Preferences are given by U (ct, ct+1) = log

Consider the situation of the 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 A?· log (ct+1)

(a) Write down the maximization problem for this individual.

(b) Solve the maximization and find current consumption, future consumption and savings (or assets)

(c) What would be the consumption and saving decision if current income was $1,000 and future income $3,000

(d) How would your response to part (b) and (c) change if the interest rate were 20%?