Final answer:
Option 3 is the relevant true statement: an increase in labor input (L) by 1 percent leads to an increase in output by a percentage corresponding to the exponent of labor in the Cobb-Douglas production function, which may not equate to 1 percent. The marginal product of labor does not have a fixed value of 1 and neither does the average product of labor have a fixed value of 2.
Step-by-step explanation:
In the context of a Cobb-Douglas production function, it is not accurate to say that the marginal product of labor (MPL) is equal to 1, nor that the average product of labor (APL) is equal to 2 as a general statement. The Cobb-Douglas production function is characterized by variable factor proportions, where the output elasticity with respect to labor depends on the exponent of labor in the function. The correct statement from the options provided would be that if the amount of labor input (L) is increased by 1 percent and all other factors remain constant, the output will increase by a proportion that corresponds to the exponent of labor in the production function, which is not necessarily 1 percent.
The value of the marginal product (VMP) of labor is the market price of the output multiplied by the MPL, and it decreases as additional labor is employed due to diminishing marginal returns, assuming other factors like capital are held constant. In a perfectly competitive labor market, the firm can hire all the labor it wants at the market wage. The profit-maximizing level of employment occurs where the market wage equals the VMP of labor.