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 Apr22 reviewed Approve Minimum Volume of a circular, right cone, with a sphere inscribed in it. Apr22 comment How do I weight votes based on number of possible voters? Nice! But it is hardly THE solution, merely A (albeit elegant) solution. Apr22 reviewed Approve Summation of trigonometric series Apr22 reviewed Approve How to prove $\operatorname{Span}(\operatorname{Span}(S)) = \operatorname{Span}(S)$ Apr22 reviewed Reject For what values of a does the system havea) No solution; b) More than one solution; c) A unique solution. Apr20 comment Non-uniqueness of worst-case (max-min or min-max) optimization I think I was unclear before, so I edited and tried to give you the rough steps you could take to find the policy that maximizes the worst possible outcome. I hope this helps! Apr20 revised Non-uniqueness of worst-case (max-min or min-max) optimization added 525 characters in body Apr18 comment Gross Substitutes under continuous perturbations Could you provide a definition of the gross substitute property? Apr17 revised Method of moments estimation for $\theta$ Fixed typos / English Apr17 answered Profit Function where total revenue is re-spent on production? Apr17 answered Comparison of parameter: two different populations Apr17 answered Non-uniqueness of worst-case (max-min or min-max) optimization Apr14 awarded Popular Question Mar25 awarded Yearling Dec19 awarded Constituent Dec17 comment Sufficient conditions for monotonicity with probability distributions No, a negative $\delta$ reverses everything: larger $n$ reduces $A_n$. Dec17 answered Assumptions of a probability distribution Dec17 comment Derivatives defined on a discrete state space Well this is standard economics; deriving demand functions should be explained in every microeconomics textbook. The above decision problem seems a bit macroish, so you might also find something useful in macroeconomics textbooks, typically with infinitely many future periods and a discount factor ("infinite horizon decision problem") instead of just two periods as in your case. Acemoglu: "Introduction to modern economic growth", ch. 5 and others work with suchs problems. Dec17 comment Derivatives defined on a discrete state space Not necessarily: typically the demand function is defined/constructed for all $\omega\in[0,\bar{\omega}]$, where $\bar{\omega}$ is the largest possible realization of $\omega$. So the function can be continuous in $\omega$ (Berge's maximum theorem guarantees the demand function will be upper hemi-continuous in $\omega$). The demand function is like a plan: it gives you a consumption level for each value $\omega\in[0,\bar{\omega}]$. But since not every value in that set actually realizes, it is true that the actual consumption may be discontinuous, because wealth is discrete. Dec17 comment Derivatives defined on a discrete state space Here's how I think it works: at some point $t$, the decision maker (DM) has wealth $\omega$. This is the state variable. Wealth may be exogenous or evolves according to some process. At time $t$, the DM knows $\omega$, and he chooses consumption this period and saves the rest for next period. Next period, there is some uncertainty (over $\omega_{t+1}$?), hence the E-operator. So the demand/consumption function is a mapping $C:[0,\omega]\to[0,\omega]$ which tells you which part of wealth is consumed now and which is saved. I think just the the $\omega$ process over time is discrete.