6.9. Suppose the production function for automobiles is Q = LK, where Q is the quantity of automobiles produced per year, L is the quantity of labor (man-hours), and K is the quantity of capital (machine-hours). a. Sketch the isoquant corresponding to a quantity of Q = 100. b. What is the general equation for the isoquant corresponding to any level of output Q? c. Does the isoquant exhibit diminishing marginal rate of technical substitution? 6.10. Suppose the production function is given by the equation Q = L+/K. Graph the isoquants corresponding to Q = 10, Q = 20, and Q = 50. Do these isoquants exhibit diminishing marginal rate of technical substitution? 6.11. Consider again the production function for DVDs: Q = KL? - L3. a. Sketch a graph of the isoquants for this production function. b. Does this production function have an uneconomic region? Why or why not? 6.13. You might think that when a production function has a diminishing marginal rate of technical substitution of labor for capital, it cannot have increasing marginal products of capital and labor. Show that this is not true, using the production function Q = K2L?, with the corresponding marginal products MPg = 2KL? and MPy, = 2K2L