$2.$ Suppose the representative consumer$$s preferences are such that consumption and leisure are

perfect complements, i$.$e$.$ the consumer sets always leisure and consumption equal C $=$ l$,$ where

again we denote leisure by l$.$ Lump$-$sum taxes are zero, but the consumer pays a proportional tax

$=0\mathrm{.}2$ on labor income. The wage rate is w $=1$ and the time endowment denoted h $=100.$ The

consumer receives non$-$labor income in the form of real dividends D $=10.$

a$.$ Solve for the consumer$$s optimal bundle showing your steps along the way. Show the optimal

choice visually in a diagram, which includes the numerical values given.

Next consider a situation where the government implements the following tax deduction: the

tax rate equals zero as long as labor income is less or equal to $20.$ After that, the tax rate on labor

income is $=0\mathrm{.}2.$

b$.$ Solve for the consumer$$s optimal bundle showing your steps along the way. Show the optimal

choice visually in a diagram, which includes the numerical values given. Explain your result in

terms of substitution and income effects

$**$ANSWER ALL PARTS ON PAPER BY HAND$**$