Allocative Efficiency:

Note that resources must be allocated in efficient way such that overall productive efficient is ensured. That is, the marginal physical product of any resource in  the  production of particular good is the  same irrespective of  the firm producing it.

The cost of one more unit of X therefore is best measured as the rate of product transformation (RPT) of X for Y  at the prevailing point on  the PPF.

Suppose  that two firms are producing the same good  (X) and their production functions are given as  

Assume that total  supplies of capital and  labour are given by  K and  z.  The allocation problem  is then to maximise