We consider a neoclassical one-sector economy in which—in addition to physical capital—there exists a second asset. This asset is unproductive, cannot be consumed, and does not pay dividends. A no-arbitrage condition is imposed so that the two assets are equivalent stores of value. Finally, we assume that consumption (respectively, investment) is a fixed fraction of the sum of aggregate factor income (GDP) and capital gains. In this modified Solow–Swan model, we characterize the conditions under which bubbles can exist, i.e., under which the useless asset can have a positive price. We find that these conditions do not imply that the original Solow–Swan equilibrium is dynamically inefficient, and we demonstrate that asset price bubbles can lead to non-monotonic and even periodic capital accumulation paths.