Optimal production and consumption mix:

Let, every individual of the society has preference function. A social welfare function (SWF) is a function of utility of all the members of the society.

Thus, it is in  turn a function of the output level.

Plotting  the SWF  in output space as is done in Figure we get the different possible social utility corresponding  to the different output mix. Optimality is achieved when SWF  is tangent to production possibility locus.  

Mathematically, Let the SWF be given w = w (y₁, y₂) Then the optimisation problem to find equilibrium point E is-
maximise  w (y₁, y₂)
subjectto,  G(y₁, y₂)=0; y₁, y₂ ≥ 0

where G is the production possibility locus.