A non-calculus approach to solving the utility maximization problem using the Cobb-Douglas and CES utility function

Abstract

This paper proposes a new original non-calculus method to solving the utility maximization problem using the Cobb-Douglas and the CES utility functions, and incorporating the weighted arithmetic-geometric-mean inequality (weighted AM-GM inequality) and Jensen’s inequality. Instead of using calculus, the substitution method or the Lagrange multiplier method, the maximum utility and global maximizer for the case of the Cobb-Douglas and CES utility functions are derived in a direct way. The new method does not require checking first and second order conditions, which the substitution method and the Lagrange multiplier method normally require.