Suppose a firm's production function is given by: Q = (L^3/2)(K^1/2) The firm employs workers at a wage of w = 10 per unit, and capital at a rental rate of r = 40 per unit.

(a) Write the equation for the isoquant for Q=20. Graph this isoquant. I'm just looking for the general shape on the graph.

(b) If K is fixed at 4, compute the marginal product of labor. Does this production function exhibit diminishing marginal returns to labor? Explain briefly how you can tell. (

c) Suppose with K = 4, the firm plans to produce 20 units of output. How much labor is required? What is the total cost of producing 20 units of output? (Look at the cost of the inputs employed).

(d) What is the marginal rate of technical substitution for this production function? (e) What are the returns to scale for this production function?