Question

$1200 $1100 Budget Line C = V+ WIT-L) $500 $100 70110 Hours of Leisure Hours of Work

What determines the number of hours worked or whether a worker enters the labor force at all? Be precise and stay within the assumptions and mechanisms of the model.

Answer 1

$1200 $1100 Budget Line C = V+ wT-L) $500 $100 Hours of Leisure Hours of Work

This model analyzes consumer choice between leisure and consumption, which is determined by the interaction of consumer's preferences and budget constraint. On the other hand, the consumer splits the available time into leisure and and work. The difference of the total available time and the optimal leisure level determines the labor supply or the consumer's decision to enter the labor market.

Let us look at the budget constraint, which is given as C = V + w(T-L), where C denotes spending on consumption, which is met by the income of the consumer. The income can come from two sources such as non-labor income (V) and labor income (i.e., the income earned by the consumer at market rate of wage, w). Total available time is denoted by T and total amount of leisure is denoted by L in the budget constraint. The difference between T and L is the amount of time the consumer chooses for labor and hence the total labor income is wage per unit of time (w) and total time for labor (T-L), i.e., w(T-L). Hence, the left hand side of the budget constraint shows the total spending and the right hand side shows the total income (non-labor and labor).

With this budget constraint, the consumer's objective is to maximize utility, which is determined at the tangency point of the budget constraint and the indifference curve. As shown in the figure, the budget constraint is tangent to the indifference curve U*, where the optimal level of leisure = 70 hours and optimal level of consumption spending is $500. As described above, the labor supply is determined as the difference of total hours available (110) and the total hours chosen for leisure (70). Hence, in the present case, the consumer is willing to spend 110-70 = 40 hours for work. The hours of work is also denoted by the x-axis but in opposite direction of the leisure. The total available hours can also be treated as the endowment of the consumer, which he may choose either to work or for leisure.