Answer to Question #42362 in Economics of Enterprise for Grace Ferguson
3. If a firm uses only capital and labour, show why the cost minimising combination of inputs sets:
MPK = PK
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Cost minimization is the process or goal of incurring the least possibleopportunity cost in the pursuit of a given activity. Cost minimization is comparable to other objectives, including utility maximization and profit maximization. This goal, however, is generally used when circumstances constrain a decision. For example, a government agency has been assigned the task of building a bridge. It must now do so at the lowest cost possible.
For a firm with N productive inputs, cost minimization requires that:
MP(1)/P(1)=MP(2)/P(2)=… MP(n)/P(n). This equation tells us that, to minimize cost, the additional output per dollar spent to employ one additional unit of each input must be the same.
For cost minimization and profit maximization, a firm must employ inputs in quantities such that: MRP(1)/P(1)=MRP(2)/P(2)=…=MRP(n)/P(n)=1. MRP is short for marginal revenue product, which equals to “MR*MC”.