4. Details on Deaton's paradox. Consider the linear-quadratic stochastic consumption model, in which (1+r) = 1 and G = 1 = 0 on all dates.

(a) Use the current account identity together with consumption equation (32) in the text to show that the change in consumption is the present value of changes in ex- pected future output levels, C+1 - C = 1+ . (...) 3-(1+1) (E1+1 - E) Ys In this equation, for any variable Xs, (E+1-E)X, denotes the amount by which expectations of X, are revised as a result of information that arrives between dates t and +1. (Here, the change in consumption automatically equals the unexpected change or innovation in consumption, due to Hall's random walk result.)