Suppose there are different ways of producing computer chips. If you hire one worker (for the day) for each machine that you rent (for the day), you can produce 10 chips per day with each worker/machine pair for the first 60 machine/worker pairs. For the next 60 worker/machine pairs (assuming still that you hire them as pairs for the day), you are able to produce 20 chips per day with each of the additional pairs. Once you have 120 worker/machine pairs, you can only get 5 additional chips per day for each additional pair.
But hiring 1 worker for each machine is not the only way to produce computer chips. Suppose you are starting from a production plan where you are using exactly as many workers as machines to produce a given level of chips. The technology is such that, starting at the
production plan where you are using the same number of workers as machines, you can replace 1 or more workers with two machines (for each worker) and get just as many chips produced. Alternatively (and again starting at the production plan where you use exactly as many workers as machines), you can replace 1 or more machines with 2 workers (for each machine) and get just as many chips produced.
Suppose the daily wage and rental rate are both equal to $100 and the firm currently has 120 units of capital.
a. Illustrate the short run production function (assuming labor is variable in the short run but capital is not). (Label the intercept as well as any kink points.)
b. Derive the short run cost function. (Label the intercept as well as any kink points.)
c. Derive the short run marginal and average cost functions.
d. How low can price fall in the short run before a firm shuts down?
e. What does the average expenditure - i.e. the curve that includes all short run costs but also expenditures that are not costs in the short run - look like? Explain how this curve relates to the long run average cost curve.
f. We have said that the long run supply responses to output price changes are larger than short run supply responses. In what sense is this true for the firm you have analyzed here?
What will be an ideal response?
c.
d. The lowest point on the short run AC curve is at 0. Price can therefore fall to zero without the firm shutting down (because the firm can produce with just machines whose cost is sunk in the short run.)
e. The AE curve is illustrated in the graph above. It shares one point in common with the LR average cost curve -- the minimum point. Everywhere else it is higher because the fixed SR level of capital (k=120) is not cost-minimizing for any output level other than 1,800.
f. From the graph above, you can see that the firm will not deviate from producing 1800 units of output so long as the price remains between $7.50 and $60.00. The lowest point of the AE and LR AC curves occurs at $13.33. The long run MC above 1800 units of output is $40. Thus, in the long run the firm will not deviate from producing 1800 units so long as price falls in the interval between $13.33 and $40. Thus, it takes less of a price change in the long run to induce a supply response from this firm.
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