5. Consider the following three production functions: f(K,L) = KZL f(K,L) = Km'Ll/3 f(K,L) = 2K + L a) In the (K,L) space, sketch the map of isoquants for each of them. b) Give some economic interpretation for MPK and MPL (for an abstract production function). c) Find analytically MPK for each production function above and plot it in the graph, with K on the horizontal axis and MPK on the vertical axis, assuming L = 1. Is MPK increasing, decreasing or constant? d) Find MPL for each of the four production functions and plot it on the graph, with L on the horizontal axis and MPL the vertical axis, assuming K = 2. Is MPL increasing, decreasing or constant? e) Provide some economic intuition behind increasing, constant and decreasing returns to scale. Give an example of technology from real life that captures each ofthe three cases (one example per technology). f) For each of the three production functions above, show formally whether it exhibits increasing, decreasing or constant returns to scale