Stolper-Samuelson Theorem:

To  determine the effects  of  changes  in  output prices  on  factor prices we differentiate the above two cautions with respect to prices. We have,  

That  is, if  one  industry  is more labor  intensive  than  the other, the  above comparative  - statics  result is well defined.
For example, suppose industry-l  is labor intensive,  then

These  results are known  as the Stolper-Samuleson theorem. Essentially, the insight thrown by  these is:  if the price of labor-intensive industry is increased, nominal wage  rate will rise whereas  capital  rental  rates will  fall. Generally speaking, the price of a factor of production will rise  if the output price of the industry,  in which that factor is most intensively used, rises;  it will  fall if  the output price of the  industry, which  is  less intensive  in  that  factor,  increases.

Let us now present this diagrammatically.

Consider an  increase in P₁/P₂ such  that the price line (t₁) is steeper than (t₂).  In a full employment economy, efficient  production point moves from C to D such that production of y_l  rises and y₂  falls. Correspondingly,  the economy moves from  E₀  to E₁  along the contract curve O₁ O₂. Due  to CRS, along any  ray through  the origin  MRTS₁₂  is  the  same.  Thus,  we  have

. Given  diminishing MRTS,  along  on  isoquant we 4 W have is the optimum point, we get

 rises. Thus, producers in both sectors

substitute K for L. The increase in capital intensity implies MP_L  rises and MP_k falls in both the sectors. Profit maximisation requires, MP_L  =  real wage to rise and MP_K  =  real rental to fall.