Time Derivative - Use in Economics

Use in Economics

In economics, many theoretical models of the evolution of various economic variables are constructed in continuous time and therefore employ time derivatives. See for example exogenous growth model and ch. 1-3. One situation involves a stock variable and its time derivative, a flow variable. Examples include:

• The flow of net fixed investment is the time derivative of the capital stock.
• The flow of inventory investment is the time derivative of the stock of inventories.
• The growth rate of the money supply is the time derivative of the money supply divided by the money supply itself.

Sometimes the time derivative of a flow variable can appear in a model:

• The growth rate of output is the time derivative of the flow of output divided by output itself.
• The growth rate of the labor force is the time derivative of the labor force divided by the labor force itself.

And sometimes there appears a time derivative of a variable which, unlike the examples above, is not measured in units of currency:

• The time derivative of a key interest rate can appear.
• The inflation rate is the growth rate of the price level—that is, the time derivative of the price level divided by the price level itself.