4. The production function for a firm is given by:Q=L2K

Where L denotes Labor (measured in hundred man hours), K capital (measured in numbers of equipments) and Q the amount of output. The wage rate of labor is denoted by w and the rental rate for capital is given by r.

(a)Show whether or not the above production function exhibits diminishing returns (with respect to labor).

(b)Calculate the output (or production) elasticity with respect to labor.

(c) Determine the nature of returns to scale.

(d) Determine the long run cost function for this production function in terms of w, r and Q.