Course: Introduction to Economics We have the following production function Y = L^0.5K^0.5. In addition, the firm has a fixed capital of K = 1. This capital allows it to employ a maximum of 4 workers. a) Plot the production function and the average product, identify the maximum level of the average product and interpret your results economically. Identify, in addition, what is the associated marginal product of moving from the 3rd to the 4th worker, interpret your results economically. b) Point out, in addition, what is the associated marginal product of moving from the 3rd to the 4th worker, and from the 4th to the 5th, interpret your results economically. c) Now consider a short-run production function: Y = 6L - L², , with the same level of capital as before. The firm now does not have the 4 workers constraint, Graph the production function and the average product, identify when the latter is decreasing or increasing. d) Now consider a short-run production function, with the same level of capital as before: Y = 6L - L². The firm now does not have the 4 worker constraint, so it asks you to find the point up to which it is reasonable to add workers (Suppose the only condition imposed on it is that adding workers does not reduce output). Hint: PMgL = 6 - 2L