(a) Home receives perishable endowments Y and Y2 in the two periods. Show that the Home date 1 consumption function is a function of r, C(r)= 1 1+B Y2 +r (This equation shows a general property of logarithmic preferences that we will use many times in this book: expenditure shares on the available goods are constants that correspond to the relative weights on the logarithmic summands in U. Thus spending on date 1 consumption, C1, is a fraction 1/(1+B) of lifetime income (measured in date 1 consumption units), and spending on date 2 consumption, C/(1+r), is a fraction B/(1+ ) of lifetime income. This property follows from the unitary intertemporal substitution elasticity.]