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Part II: Considering Which Side You’re On in the Decision-Making Process Remember, the term 5,600/q can also be written as 5,600q-1, so its derivative is –5,600q-2 or –5,600/q2.
2. Set the derivative equal to zero.
3. Multiply both sides of the equation by q2.
4. Solve for q.
This step is a little tricky with q raised to the third power, but your calculator or computer should be able to handle it. Average total cost is minimized at 20 units of output. Marginal cost always equals the minimum values of average variable cost and average total cost.
Identifying Long-Run Production Costs In the long run, none of your inputs are fixed. You can choose any input combination to produce a given quantity of output. This decision ultimately leads to the selection of some inputs that become fixed after their initial selection. For example, when considering whether or not to produce the Saturn, General Motors could have chosen a variety of configurations for the factory. Each configuration General Motors evaluated had its own short-run average-total-cost curve. After a configuration was chosen, it became a fixed input, and General Motors subsequently operated on the short-run averagetotal-cost curve associated with that configuration. Therefore, General Motors’ long-run decision amounted to choosing the best possible short-run average-total-cost curve from a variety of possibilities.
Putting costs in the envelope curve Because there are no fixed inputs in the long run, the long-run total cost function doesn’t have a constant. Therefore, if you decide to produce zero units of output in the long run, your total cost equals zero. The long-run average-total-cost curve is derived by dividing the long-run totalcost function by the quantity of output. Another way to view long-run average
