Dissertation supervisor: Dr. Chao Gu. ; Includes vita. ; This dissertation consists of two essays on monetary economics. The first essay studies a monetary model in which the lack of repayment enforcement causes the agent's credit limit to bind. When the credit constraint binds, the allocation is usually not efficient. I show that government bonds are candidates to alleviate this problem. I also show that liquid bonds, as a perfect substitute to fiat money, can only change the equilibrium price of good markets but cannot change the allocation. On the other hand, illiquid bonds can help improve social welfare. The second essay studies a pure credit model with productivity shocks. When record keeping and information are perfect, the existence of defaulters has no effect on other agents' consumption and output. But, if access to the agent's trading history is limited, the existence of defaulters can change other agents' allocation because sellers will charge all the buyers a default premium. The optimal punishment in a narrow class of credit contracts is also calculated. ; Includes bibliographical references.