Question

Please type or write legibly, show graphs, and show full work and I will give the question a tumbs up rating.

You are an analytics expert for the San Diego Padres professional baseball team hired to track player productivity of time spent in the team batting machine (ie., capital, K). You estimate the relationship between hours operating the batting machine (K) and player hours using the machine (L) as Q is Q = 50K^0.5*L^0.5 where Q is measured as player hitting production (eg., base hits, etc.) The Padres have experimented with a new computerized batting machine system that is supposed to improve training, you estimate the new batting machine has a production function QNew = 72K^0.5*1^0.5. Does the new batting machine improve the player's batting production (Q)? Explain. Sketch out the marginal product of L curves for both machines to help you answer the question

Answer 1

We have 2 Scenarios Scenario 2 Chi 72K" 72 KS Scenario 1 Q = 50 kos Los Now we need to find Marginal product Function for the 2 scenasios to see whether there is an improvement under scenario 2. So mpL: Marginal product for L MPL= ao First Derivative of Q with respect to 't gives PL — 22 Sog MPL = 20 Scenario Scenario 2 MPL New a new IL IL MP Low - 724 0.5ks l' = 25 Ko.5 » Los = 36koislois L in denominator raised to power 0.5. New 2MPL=25/k. MPL 36/k 50* 0.5 Kos los Taking 05 0.5 25%DUS Now For all values (same of course) (K/L) remains or gives same value but the coefficient of (k/Ljos is greater for MPL New. This implies that productivity of player's has improved due to new batting machine