4. Consider the production functions given below: a. Suppose that the production function faced by a cheese producer is given by Q = 2K L, where M PK = 2L and MPL = 2K. i. Do both labor and capital display diminishing marginal products in the short run? ii. Find the marginal rate of technical s substitution for this production function. . . . . 4 111. Does this production function display a diminishing marginal rate of technical 3 substitution? 2 1 0 OHde'U'Ei-DF'DOOWOHNMTI'U'! HHHHHH . . L 1v. Graph isoquants for Q : 6, and Q = 10. Put capital on the y-axis and labor on the x-axis. Label the isoquants with their quantities. v. What are the returns to scale for this firm? Explain. b. Suppose that the production function faced by a milk producer is given by Q = 2K 0'51.\"5 = 24? x/E, _ v'f _ J? _ 0.5 0.5 _ _ _ 0.5 0.5 _ _ whereMPKK L RandMPL K L _v'E' i. Do both labor and capital display diminishing marginal products in the short run? ii. Find the marginal rate of technical substitution for this production function. (Hint: The M RTS = %. K iii. Does this production 20 function display a diminishing i3 marginal rate of technical 17 substitution? i2 14 13 12 11 x 10 9 3 7 6 5 4 3 iv. Graph isoquants for Q : 3 6, and Q :10. v. What are the returns to scale for this rm? Explain