Paul values consumption in period 0 (co) and in period 1 (Cl) using u = In(co) + 0.8 In(cl). 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 (Yi) is 110. Paul does not pay

any taxes.

a)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)? Explain why it is not optimal for Paul to chocse the consumption plan co = yo and Cl = UI. Illustrate with a graph.

b)Find Paul's optimal consumption choice. Calculate so. Does Paul lend or borrow in period 0?

c)Suppose that Paul's income in period 1 increases by 11. Explain why Paul will not increase Cl by 11. What should he do?

d)Would an increase in the interest rate necessarily lead Paul to save more? Explain why or why not.