For the Cobb-Douglas production function q (K, L) = AKL-a prove that it is subject to the three properties of linearly homogeneous production functions, i.e., 1. APL and APK are both function of the capital-labor ratio k alone. 2. MPL and MPK are both function of the capital-labor ratio k alone. 3. Euler theorem - if we pay for each input a price equal to its marginal product exactly, we get output, i.e., K.MPK + L. MPL = q