Jerusha, a woodworker, builds coffee tables using both labor (L) and tools (capital, or K). Her production function for coffee tables is a Cobb-Douglas production function: Q = 4 K5 L5.
a. Can Jerusha build any coffee tables without tools?
b. Can Jerusha completely mechanize coffee table production?
c. Jerusha currently has 16 tools, and in the short run can neither acquire more tools nor sell existing tools. Her woodshop is capable of holding up to 49 employees. What is Jerusha's short-run production function?
d. Graph the production function you found in (c), with labor on the horizontal axis and output on the vertical axis.
e. Determine the average and marginal products of labor at each level of labor you worked with in (d).
f. Suppose that overnight, 7 of Jerusha's machines fail. Show what happens to the total, marginal, and average products of labor as a result.