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The transition to electric vehicles (EVs) shifts the complementary market for passenger transport from oil to electricity. We develop and estimate a joint equilibrium model linking the German vehicle and electricity markets, emphasizing the timing of EV charging as generation costs and emissions vary intraday. A 10% EV stock raises wholesale electricity prices by about 2%, creating a sizable pecuniary externality. Time-varying tariffs shift charging to cheaper hours and spur adoption, only partially alleviating the aggregate price pressure. Time-varying tariffs sustain EV adoption when the electricity market faces higher demand or carbon costs.