Suppose x1 and x2 are used in fixed proportions and f(x1, x2) = min{x1, x2}.
(a) Suppose that x1 < x2. The marginal product for x1 is _______and (increases, remains constant, decreases) _______for small increases in x1. For x2 the marginal product is _______, and (increases, remains constant, decreases) _______for small increases in x2. The technical rate of substitution between x2 and x1 is _______. This technology demonstrates (increasing, constant, decreasing) _______ returns to scale.
(b) Suppose that f(x1, x2) = min{x1, x2} and x1 = x2 = 20. What is the marginal product of a small increase in x1? _______. What is the marginal product of a small increase in x2? _______. The marginal product of x1 will (increase, decrease, stay constant) _______ if the amount of x2 is increased by a little bit.