Monday, September 25, 2017

Optimal use of an input in production process

Under adverse economic conditions, managers face the decision of whether to cease production of a product altogether, that is, whether to shut down. Although the choice may appear obvious (shut down if the product is generating monetary losses), a correct decision requires a careful weighing of relevant options. These alternatives differ depending on the firm’s time horizon. In the short run, many of the firm’s inputs are fixed. Suppose the firm is producing a single item that is incurring economic losses—total cost exceeds
revenues or, equivalently, the average total cost exceeds price. Figure displays the situation. At the firm’s current output, average cost exceeds price: AC>P*;
Thee firm is earning a negative economic profit. Should the firm cease production and shut down? The answer is no. To see this, write the firm’s profit as
















           
π= (R-VC)-FC=(P-AVC)*Q-FC

The first term, R _ VC, is referred to as the product’s contribution. As long as revenue exceeds variable costs (or, equivalently, P>AVC), the product is making a positive contribution to the firm’s fixed costs. Observe that price exceeds the average variable cost in Figure (The average variable cost curve is U-shaped and it lies below the AC curve because it excludes all fixed costs.)
Therefore, continuing to produce the good makes a contribution to fixed costs. (In fact, output Q* delivers maximum contribution because MR _ MC.) If instead, the firm was to discontinue production (Q _ 0), this contribution would be lost. In the short run, the firm is stuck with its fixed costs. It will incur these costs whether or not it produces output. If the firm shuts down, its profit
will be   π = FC. (The firm will earn no revenues but will pay its fixed costs.)
In sum, the firm should continue production because the product generates a positive contribution, thereby minimizing the firm’s loss. The firm suffers an economic loss in the short run; nevertheless, this is better than shutting down. 
      Thus, we have the following general rule: In the short run, the firm should continue to produce as long as price exceeds the average variable cost. Assuming it does produce, the firm maximizes contribution
(and minimizes any losses) by setting marginal revenue equal to marginal cost.
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