Question

The production function in an economy is:

Y=4(3.00N−0.0064N²).
where the marginal product of labor is given by:
MPN=4(3.00−0.0128N)
The equation for the labor supply curve is:
NS=62.0+15(1−t)w
where NS is the amount of labor supplied, w is the real wage and t is the tax rate on wage income. The tax rate is t=0.25.
Determine the labor demand function. (Enter your responses rounded to two decimal places):
ND= ___-____w.

Answer 1

The labor demand function is derived from the value of the marginal product of labor, which equals the real wage in a competitive market. By setting the marginal product of labor equal to the real wage and rearranging the equation, we find the labor demand function to be ND = 234.375 - 19.53w.

Step-by-step explanation:

The labor demand function reflects the relationship between the quantity of labor demanded by firms and the real wage rate. In a perfectly competitive labor market, the demand for labor is determined by the value of the marginal product of labor (VMPL), which is the additional revenue a firm earns from employing one more unit of labor. Since real wage (w) should equal VMPL and we are given that marginal product of labor MPN is 4(3.00 - 0.0128N), we can find the demand for labor.

To calculate the demand function, we need to find N in terms of w:

1. Firstly, set MPN equal to w: MPN = w
2. So, 4(3.00 - 0.0128N) = w
3. Divide both sides by 4: 3.00 - 0.0128N = w/4
4. Finally, rearrange the equation to solve for N: N = (3.00 - w/4) / 0.0128 which simplifies to N = 234.375 - (w/0.0512).

Therefore, the labor demand function is ND = 234.375 - 19.53w, where ND represents the quantity of labor demanded and w represents the real wage.