Link between Goods and Factor Prices:

The link between prices of goods and prices of factors can be seen from

Note that we can write the analogous equations for  P_K,  P_L  in the production of Y rather than X.
These equations indicate that  P_x,P_L,  reflect the marginal contribution of K,  L to consumer utility though their production of consumer goods X and Y. So in short these equations say,

Remember  that consumers  do  not  obtain utility  from  capital  and labour. However,  the prices  of K  and  L,  reflect  the  'indirect  utility'  generated by capital and labour through transformation into X and Y, which are consumed.