Problem 1: Log-linearize the following equations 1. Yt = Cuth + Gt (resource constraint). 2. Yt = (ake + (1 - a) (A, L ) p ) 1/p (CES production function; A is the level of technology; L is labor; K is capital; p, a are constants). 3. Kt = (1-8)Kt-1 + It (It is investment; Ke is capital stock, 8 is a fixed depreciation rate). 4. exp(it) = (p. = ( )"(")"exp(pic-1) (Fed's reaction function for interest rate i as a function of prices P and output Y; $7, dy, p are constants; note that inflation rate is It = log (Pt/Pt-1), growth rate of output gyt = log(Y;/Yt-1)). 5. Yt = Katz, " (Cobb-Douglass production function with variable capital share at). 6. Ct = ET it (Dixit-Stiglitz aggregator of consumption goods, C, is the consumption basket, c is an individual good)