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+r +1 (1) 8-(1+1) (Ex+1-E)Y.