We can break this problem up into two parts by partitioning your budget into a spending and saving component.
You can get a diminishing marginal utility curve for spending, by looking at what your total purchases would be at different budgets. Then you can estimate marginal expected value of cash on hand (the complement of your spending budget spending). Then you hold enough cash for the curves to intersect, and spend the rest.
In practice this isn’t always tractable, but usually it’s overdetermined anyway since the vast majority of decisions are strongly inframarginal.
We can break this problem up into two parts by partitioning your budget into a spending and saving component.
You can get a diminishing marginal utility curve for spending, by looking at what your total purchases would be at different budgets. Then you can estimate marginal expected value of cash on hand (the complement of your spending budget spending). Then you hold enough cash for the curves to intersect, and spend the rest.
In practice this isn’t always tractable, but usually it’s overdetermined anyway since the vast majority of decisions are strongly inframarginal.