suppose that the marginal product of the last worker employed by a firm is 40 units of output per day and the daily wage that the firm must pay is $20 while the marginal product of the last machine rented by the firm is 120 units of out put per day and the daily rental machine is $30.
a) why is this firm not max. output or min. cost in long run?
b)how can this firm max. output or min. cost in long run?
test
a) This firm is not maximizing output or minimizing cost in the long run because the ratio of the marginal product to the cost of the factors of production is not equal for both labor and capital. The marginal product of the last worker is 40 units per day, while the daily wage is $20. This means that the firm is paying $0.50 per unit of output for labor ($20 / 40). On the other hand, the marginal product of the last machine rented is 120 units per day, while the daily rental cost of the machine is $30. This means that the firm is paying $0.25 per unit of output for capital ($30 / 120).
Since the marginal product to cost ratio is higher for capital (0.25) compared to labor (0.50), the firm can reduce costs and increase output in the long run by reallocating resources, shifting more resources towards capital and reducing labor.
b) To maximize output or minimize cost in the long run, this firm can adjust the allocation of its resources by employing more machines and reducing the number of workers. By doing so, the firm can take advantage of the higher marginal product of machines while reducing labor costs.
For example, if the firm employs one machine and one worker, it currently pays a total of $50 ($20 for labor and $30 for machine rental) and produces a total of 160 units of output (40 units from labor and 120 units from capital). In this scenario, the average cost per unit of output is $0.31 ($50 / 160).
However, if the firm employs two machines and no workers, it would pay a total of $60 ($30 for each machine rental) and produce a total of 240 units of output (120 units from each machine). In this case, the average cost per unit of output is $0.25 ($60 / 240), which is lower than the previous scenario.
By increasing the use of machines and reducing reliance on labor, the firm can achieve a more efficient allocation of resources, leading to lower costs and higher output in the long run.