Essay About Growth Theory1        Growth Accountingnotations And A.Growth Rate Γx Of Variable X

Basic Growth Theory
Notes on Growth Theory1        Growth AccountingNotations: Y –output or GDP, K–capital, L–labor, A–technology or total factor productivity (TFP); subscript t denotes the time, e.g.  Yt  is the output at time  t.The change of variable X is defined byX can be Y, K, L, or A.Growth rate γX of variable X is∆Xt = Xt+1 − Xt,γX =Xt+1 − XtXt= ∆Xt . Xt– For example, growth rate of GDP, γY  = ∆Yt/Yt, growth rate of capital γK = ∆Kt/Kt.The aggregate production function has the formYt = AtKαL1−α,t        ti.e. the Cobb-Douglas production function, where 0 < α < 1.Basic Introduction of Natural Logarithm Function  lnDeftnition 1.1. A real number y = ln x if ey = x.Properties of natural logarithm   functionProposition 1.1. For any two strictly positive real numbers a and b, ln ab = ln a + ln b. Proof.  Note thattherefore, ln a + ln b = ln ab.eln a+ln b = .eln a. .eln b. = ab,Proposition 1.2. For any strictly positive number a and any real number β, ln(aβ ) = β ln a. Proof.  Note that