We consider a pure-exchange general equilibrium economy populated by investors with heterogeneous preferences and beliefs. The investors receive labor incomes, which are not fully pledgeable, and can potentially default on their risky positions unless their asset holdings are collateralized. We study the equilibrium implications of a constraint that requires investors to keep their financial capital above a certain minimum level to provide sufficient collateral. We characterize periods in the economy in which mere possibility of a crisis makes constraints binding and significantly depresses interest rates and increases Sharpe ratios. We find that stock price-dividend ratios are higher in the constrained economy and the tightening of constraints emerges as a viable instrument for curbing asset volatilities in bad times. Our equilibrium is stationary, and both investors survive despite differences in beliefs. The equilibrium processes are derived in closed form.