The Marginal Productivity of Labor (MPL) is defined as dY/dL, meaning it measures how much more output (Y) is produced with one more additional unit of Labor (L). Likewise the Marginal Productivity of Capital (MPK) is defined as dY/dK, meaning it measures how much more output (Y) is produced with one more additional unit of Capital (K). MPL and MPK respectively are equal to wage and to rent given our assumption that compensation equals productivity.
Given the following information please find the wage and rent rate: Y=1/2L1/4K3/4 and L=64 and K=256