1. Suppose that δ = 0. Using the equations in (e), show that the consumer makes all planned durable purchases in one lump sum in the first period, and absent shocks, makes no further purchases thereafter.
2. Discuss the implication of (f) on the property of durable stock and durable expenditure in a linear-quadratic variant of this same simple case where income is stochastic. (Hint: You may want to look at the exercise 8.12 in Romer (4th edition).)