Product-mix Efficiency:

If the product-mix is inappropriate, then a change in it can help reach a Pareto-superior  allocation.  In  order  to ensure  Pareto efficiency, we need  to consider individual's preferences and  production possibilities together. The necessary condition to achieve  this is that the marginal rate of substitution for any two goods must be equal to the rate of product transformation of the two goods. Thus, consider that goods are X and Y; one individual (or, community) whose utility function is given by U(X,Y);  and  society's production possibility frontier is written as T(X,Y)=O. The problem is to maxmise utility subject to this  production  constraints. Setting up  the  Lagrangian  expression

we have,