(b) Derive the consumption function for this case, $$ C_1 = left( frac{1 + r}{2 + r} ight) Y_1 + left( frac{1}{2 + r}

(b) Derive the consumption function for this case,

$$ C_1 = \left( \frac{1 + r}{2 + r} \right) Y_1 + \left( \frac{1}{2 + r} \right) Y_2. $$

Show that \( C_2 = C_1 \) using this consumption function and the current account identity.