Solving the utility maximization problem with CES and Cobb-Douglas utility function via mathematical inequalities

Sa？etak This paper presents a new, non-calculus approach to solving the utility maximization problem with CES utility function, as well as with Cobb-Douglas utility function in case of n≥2 commodities. Instead of using the Lagrange multiplier method or some other method based on differential calculus, these two maximization problems are solved by using Jensen's inequlity and weighted arithmetic-geometric mean (weighted AM-GM) inequality. In comparison with calculus methods, this approach does not require checking the first and the second order conditions