Euler Equation
The first-order condition for optimal consumption in an intertemporal model: marginal utility today equals one plus the interest rate, divided by one plus the rate of time preference, times marginal utility tomorrow. When the interest rate exceeds the time-preference rate, the equation tilts the optimal consumption path upward over time (save today, consume more tomorrow); when the reverse holds, the path tilts downward (consume today, save less). The Euler equation is the foundation of every multi-period savings and retirement-planning model.
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