arithmetic mean of wages.
I’m proud of my work on finding a data structure for the dynamic k-smallest problem. My solution involves some interesting properties of red-black trees, some non-obvious amortized cost calculations, and a kind-of-neat generalization of the famous quickselect algorithm.
We could make it much easier to price discriminate based on income, by making it feasible to explicitly charge prices as a function of income.