Link between Factor and Goods Markets:

The linkage between factor and goods markets is given by

This equation  says that the marginal rate of substitution in  consumption must be equated with the marginal rate of transformation.

If the marginal utility of X is relatively high  (relative to Y),  then we want the marginal product of K  in  production of Y  to be relatively low (relatilie  to the marginal product of K  in Y). The reason  is  that  if we  get more utility  from consumption  of X  at the margin, we must  be willing to  allocate relatively more K  to its production.

The marginal condition is satisfied because of the tangency condition between the community indifference curve and the PPF. That is,

MRTS (X for Y) = MRPT (X  for Y).

If you  consider shifting one unit of K  from  the production of X  to that of Y, then using PPF we get