Jack is a football player who earns $100 when he is young and $300 when old. Assume that his all lifetime can be summarized with these two periods i.e., the period when he is young and the period when is old. Also, let assume that the interest rate between two periods is equal to a constant, ??.
a) Please calculate both the present value and future value of Johnâ€™s total lifetime $ income as a function of ??.
b) Please write down the budget constraint of John and plot the budget set in the graph with a ?? = 200%. On the graph please demonstrate the endowment point, present value and future value of the $ income.
c) Please discuss the saving and borrowing points on the budget line (plot on the graph) for all the consumption plans.
d) Now assume that Johnâ€™s intertemporal preferences can be demonstrated as ??(??1, ??2 ) = ln(??1 ) + 1 1+?? ln(??2 ) and the discount rate is ?? = 2. Please make an economic interpretation of the constant ??. Find the optimal consumption and saving plan for John. Discuss if John smooths his consumption or not.