Suppose the production function is Cobb-Douglas and f(x1, x2) = x1/2 1 x3/2 2.
(a) Write an expression for the marginal product of x1 at the point (x1, x2). 1 /2x1−1/2 x 3/22.
(b) The marginal product of x1 (increases, decreases, remains constant) ______ for small increases in x1, holding x2 fixed.
(c) The marginal product of factor 2 is 3/2x1/21 x1/2 2, and it (increases, remains constant, decreases) ______ for small increases in x2.
(d) An increase in the amount of x2 (increases, leaves unchanged, decreases) ______the marginal product of x1.
(e) The technical rate of substitution between x2 and x1 is ______.
(f) Does this technology have diminishing technical rate of substitution?
(g) This technology demonstrates (increasing, constant, decreasing) ______ returns to scale.