Sales and Profit - Input Ratios in the Firms Objective Function

It is argued that where static bicriteria models of the firm are specified with a profit-input ratio and sales (or output) in the managerial utility function, the normal restrictions on the managerial utility function, and on revenue and production functions, are insufficient in general to satisfy the relevant second order conditions for a utility maximum at the point where first derivatives are zero. The problem is at its most severe in the case of a linear objective function where it is shown that, for the C.E.S. production function, the second order conditions are never satisfied.