Income Effect and utility

Ch 12 – Numerical Problem 6

Jake Goldstone is working 30 hours per week. His marginal utility of income is 2, his marginal utility of leisure is 60, and his hourly wage is $20. Assume throughout this problem that the income effect is zero.

1. Is Mr. Goldstone maximizing his utility?
2. Would working more or less increase his utility?
3. If his wage rose to $30 per hour, would he be maximizing his utility by working 30 hours per week? If not, should he work more or fewer hours?
4. At a wage of $40 per hour, would he be maximizing his utility? If not, would working more or less than 30 hours per week increase his utility?