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Producers Equilibrium or Optimal Combination of Inputs
The analysis of production function has demonstrated that alternative combinations of factors of production that are technically efficient can be used to produce a given level of output. Of these, firm will have to choose that combination of factors that will cost it the least. In this way firm can maximise its profits. Choice of any particular method from a set of technically efficient methods is an economic one and it's based on the prices of factors of production at a specific time.
Firm can maximise its profits either by maximising the level of output for a given cost or by minimising the cost of producing a given output. In either case, factors would have to be used in optimal combination at which the cost of production will be minimum.
There are two ways to determine the least cost combination of factors to produce a given output. Which is,
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p=10, TC= 1000+2Q+.01Q^2, Q=?
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