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An alternative approach to solving cost minimization problem with Cobb–Douglas technology

We propose a new method for solving the production cost minimization problem with Cobb– Douglas technology. The method is based on weighted arithmetic–geometric-mean inequality (weighted AM–GM) and it does not use calculus. In comparison to methods which use calculus (like substitution method or the Lagrange multiplier method), our method derives the global minimum costs and unique global minimizer in case of the Cobb–Douglas production function in a new and easier manner. Another benefit of this method is that it derives the exact formula for the optimal level of inputs as well as the formula for minimum costs in general case of n>2 inputs. Also, it is important to emphasize that our method does not require checking the first and the second order conditions, which is a necessary step in methods using calculus. The result is first derived for the case of two inputs and then generalized for the problem with n>2 inputs.

Economics ; Constrained optimization ; Cost minimization ; Cobb–Douglas technology ; Weighted AM–GM inequality M

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