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How do discount rates affect agents' decisions and valuations? This paper provides a general method to analyze this question, allowing stochastic and managed cash flows, stochastic discount rates, and time inconsistency and including arbitrary learning and payoff or utility processes. We show that some of these features can lead to counterintuitive answers (e.g., "a more patient agent stops earlier"), but we also establish, under simple conditions, theorems yielding robust predictions concerning the impact of discount rates on control and stopping decisions and on valuations. We apply our theory to models of search, experimentation, bankruptcy, optimal growth, investment, and social learning. [ABSTRACT FROM AUTHOR]
