Consider the monthly production function P(8.c) = 58/21/3+ where e represents the labor in worker-hours, c represents the capital in thousands of dollars and P the production in hundreds of units. It is okay to approximate values on a calculator in this exercise, but show all steps of computations (partials, differentials, elasticities...) (a) Find and interpret the partial elasticity of production with respect to labor when the labor is 1024 worker-hours and the capital is 27000 dollars.
(b) Suppose that we are at the same levels in part (a), and we are trying to decide between:
• increasing labor by 10 worker-hours while decreasing the capital by 500 dollars, or
• decreasing labor by 5 worker-hours while increasing the capital by 2500 dollars.
Use differentials to tell which choice, if any, is better. Clearly explain why.