A firm has the following short-run production function:
Q = 100L + 10L2 - 0.7L3
Where Q = quantity of output per week; L = Labor (number of workers)
a. When does the law of diminishing returns take effect?
b. Calculate the value for Stage I in the production process?
c. Assume the firm hires 10 workers, each worker is paid $800 per week, and the price of output is $15 per unit sold. Determine whether the firm is maximizing profit, or in other words, using the optimal amount of their input (labor).
d. Given the answer to part c, what is your recommendation to the firm if their objective is profit maximization?
I assume L2 means l squared, and L3 means L cubed.
Q=100L + 10L^2 - 0.7L^3
dQ/dL= 100-20 L -3.1L^2
to maximize profit, set to zero, and solve for L. If the 10 workers are not equal to L, the firm is not maximizing.
3 answers
3 answers