growth rate

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The proportional or percentage rate of increase of any economic variable over a unit period, usually a year. If a variable measured over discrete time intervals grows from 1 to 1 + x, this is a proportional growth rate of x, or a percentage growth rate of 100x. If working in continuous time, a continuous constant growth rate g means that a variable grows from 1 at time 0 to egt at time t. If

yt = y0egt,

dyt/dt = gy0egt,


(dyt/dt)/yt = g

. As

ln(yt) = In (ijy0) + gt,

dln (yt)/dt = g;

the rate of change of the natural logarithm of any variable equals its growth rate. See also natural growth rate; warranted growth rate.

Subjects: Economics.

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