Consider the production function given by q=(1+L^-1K^-1)^-1

(a) Determine the marginal products of labor and capital.

(b) Determine the marginal rate of technical substitution.

(c) Show that the given production function exhibits diminishing marginal products.

(d) Taking an appropriate limit, find the upper bound on q for the given production function.

(e) Determine the average product of labor and show that it is a decreasing function of labor employed.