$($Bascd on Chapter $2,$ Problem $1$ of Benjamin ct al$.,2031)$ Amit has $$2000$ of annual non$-$labour income. He has $80$ hours per week that he can allocate between labour and leisure, for $8052=4160$ hours per year. His current wage rate is $$20$ per hour and he chooses to work $2200$ hours a year.

$($a$)$ Draw a leisure$-$labour diagram, clearly indicating Amit's current labour supply decision. $($Your diagram should be clearly labeled and include Amit's budget line and an indifferent curve showing his leisure and consumption of goods and services at his optimal choice. Use the figures provided to find the y$-$intercept and his consumption if he doesn't work.$)$

$($b$)$ Amit's wage rate increases to $$25$ per hour. In response, he increases his labour supply to $2300$ hours. If he were "compensated" accordingly, ${?}^1$ at this new wage rate he would be just indifferent to working $2200$ hours at his original wage rate and working $2400$ hours at the new wage. Illustrate Amit's new optimal choice. Use the information provided in the previous sentence to determine whether leisure is a normal or an inferior good for Amit.