Uploaded on 2014-11-16 by yorishawki

The ratio of a stock over a flow has units of (units)/(units/time) = time. For example, the debt to GDP ratio has units of years (as GDP is measured in, for example, dollars per year whereas debt is measured in dollars), which yields the interpretation of the debt to GDP ratio as "number of years to pay off all debt, assuming all GDP devoted to debt repayment". The ratio of a flow to a stock has units 1/time. For example, the velocity of money is defined as nominal GDP / nominal money supply; it has units of (dollars / year) / dollars = 1/year. In discrete time, the change in a stock variable from one point in time to another point in time one time unit later (the first difference of the stock) is equal to the corresponding flow variable per unit of time. For example, if a country's stock of physical capital on January 1, 2010 is 20 machines and on January 1, 2011 is 23 machines, then the flow of net investment during 2010 was 3 machines per year. If it then has 27 machines on January 1, 2012, the flow of net investment during 2010 and 2011 averaged 3 \tfrac{1}{2} machines per year. In continuous time, the time derivative of a stock variable is a flow variable.![enter image description here][1] A stock (or "level variable") in this broader sense is some entity that is accumulated over time by inflows and/or depleted by outflows. Stocks can only be changed via flows. Mathematically a stock can be seen as an accumulation or integration of flows over time – with outflows subtracting from the stock. Stocks typically have a certain value at each moment of time – e.g. the number of population at a certain moment. A flow (or "rate") changes a stock over time. Usually we can clearly distinguish inflows (adding to the stock) and outflows (subtracting from the stock). Flows typically are measured over a certain interval of time – e.g., the number of births over a day or month![enter image description here][2] [1]: https://edxuploads.s3.amazonaws.com/14161796811064828.png [2]: https://edxuploads.s3.amazonaws.com/14161798099015731.gif