We present a rule-of-thumb consumption model with participation in a Save More Tomorrow (SMarT) plan, and we analytically derive the fraction of life-cycle wage increases that must be saved to offset a reduction in social security benefits resulting from an aging population (holding taxes fixed...

Hyperbolic discounting with naiveté is widely believed to provide a better explanation than exponential discounting of why people borrow so much and why they wait so long to save for retirement. We reach a different set of conclusions. We show that if financial planning is enriched to include...