Obsolescence of Durable Goods and Optimal Consumption

We study a model with a durable good subject to abrupt, periodic obsolescence, and characterize the optimal purchasing policy. Consumers optimally synchronize new purchases with the arrival of new durable models. Hence, some agents use a "flexible" optimal replacement rule that switches between two adjacent replacement frequencies at irregular intervals. These agents react to wealth shocks by changing the timing of future purchases. The model has distinct comparative statics on obsolescence and durability and can explain how durables with high depreciation rates may have more volatile expenditure. The model also predicts how demand fluctuations respond to a change in product variety. These predictions match the observed changes in volatility of the US auto sales after the introduction of smaller foreign cars in the 1970s