Examine the Cobb-Douglas production function f(x₁,x₂) = x₁^(1/2)*x₂^(3/2)

• (a) Solve for the marginal products of both inputs.
• (b) Demonstrate whether the marginal products are increasing, decreasing, or constant with respect to the amount of each respective input.
• (c) Show whether the marginal product of each input is increasing, decreasing, or constant with respect to the amount of the other input.
• (d) What is the technical rate of substitution of the inputs? Is it decreasing?
• (e) proof whether the scale of production of this technology is increasing, decreasing, or constant.