Appendix to Deflation : Prevention and Cure

Households First, I consider the individual consumption behaviour of households that operate in perfect financial markets and can borrow freely against the security of their future disposable labour income. In the body of the paper these are called permanent income consumers. Next aggregate consumption is derived on the assumption that all consumers are permanent income consumers. The final step is to derive aggregate consumption behaviour when a constant fraction of households is constrained to consume their disposable labour income in each period. A representative member of the generation born in period t-s, 0 s ≥ , maximizes at time t the expected utility of lifetime sequences of consumption of domestic goods, imported goods and real money balances. The objective functional (,) vtst − is given in equations (1), (2) and (3). The period household budget identity is given in equations (8) or (9) and the household solvency constraint in (10). There is a constant (that is, both time-independent and age-independent) probability of survival till the next period, given by 1 ,0 1 δ δ ≥ + ; δ can be thought of as the death rate. The pure subjective rate of time preference is 0 ρ >. Uncertainty about the time of death is the only uncertainty in the model, and its only effect on the objective functional is to raise the effective subjective discount factor from 1 ρ + to (1)(1) ρδ ++. Period felicity of a household born at time ,0 tss −≥ and surviving at time t is given by a constant intertemporal elasticity of substitution function of (,) ztst − , where z is a CES function of a composite consumption good, (,) ctst − % ,