Stages of Production - Law of diminishing Returns

Problem
2. A firm has following short-run production function:
Q=50L+6L^2-0.5L^3
Q=quality of output per week
L= number of worker
a. When dose the law of diminishing returns take effect?
b. Calculate the wage of the values for labor over which stage I, II, and III occurs.
C. Assume each worker is paid $10 per hour and works a 40-hours week. How many workers should the firm hire if the price of the output is $ 10? Suppose the price of the output falls to $7.50.What do you think would be the short-run impact on the firm's production? The long-run impact?

Problem
1. Indicate whether each of the following statement is true or false. Explain why.
a. when law of the diminishing returns takes effect, firm's average product will stats to decrease.
b. Decreasing returns to scale occurs when a firm has to increase all its input at an increasing rate to maintain constant rate of increase in its output.
c. A linear shot-run production function implies that the law of diminishing returns dose not take effect over the range of the output being considered.
d. Stage I of the production process ends at the point where the law of diminishing returns occurs.

Solution Summary

Solution explains the stages of Production for a given algebric non-linear production function. Marginal Product, Average Product and their optimum values are worked out by the use of calculus.
In second part short discussion type questions are explained about Marginal Product, Average Product, Stages of Production.