We document a new stylized fact for the life-cycle behavior of consumer prices: relative to a narrowly defined set of competing products, the price of individual products tends to fall over the product lifetime. This holds true for more than 90% of the expenditure items underlying the U.K....

We present a sticky-price model incorporating heterogeneous firms and systematic firm-level productivity trends. Aggregating the model in closed form, we show that it delivers radically different predictions for the optimal inflation rate than canonical sticky price models featuring homogenous...