(a) Show that the optimal ad valorem borrowing tax [such that \( (1 + \tau)(1 + r^*) \) is the gross interest rate domestic residents face when the world rate is \( 1 + r^* \)] is given by \( \tau = \frac{1}{(\zeta^* - 1)} \), where \( \zeta^* \) is the elasticity with respect to \( 1 + r \) of Foreign's demand for imports of date 2 consumption. (The elasticity \( \zeta^* \) is defined formally in the chapter appendix.)