Exam 13: Production Decisions in the Short and Long Run

The fixed expense on a fixed level of capital in the short run becomes a fixed cost for the firm in the long run.

The cross-price demand for capital (relative to the wage) may slope up or down.

The greater the degree of substitutability between capital and labor, the greater will be the downward shift in the cost curve when wage falls.

(Long run) average cost curves are U-shaped when the production technology has decreasing returns to scale and the firm faces recurring fixed costs.

If the rental rate increases, we know that output and labor input will fall in the long run.

Output price changes cause substitution effects and scale effects.

The parameter A re-scales the production function -- allowing us to transform a decreasing returns to scale production function to an increasing returns to scale production function.

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?

If the wage falls, we know for sure that the firm will produce more in the long run but we cannot be sure whether it will use more or less capital.

Suppose the AC curve is U-shaped.Then an increase in a recurring fixed cost will cause the AC curve to shift up, with its lowest point shifting to the right.

The more substitutable capital and labor are in production, the more likely it is that the cross-price demand curve for capital (relative to the wage) is upward sloping.