Restricted Maxima and Minima And Lagrange Multipliers
Often we are faced with a problem in which we wish to maximise a certain function subject to certain restrictions, or conditions. For example, we may wish to maximise utility subject to the restriction that our total spending does not exceed a certain amount; or to maximise net revenue subject to the condition that the total labour force is kept constant. Problems of this kind can be solved by using the method of Lagrange’s Undetermined Multipliers. Although we shall not prove the validity of this method, the principle of its application is quite simple. In this chapter we shall state the principle generally, and illustrate it with a reasonably simple numerical example, before using the principle to consider a problem in economic theory.
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