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Short Run vs. Long Run optimum given increase in demand

I need some help on the below detailed, not much required approx 350 words....

A firm finds there is a sudden increase in the demand for its product. In the short run, it must operate longer hours and pay higher overtime wage rates. In the long-run, however, the firm can install more machines and operate them for various periods of time. Which do you think will be lower, the short-run or long-run average cost of the increased output? How is your answer affected by the fact that the long-run average cost included the cost of the new machines the firm buys, while the short-run average cost includes no machine purchases? Explain your answer.

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Solution Preview

I am using a graph of the LRAC curve and its relationship to the SRATCs (short run average total cost curves) which you can see in the attached document. The LRAC envelopes the lowest points of all SRATCs and each SRATC is related to a specific level of capital. Q* and C* are the original equilibrium before the surge in demand and it is the SRTAC* curve of the firm. Demand goes up from Q* to Q1. The firm is initially stuck with its SRTAC and thus must increase its variable costs (it must operate their available capital for longer hours and pay higher ...

Solution Summary

This answer (in short essay format and graphs) illustrates the differences between the short-run and long-run situations facing a firm that has to increase its production to respond to demand. It includes an explanation of how capital costs influence optimization in both the short run and the long run.