. Suppose that you have won the lottery and will receive 100 pounds this year and another 100 pounds in a year from now. The annual interest rate is 15% (R = 0.15). The lottery ticket says that you have won 200 pounds. Is this statement correct? What is the present discounted value of what you won? . You are offered two options: you can receive 50 pounds this year or 60 pounds in a year from now (again, R = 0.15). Which of the two options is preferable? Explain. . Suppose that the interest rate is 25% (R' = 0.25). Which of the two options is prefer able now? Explain any difference from your answer to the previous question. Consider an agent who lives for two periods. His income is Y1 in the rst period and Y2 in the second period. In period 1 he decides how much to consume Cl, and how much to save, S. His second period consumption is denoted by C2. Savings are invested and earn interest rate R. There are no taxes. . Write down the agent's period 1 and period 2 budget constraints separately and then combine them to get his lifetime budget constraint. . Suppose that Y1 = 90, Y2 = 110 and R = 0.2. Calculate the lifetime income of the agent (i.e. the present value of his current and future labour income) and denote it by W. . For this question only suppose that in the rst period the agent receives a bonus which is equal to 15% of rst period's income. Calculate his new lifetime income W'. Did it also increase by 15%? Explain why or why not. . Draw the agent's lifetime budget constraint on a graph with period 1 consumption on the horizontal axis and period 2 consumption on the vertical axis. Denote the agent's endowment point by E. This is the point on the budget constraint where the agent's consumption is exactly equal to that period's income (i.e. the point where saving and borrowing is equal to zero)