For each of the following production functions, sketch a representative isoquant [2*3 points]. Calculate the marginal product for each input, and indicate whether each marginal product is diminishing, constant, or increasing (3*3 points). Calculate the marginal rate of technical substitution for each function (2*3 points). Also indicate whether the function exhibits constant, increasing, or diminishing returns to scale (2*3 points).
a. F(L, K) = LK3
b. F(L, K) = L + 3K
c. F(L, K) = min{L, K})1/3