## The Structure of Costs in the Long Run

Read these sections to learn about the long-run analysis in production. Pay attention to economies of scale and to the long-run average cost curve.

### The Structure of Costs in the Long Run

#### Choice of Production Technology

Many tasks can be performed with a range of combinations of labor and physical capital. For example, a firm can have human beings answering phones and taking messages, or it can invest in an automated voicemail system. A firm can hire file clerks and secretaries to manage a system of paper folders and file cabinets, or it can invest in a computerized recordkeeping system that will require fewer employees. A firm can hire workers to push supplies around a factory on rolling carts, it can invest in motorized vehicles, or it can invest in robots that carry materials without a driver. Firms often face a choice between buying a many small machines, which need a worker to run each one, or buying one larger and more expensive machine, which requires only one or two workers to operate it. In short, physical capital and labor can often substitute for each other.

Consider the example of a private firm that is hired by local governments to clean up public parks. Three different combinations of labor and physical capital for cleaning up a single average-sized park appear in Table 7.4. The first production technology is heavy on workers and light on machines, while the next two technologies substitute machines for workers. Since all three of these production methods produce the same thing – one cleaned-up park – a profit-seeking firm will choose the production technology that is least expensive, given the prices of labor and machines.

Production Technology 1 10 workers 2 machines
Production Technology 2 7 workers 4 machines
Production Technology 3 3 workers
7 machines

Table 7.4 Three Ways to Clean a Park

Production technology 1 uses the most labor and least machinery, while production technology 3 uses the least labor and the most machinery. Table 7.5 outlines three examples of how the total cost will change with each production technology as the cost of labor changes. As the cost of labor rises from example A to B to C, the firm will choose to substitute away from labor and use more machinery.

 Example A: Workers cost $40, machines cost$80 Labor Cost Machine Cost Total Cost Cost of Technology 1 10 × $40 =$400 2 × $80 =$160 $560 Cost of Technology 2 7 ×$40 = $280 4 ×$80 = $320$600 Cost of Technology 3 3 × $40 =$120 7 × $80 =$560 $680 Example B: Workers cost$55, machines cost $80 Labor Cost Machine Cost Total Cost Cost of Technology 1 10 ×$55 = $550 2 ×$80 = $160$710 Cost of Technology 2 7 × $55 =$385 4 × $80 =$320 $705 Cost of Technology 3 3 ×$55 = $165 7 ×$80 = $560$725 Example C: Workers cost $90, machines cost$80 Labor Cost Machine Cost Total Cost Cost of Technology 1 10 × $90 =$900 2 × $80 =$160 $1,060 Cost of Technology 2 7 ×$90 = $630 4 ×$80 = $320$950 Cost of Technology 3 3 × $90 =$270 7 × $80 =$560 $830 Table 7.5 Total Cost with Rising Labor Costs Example A shows the firm's cost calculation when wages are$40 and machines costs are $80. In this case, technology 1 is the low-cost production technology. In example B, wages rise to$55, while the cost of machines does not change, in which case technology 2 is the low-cost production technology. If wages keep rising up to \$90, while the cost of machines remains unchanged, then technology 3 clearly becomes the low-cost form of production, as shown in example C.

This example shows that as an input becomes more expensive (in this case, the labor input), firms will attempt to conserve on using that input and will instead shift to other inputs that are relatively less expensive. This pattern helps to explain why the demand curve for labor (or any input) slopes down; that is, as labor becomes relatively more expensive, profit-seeking firms will seek to substitute the use of other inputs. When a multinational employer like Coca-Cola or McDonald's sets up a bottling plant or a restaurant in a high-wage economy like the United States, Canada, Japan, or Western Europe, it is likely to use production technologies that conserve on the number of workers and focuses more on machines. However, that same employer is likely to use production technologies with more workers and less machinery when producing in a lower-wage country like Mexico, China, or South Africa.