**3.2 Utility function**

Assume that an individual can allocate his/her time between two activities: *work and leisure*. Assume that the total time the individual can allocate a day is *T*. Let *I* denote the hours of leisure the individual spends. The individual's hours of work are *T* � *I*. Choosing to work *T* � *I* hours at a given wage is equivalent to consuming *I* hours of leisure. Therefore, we can model either the individual's leisure demand or the individual's labor supply. We will model the individual's leisure demand here.

Assume there are two categories of goods that an individual can consume: *leisure and consumption goods*. We can describe the individual's preferences by an utility function

$$U = U(\mathbf{C}, I) \tag{1}$$

where *C* is the quantity of the consumption goods. The utility function measures the individual's satisfaction or happiness at any quantities of the consumption goods and the individual's leisure hours. In addition, we assume that buying more consumption goods or having more leisure hours both increase the individual's utility. **Figure 1** shows a typical indifference curve.
