Price Vector's Derivative

Let us briefly consider the derivative P'(t) of a price vector P(t). P'(t) is the marginal price vector with respect to time. It represents the rates at which the prices of all the commodities are changing. In a time of pure inflation, prices will increase but the ratios between prices of different commodities will stay the same, hence P'(t) will have the same direction as P(t). In a time of pure deflation P'(t) will have the opposite direction from P(t). Usually P'(t) is not parallel to P(t) at all, because the prices of some commodities are changing relative to others.