Exercise 2. The basic Solow model in continuous time This exercise asks you to analyse the Solow model in continuous time as given by the six equations (21)-(26). The restrictions on the parameters a, B, s, n and o are the same as in the model in discrete time, except we do not have to assume n>-1. It is assumed that 021 sol n+ d> 0. We use (for any point t in time) the definitions k = K/L and y = Y/L etc. 1. Show that from k= K/L it follows k/k =K/K-L/L. (Hint: You can do the 'log-dif-trick', that is, first take logs on both sides of k = K/L and then differentiate with respect to time). Then show that the Solow model in continuous time implies the Solow equation: k = SBK" - (n+ 0)k. (41) Compare with (32) for the model in discrete time and give an intuitive explanation like the one given for (32) in this chapter