Question

Say there is labour market where the labour demand curve of VMP=100-Ld where VMP is the value of marginal product. The labour supply of adults is 30 and there are also 40 children. The effective labour supply of each child is equivalent to half and adult. If the wage falls below 60 all adults will send their children to work. What is the equilibrium in the labour market?

Answer 1

The equilibrium in the labor market described would be at a wage rate at or above 60, taking into account the fixed adult labor supply of 30 and the additional child labor that would come into play if wages fall below 60.

Step-by-step explanation:

Equilibrium in the Labor Market

Considering the labor market with a labor demand curve described by VMP=100-Ld, where VMP is the value of marginal product and Ld is the quantity of labor demanded, we can determine the market equilibrium. The labor supply of adults is fixed at 30. In addition, there are 40 children, with each child's effective labor supply equivalent to half an adult. If the wage were to fall below 60, all adults will choose to send their children to work, effectively doubling the labor supply with children's lower productivity adjusted.

To find the equilibrium, the supply of labor must equal the demand for labor. In this situation, the equilibrium wage must be set at a rate where no additional workers (adults or children) would enter or leave the market. Considering the scenario provided, all adults will send their children to work if the wage falls below 60, suggesting that the equilibrium wage must be at or above 60 to prevent the influx of children into the labor force.

To calculate exact equilibrium, we set the VMP equal to the wage and solve for Ld. With the presence of only adult workers (30), at a wage of 60, the demand would be VMP=100-Ld, Ld = 40 (100-60). However, if wages drop, children will enter the market, and the calculation will be different since each child is equivalent to half an adult. The effective adult-equivalent labor supply would then be 30 adults + (40 children * 0.5) = 50.

Answer 2

The equilibrium in the labor market is reached when the wage is set at 50, where both adults and children will be working, with adults supplying 30 units of labor and children supplying an effective additional 20 units.

Step-by-step explanation:

The labor market equilibrium involves finding the wage and quantity of labor where the supply equals demand. According to the given labor demand function VMP = 100 - Ld, the value of marginal product (VMP) decreases with an increase in labor demand (Ld). The labor supply of adults is fixed at 30. Children will only enter the workforce if the wage falls below 60, with each child supplying the equivalent of half an adult's labor. This creates an effective labor supply increase of 20 (40 children * 0.5) when wage is below 60.

To find the equilibrium, we set the VMP equal to the wage. Without children in the labor force, equilibrium is when VMP = 100 - Ld = wage. For adults alone, this would be 100 - 30 = 70. However, the question states that if the wage falls below 60, the children will enter the labor force, which implies that the adult labor supply equilibrium wage of 70 is not possible as it does not trigger child labor. So, we then consider the child labor being added to the supply. Thus, we need to solve for 100 - Ld = wage, where Ld now includes the adult and effective child labor supply, which would be 30+20 = 50. Hence, the equilibrium wage will be 100 - 50 = 50. At a wage of 50, all adults and children will be working.