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

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Chapter1: Making Economics Decisions

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Question

1.1.
Basic properties of growth rates. Use the fact that the growth rate of a variable equals the time derivative of 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)Y(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)]-[Y(t)/Y(t)].
(c) If Z(t) = aX(t)a, then Ż(t)/Z(t) = aX(t)/X(t).

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