Problem 2. Capital taxation in the Ramsey model Consider a Ramsey-Cass-Koopmans economy that is on its balanced growth path. Suppose that at some time, which we will call time 0, the government switches to a policy of taxing investment income at rate t. Thus, the real interest rate that households face is now given by r(t) = (1 -o)f(k(t)). Assume that the government returns the revenue it collects from this tax through lump-sum transfers, meaning that the * =0 locus is unaffected, i.e. is still the same equation as in the text-book. Finally, assume that this change in tax policy is unanticipated. (a) How, if at all, does the tax affect the c=0 locus? (b) How does the economy respond to the adoption of the tax at time 0? What are the dynamics after time 0? (c) How do the values of c and k on the new balanced growth path compare with their values on the old balanced growth path