We can linearize the Cobb-Doublas production function (equation 1) by taking the natural log on both sides: In (Yi) = In (Ai) + Boln (Ki) + 70 In (Li) . (2) From equation (2), we can obtain bivariate linear regression models In (Y4) = at + 70 ln (Li) + Ui In ( Y4) = QK + Bo In (Ki) + Vi where OL = BORK + HA OK = YOUL + HA Ui = Bo (In (Ki) - MK) + (In (A;) - MA) Vi = To (In (Li) - ML) + (In (A;) - HA) HK = E [In (K;)] (pronounced "mu K") AL = E [In (Li)] (pronounced "mu L") HA = E [In (A;)] (pronounced "mu A"). (a) Consider cov (In (Li) , In (K;)). For the purpose of analytical thinking, you may disregard the natural log and simply consider the covariance between the number of employees and the capital stock. Do you think cov (In (L;) , In (K.)) is positive, negative, or zero? Explain your reasoning. (b) Consider cov (In (Li) , In (A;)). For the purpose of analytical thinking, you may disregard the natural log and simply consider the covariance between the number of employees and the TFP. Do you think cov (In (L;) , In (A;)) is positive, negative, or zero? Explain your reasoning. (c) Show that cov (In (L;) , Uj) = Bocov (In (Li) , In (K.)) + cou (In (Li) , In (At)). Similarly, conclude that cov (In (K;) , Vi) = Tocou (In (Ki) , In (Li)) + cov (In (Ki) , In (Ai))