We present plausible economic models in which an equilibrium with rational asset price bubbles exists but equilibria with asset prices equal to fundamental values do not. These economies feature multiple sectors with faster economic growth than dividend growth. In our two-sector endogenous growth model, entrepreneurs have access to a production technology subject to idiosyncratic investment risk (tech sector) and trade a dividend-paying asset (land). When leverage is relaxed beyond a critical value, the unique trend stationary equilibrium exhibits a phase transition from the fundamental regime to the bubbly regime with growth, implying the inevitability of bubbles with loose financial conditions.