Hyperbolic Discounting 2D: Present Bias Curves & Reversal Map

This simulator renders two discounting models — Mazur's hyperbolic curve and the classic exponential curve — across three linked 2D panels: a discount-curve chart, a draggable decision timeline, and a k-vs-elapsed preference-reversal map. Two reward markers, a smaller $50 arriving sooner and a larger $100 arriving later, slide toward "now" as you advance an elapsed-time control, exactly the way a real decision-maker's vantage point moves forward each day. Because exponential discounting is time-consistent, the preferred reward never changes as elapsed time increases; because hyperbolic discounting is not, the preference can flip from "wait for the bigger reward" to "take the smaller one now" as its delay shrinks toward zero — the mechanism behind present bias, procrastination and self-control failure in real economic choices.