(d) Does zero intertemporal substitutability necessarily imply a literally constant consumption path, as in parts a-c, under all possible preference assumptions? [Hint: Suppose lifetime utility is

$$ U_1 = \frac{1}{1 - 1/\sigma} \left( C_1^{-1/\sigma} + \beta/\sigma C_2^{-1/\sigma} \right). $$

Show that as \( \sigma \to 0 \), we approach \( C_2 = \beta C_1 \), which corresponds to the consumption pattern chosen under the Leontief utility function \( U_1 = \min(\beta C_1, C_2). $$