for a multiplant monopolist what is the first order condition for minimising total cost subject to producing a given output
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If the monopolist produces his product in more than one plant, then his organisation is called a multi-plant monopoly. We shall now discuss how the multi-plant monopolist would determine the quantity of output to be produced with a view to earning the maximum amount of profit.
For the sake of simplicity, we shall assume that the monopolist produces his output in only two plants. Let us first see how he would distribute the production of any particular quantity of output (q) between the two plants, so that the cost of production may be minimum. The total cost (C) of producing any particular quantity of output, q, is
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