ECON 330 Problem Set I

ECON 330 Problem Set I(Due in class by the date stated on the syllabus)You can work the problems in groups and turn in a single answer sheet with your names on it. 1.(Probably you want to do it in excel or your spreadsheet of choice) Consider the following table with the values for two variables at three points in time.tY(t)X(t)1950100,0001001951104,0801012000815,900210For the growth rate between 1950 and 1951 and the average yearly growth rate between 1950 and 2000.a)Calculate them exactly, i.e. without using the log approximation.b)Calculate them using the log approximation.No consider an additional variable, Z(t), which is defined in the following waysi)Z(t) = Y(t) * X(t)ii)Z(t) = Y(t) / X(t)iii)Z(t) = Y(t)^2iv)Z(t) = 2 * Y(t)c)Calculate the values of Z(t) in each case, for the three years under considerationFor the growth rate of Z(t) between 1950 and 1951 and the average yearly growth rate between 1950 and 2000.d)Use the data in c) to calculate them exactly, i.e. without using the log approximation.e)Use the data in c) to calculate them using the log approximation.f)Use only data from your answers tob) to calculate the growth rates of Z(t).By now you should be convinced that the log approximation works well. In the remaining of the course feel free to use any of the two methods (exact or logs).2. Consider three variables that change through time; xt(),yt()and zt(). The first two variables grow at the constant rates gxand gyrespectively. Calculate the growth rate of zt()in the following cases, where kis some constant.a) zt()=kxt()yt()b) zt()=xt()()kyt()c) zt()=xt()()kyt()()k−1d) zt()=−1yt()