Given a production function f(x₁, x₂) = x ^1/3₁ x ^2/3₂

(a) Give an expression for the marginal product of x₁ at the point (x₁, x₂)

(b) Does the marginal product of x₁ increase, decrease or remain constant for small increases in x₁, holding x₂ fixed?

(c) Does the marginal product of x₂ increase, decrease or remain constant for small increases in x₂, holding x₁ fixed?

(d) Does an increase in the amount of x₂ increase, decrease or leave unchanged the marginal product of x₁?

(e) What is the technical rate of substitution between x₁ and x₂? (f) What type of returns to scale does this technology exhibit?