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We develop a theory of rational addiction in which rationality means a consistent plan to maximize utility over time. Strong addiction to a good requires a big effect of past consumption of the good on current consumption. Such powerful complementarities cause some steady states to be unstable. They are an important part of our analysis because even small deviations from the consumption at an unstable steady state can lead to large cumulative rises over time in addictive consumption or to rapid falls in consumption to abstention. Our theory also implies that "cold turkey" is used to end strong addictions, that addicts often go on binges, that addicts respond more to permanent than to temporary changes in prices of addictive goods, and that anxiety and tensions can precipitate an addiction.