Saving for the future. Consider the situation of an individual with current income of $3,000 and future income of $1,000. The interest rate is 10%. Preferences are given by U (ct,ct+1) = log (ct) + 0.8·log (ct+1).
(a) Write down the maximization problem for this individual.
(b) Solve the maximization problem and nd current consumption, future consumption and savings (or assets).
(c) What would be the consumption and savings decision if current income was $1,000 and future income $3,000?
(d) How would your response to parts (b) and (c) change if the interest rate were 20%?