The production function is Q = ALaKb, where a > 0 and b > 0.
a. The marginal product of labor is MPL =
b. The marginal product of capital is MPK =
c The marginal rate of technical substitution is MRTS =
d. Show that the isoquants for this production function are convex. [hint: Show that MRTS diminshes as L increase. Why?]
For the production function above let the price of labor be w and the price of capital be r.
a. the efficient usage function for labor is L* =
b. The efficient usage function for capital is K* =
c. Find the long run cost functions. LTC, LAC, and LMC
d. Show that both LAC and LMC increase at any Q when either w or r increase.