Mr$.$ Joseph Average$$s utility function is

U$($s$,$ m$)=$ s $$ m$,$

where s is time per day spent on leisure and m is his daily income. Joe can spend at most

$24$ hours per day on leisure, and the time that is not allocated to leisure is the time he

spends on work. Joe gets all of his income by working for an hourly wage of w$.$

$($a$)$ What is the labor supply and corresponding income that maximise Joe$$s utility. $[$Hint:

For the budget constraint use the fact that a day has $24$ hours and that Joe works all

the time that he does not spend on leisure.$]$

$($b$)$ The government introduces a $10\%$ income tax. How does this affect Joseph$$s labor

supply decision?