Laura (of Luke and Laura’s Itty-Bitty Drink Umbrella Inc.) is trying to decide how many workers to hire. The Itty-Bitty Drink Umbrella production function is given by: Q = 6L^(1/3)K^(1/2). The price of output is p, the wage rate is w, and the rental rate for capital is r.
Is labor demand more elastic in the long-run or the short-run, and WHY? Show the math and explain why your answer in words.