sentences:  "Smooth" here means that small changes in relative prices for a good will be associated with small changes in the quantity of it used.The Törnqvist corresponds exactly to the translog production function, meaning that given a change in prices and an optimal response in quantities, the level of the index will change exactly as much as the change in production or utility would be.To express that thought, Diewert (1978) uses this phrasing which other economists now recognize