Với hạn chế thanh khoản ràng buộc, tăng thu nhập, mặc dù hoàn toàn dự đoán, ảnh hưởng đến tiêu thụ chỉ khi nó thực sự Một lý do khác nhau về sự nhạy cảm quá mức, dựa trên động cơ tiết kiệm phòng ngừa, sẽ được phân tích trong mục | CONSUMPTION 43 Exercise 8 Suppose that labor income y is generated by the following stochastic process yt Xyt 1 xt 1 S1t Xt S2t where xt S2t does not depend on its own past values xt 1 xt 2 . and E s1t S2t 0. xt 1 is the only additional variable realized at time t 1 which affects income in period t besides past income yt 1. Moreover suppose that the information set used by agents to calculate their permanent income ytP is It 1 yt 1 xt 1 whereas the information set used by the econometrician to estimate the agents permanent income is fit 1 yt 1 . Therefore the additional information in xt 1 is used by agents in forecasting income but is ignored by the econometrician. a Using equation in the text lagged one period find the changes in permanent income computed by the agents AytP and by the econometrician AytP considering the different information set used It 1 or t 1 . b Compare the variance of AytP e A ytP and show that the variability of permanent income according to agents forecast is lower than the variability obtained by the econometrician with limited information. What does this imply for the interpretation of the eXcess smoothness phenomenon Exercise 9 Consider the consumption choice of an individual who lives for two periods only with consumption c 1 and c 2 and incomes y1 and y2. Suppose that the utility function in each period is ac b 2 c2 for c a b u c . a2 2b for c a b. Even though the above utility function is quadratic we rule out the possibility that a higher consumption level reduces utility. a Plot marginal utility as a function of consumption. b Suppose thatr Ò 0 y1 a b and y2 is uncertain a b a with probability a b a with probability . Write the first-order condition relating c1 to c2 random variable if the consumer maximizes expected utility. Find the optimal consumption when a 0 and discuss the effect of a higher a on c 1. FURTHER READING The consumption theory based on the intertemporal smoothing of optimal consumption paths builds on
