Question

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.

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.

Answer 1

c) Before:

$132-22+99-22=187$

after

$132-12+99-33=186$

She lost 1

$u=ln110+0.8*ln77=818$

$u^*=ln120+0.8ln66=8.14$

u^*-new value

d) Before:

$102-22+132-22=190$

after

$102-12+132-33=189$

He lost 1

$u=ln80+0.8*ln110=8.14$

$u^*=ln90+08*ln99=8.18$