Question

4. Consider the production functions given below: a. Suppose that the production function faced by a milk producer is given by Q = 40.5 20.5 = 4VK VL, where MPx = 2K-0.5 20.5 = 2 and MP, = 2 K0.5L-05 = 2 * 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 MRTS = 1) iii. Does this production function display a diminishing marginal rate of substitution? --- Capital (K) - - - iv. Graph isoquants for Q = 4, Q = 8, and Q = 12. Put capital on the y-axis and labor on the x-axis. ----- - ---L----- - - - - - - --- --- - - 1 1 8 12 16 20 N Labor (L) b. Suppose that the production function faced by a cheese producer is given by Q = 4KL, where MPx = 4L and MP, = 4K 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. iii. Does this production function display a diminishing marginal rate of substitution? Capital (K) iv. Graph isoquants for Q = 4, Q = 8, and Q = 12. Put capital on the y-axis and labor on the x-axis. 0 5 10 20 25 30 15 Labor (L)

Answer 1

WUN 17 wasi) mpr - 2K-0.5 10.5 - 8 h 1/ 2 1/2 , 3/2 d (mpk- - 2K dk IL broducts in the Capital displays diminishing marginal prodeects in the short sun. MPL = 2 Ko 5 Lois d (MPL) - kºs_6 < 2. Lobor displays Limnishing marginal short rum. ii) mats MP 2K015 L-og 14) ak-0.5 0.5 MOTS2 K/L i d(mors - - K/ r To. .. the production Bunetion displays diminishing marginal rate of substitution iny RTS dL . KL 16 /0 (4) (16) satisfying 8 2 4 40.5 10.5 12