Consider an economy with two goods, consumption c and leisure l, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to l= 24?h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of ? percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function