In the two-period model of consumption and saving, assume that individuals can borrow/lend at an interest rate r > 0. Suppose that there are two consumers, = {1,2}, with utility functions given by (i,'i) = ln i + ln i.

Solve for consumer's optimization problem.In the two-period model of consumption and saving, assume that individuals can borrow/lend at an interest rate r > 0. Suppose that there are two consumers, = {1,2}, with utility functions given by (i,'i) = ln i + ln i.

a.) Solve for consumer's optimization problem.

b) Given = 0.8 , (1,1') = (100,120),(2,2') = (120,100), (,') = (20,10), and = 10%. Calculate the optimal consumption bundle (, ') and savings for each consumer.

c) Suppose that the real interest rate decreases to 5%.

(i) Determine the optimal consumption bundle for consumer 2.

(ii) Illustrate the effect(s) of the change for consumer 2 on a diagram. Ensure that you carefully label the income and substitution effect of the change.

(iii) Which effect dominates in this case, income or substitution effect? Justify your decision.