Exercise 1: Paul values consumption in period 0 (c0) and in period 1 (c1) using a : 1n(c0) + U.81n[c1). Paul can save or borrow at the interest rate r = 0.10. Denote net saving in period 0 by so. Paul's income in period 0 (yo) is 80 While that in period 1 (yl) is 110. Paul does not pay any taxes. a) Write down Paul's budget contraints in period 0 and in period 1. How many units of period 1 consumption does Paul have to give up to get an extra unit of consumption in period 0 (at the margin}? How many units of period 1 consumption is Paul ready to give up in order to get one more unit of consumption in period 0? b) Explain why it is not optimal for Paul to choose the consumption plan on yo and c1 : yl. Illustrate with a graph. c) Find Paul's optimal consumption choice. Calculate 30. Does Paul lend or borrow in period 0'? d) Suppose that Paul's income in period 1 increases by 11. Explain why Paul will not increase c1 by 11. What should he do? e) Would an increase in the interest rate necessarily lead Paul to save more? Explain Why or Why not