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I own two [fixed] plants and can within limits increase [decrease] a plant’s output by using...

I own two [fixed] plants and can within limits increase [decrease] a plant’s output by using more of a variable input. To minimize my total costs of a given output I should allocate the input between plants so that both are operating at the same marginal cost. Yes or no?Explain

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The marginal cost should be same in both the plants in order to minimise the cost of production. suppose that marginal cost in one plant is greater relative to the marginal cost in another plant. Then it would be better to produce in the second plant where the marginal cost is relatively lower. As production is increased, we know that marginal cost will go up in the second plant. Also production is decrease in first plant so that marginal cost will decline. Eventually declining marginal cost in first plant and rising marginal cost in the second plant will result in equalization of the marginal cost in the two plants. Therefore cost minimising allocation of inputs will result in same marginal cost in both plants.

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