Basic properties of growth rates. Use the fact that the growth rate of a variable equals the time derivative its log to show: (a) The growth rate of the product of two variables equals the sum of their growth rates. That is, if Z(t) = X(t)X(t), then Ż(t)/Z(t) = [X(t)/X(t)] + [Ÿ(t)/Y(t)]. (b) The growth rate of the ratio of two variables equals the difference of their growth rates. That is, if Z(t) = X(t)/Y(t), then Ż(t)/Z(t) = [X(t)/X(t)]-[Ÿ(t)/Y(t)]. (c) If Z(t)=aX(t)a, then Ż(t)/Z(t) =aX(t)/X(t).

Basic properties of growth rates. Use the fact that the growth rate of a variable equals the time derivative its log to show: (a) The growth rate of the product of two variables equals the sum of their growth rates. That is, if Z(t) = X(t)X(t), then Ż(t)/Z(t) = [X(t)/X(t)] + [Ÿ(t)/Y(t)]. (b) The growth rate of the ratio of two variables equals the difference of their growth rates. That is, if Z(t) = X(t)/Y(t), then Ż(t)/Z(t) = [X(t)/X(t)]-[Ÿ(t)/Y(t)]. (c) If Z(t)=aX(t)a, then Ż(t)/Z(t) =aX(t)/X(t).

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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