Problem 1 (Production Function) Consider the following three production functions; f(K, L) = KZL f(K, L) = K(1/3)L(1/3) f(K, L] = 2K + L a.) In the (K, L) space1 sketch the map of isoquants for each of them. It) Find analitically M PK for each production function above and plot it in the graph, with K on the horizontal axis and M PK on the vertical axis, assuming L = 1. Is M PK increasing, decreasing or constant? c.) Find MPL for each of the four production functions and plot it on the graph, with L on the hurizontal axis and MPL on the vertical axis, assuming K = 2. Is MPL increasing, decreasing or constant? an example of technology from real life that captures each of the three cases (one example per technology). d) For each of the three production functions above, show formally whether it exhibits increasing, decreasing or constant returns to scale