6.4 Production in the Long Run

In the long run, all factors (including capital) are variable, so our production function is Q=f[L,K].

Consider a transcription firm that does medical transcription for hire using transcriptionists for labor and computers for capital. To start, the firm has just enough business for one transcriptionist and one computer to keep busy for a day. Let’s say that’s five medical reports. Now suppose the firm receives a rush order from a physician’s office for 10 reports tomorrow. Ideally, the firm would like to use two transcriptionists and two computers to produce twice their normal output of five reports. However, in the short turn, the firm has fixed capital, i.e. only one computer. The table below shows the situation:

In the short run, the only variable factor is labor so the only way the firm can produce more output is by hiring additional workers. What could the second worker do? What can they contribute to the firm? Perhaps they can answer the phone, which is a major impediment to completing the transcription assignment. What about a third worker? Perhaps they could bring coffee to the first two workers. You can see both total product and marginal product for the firm above. Now here’s something to think about: At what point (e.g. after how many workers) does diminishing marginal productivity kick in, and more importantly, why?

In this example, marginal productivity starts to decline after the second worker. This is because capital is fixed. The production process for transcribing works best with one worker and one computer. If you add more than one transcriptionist, you get seriously diminishing marginal productivity.

Consider the long run. Suppose the firm’s demand increases to 15 reports per day. What might the firm do to operate more efficiently? If demand has tripled, the firm could acquire two more computers, which would give us a new long run production function as Table 6.12 below shows.

With more capital, the firm can hire three workers before diminishing productivity comes into effect. More generally, because all factors are variable, the long run production function shows the most efficient way of producing any level of output.