This dissertation consists of three independent essays in Macroeconomics. The first essay studies whether efficiency can be improved by introducing government-issued illiquid bonds to an economy where money is the only asset and essential. In contrast with perfectly liquid bonds, illiquid bonds can increase societal welfare in two ways: First, allocating consumption goods among heterogeneous agents more efficiently; second, stimulating consumption and output level by loosening the liquidity constraints of households. More importantly, since societal welfare is elevated persistently when the inflation rates range from a level slightly above Friedman Rule to an upper bound, this essay provides an insight into the essentiality of illiquid bonds....