Paul and Anita value consumption in period 0 (C₀) and in period 1 (C₁) using the same utility function u = ln(C₀)+0.8In(C₁). Paul's income in period 0 (y₀) is 102 while that in period 1 (y₁) is 132. Anita's income is 132 in period 0 and 99 in period 1. Both Paul and Anita pay 22 in taxes in period 0 and in period 1 (i.e. t₀=t₁= 22). Anita can borrow or save at the interest rater. However, everybody knows that Paul is dishonest; As a result, nobody is willing to lend to him. Of course, Paul can still save at the interest rate r. Suppose that r=0.1.

a) Determine how much money Paul would consume in period 0 and in period 1 if he was able to borrow. Determine his actual consumption in period 0 and in period 1. Illustrate both allocations on a graph. What is the cost of this credit constraint?

b) Determine Anita's optimal consumption plan. Find the value of so which allows Anita to achieve this plan.

Suppose that the timing of taxes is changed: taxes in period o are reduced to t₀= 12 while those in period I are increased to t₁= 33.

c) How does this change in taxes affect Anita's wealth? Does it change Anita's optimal decisions (C₀.C₁.S₀) from those in b)? Explain. Illustrate with a graph.

d) How does this change in taxes affect Paul's wealth? Does it change Paul's optimal decisions (C₀.C₁.S₀) from those in a)? Explain. Illustrate with a graph.

e) Does this change in the timing of taxes constitute a Pareto improvement? Explain