**Unit 2** Technology and incentives

## 2.4 Firms, technology, and production

- technology
- The description of a process that uses a set of materials and other inputs, including the work of people and machines, to produce an output.

Firms own or rent capital goods—such as buildings and equipment—and employ workers to produce and sell goods and services. An important decision for a firm is its choice of production **technology**: the process that it will use to convert a set of inputs—such as raw materials, and work done by people and machinery—into output that it can sell. Having chosen a technology, it will also need to decide on the amount of inputs to employ, which will determine how much output it can produce.

For example, in the production of olive oil, the olives must be graded, washed, milled to remove the stones, mashed to a paste, and pressed to extract oil and water. Finally, the oil is separated from the water and canned or bottled. For thousands of years it was produced using simple technologies in which most of the process was carried out by hand, using a pestle and mortar to mash the olives, and heavy stones to press them. The inputs were raw materials (olives and water); capital (pestle and mortar, stones); and labour. It was a labour-intensive technology: 2,000 olives had to be combined with many hours of hard work to produce a litre of oil.

- factor of production
- Any input into a production process is called a factor of production. Factors of production may include labour, machinery and equipment (usually referred to as capital), land, energy, and raw materials.
- production function
- A production function is a graphical or mathematical description of the relationship between the quantities of the inputs to a production process and the amount of output produced.

The technology used in modern commercial production employs less labour and more capital and energy. The inputs, or **factors of production**, are raw materials, labour, capital goods (milling, mashing, and pressing machines), and energy to operate the machines.

A technology can be represented by a **production function**: a relationship that tells us how much output it will produce, given the amounts of inputs used. The technology described in Section 1.6 produces agricultural output, *Y*, using labour and land. Since the amount of land is assumed to be constant, we write the production function as *Y* = f(*X*), where *X* is the number of farmers. This function is shown in Figure 1.8b.

In the case of olive oil, suppose that *N* is the number of workers employed, *M* is the number of machines, and *E* is the amount of energy used per day. Then we can summarize the technology using a production function for the amount of olive oil produced per day, *Y*:

This expression is just a shorthand way of saying ‘the daily output of oil, *Y*, depends on (or is a function of) the amounts of the inputs, *N*, *M*, and *E*, that the firm chooses to use’. We have ignored raw materials, assuming that the number of olives required is automatically determined by the volume of oil to be produced.

Figure 2.3 describes a hypothetical technology for olive oil. Imagine that there are three machines (for milling, mashing, and pressing). With the help of a single worker to operate them, and 80 kWh of energy, they can produce 50 litres of olive oil per day. If the firm wants to produce more, it needs more machines, workers, and energy. The table shows how much output is produced, for different combinations of factors of production.

Number of machines, M |
Number of workers, N |
Amount of energy, E (kWh) |
Output, Y (litres) |
---|---|---|---|

3 | 1 | 80 | 50 |

6 | 2 | 160 | 100 |

9 | 3 | 240 | 150 |

12 | 4 | 320 | 200 |

- fixed-proportions technology
- A technology that requires inputs in fixed proportions to each other. To increase the amount of output, all inputs must be increased by the same percentage so that they remain in the same fixed proportions to each other.
- constant returns to scale
- When production exhibits constant returns to scale, increasing all of the inputs to a production process by the same proportion increases output by the same proportion. The shape of a firm’s long-run average cost curve depends both on returns to scale in production and the effect of scale on the prices it pays for its inputs.
*See also: increasing returns to scale, decreasing returns to scale.*

This technology is simple to describe, for two reasons. First, it requires inputs in fixed proportions: for every three machines, one worker, and 80 kWh of energy are needed. With a **fixed-proportions technology** there is no point in increasing one input without increasing the others. For example, if you have six machines, you can’t make them run any faster even if you add a third worker or more energy: output will remain at 100 litres.

Secondly, it has **constant returns to scale**: if you double the inputs, the amount of output doubles; similarly a 50% increase in inputs (from the second row of the table to the third) increases output by 50%. (So you could easily add more rows to the table.)

We will use technologies with these two properties in Section 2.5, to model the decisions of firms in the Industrial Revolution.

### Comparing two technologies

Suppose that a new robotic technology is developed for producing olive oil. This robotic system, which is controlled by one worker and using 400 kWh of energy, can produce 100 litres of olive oil per day. As before, the technology uses inputs in fixed proportions and has constant returns to scale. Daily output is proportional to the number of systems installed. Can we say that the robotic system is better?

A simple way to compare constant-returns technologies is to compare their input requirements for producing a standard amount of output. The table in Figure 2.4 shows the inputs needed for 100 litres of oil per day.

- average product
- The average product of an input is total output divided by the total amount of the input. For example, the average product of a worker (also known as labour productivity) is total output divided by the number of workers employed to produce it.

The fourth column uses these figures to compare the **average product** of labour: output per worker. With fixed proportions and constant returns, the average product of labour is the same however many workers are employed. For example, output per worker with technology A is 100/2 = 50 litres per day. The last column shows the ratio of the two inputs: it shows that technology B is more energy intensive than technology A.

Input requirements for 100 litres of olive oil | ||||
---|---|---|---|---|

Workers | Energy | Average product of labour | Energy–labour ratio | |

A: Milling, mashing, and pressing machines | 2 | 160 | 50 | 80 |

B: Robotic technology | 1 | 400 | 100 | 400 |

The lower panel of Figure 2.4 illustrates this information graphically. In each case, it shows the input requirements for 100 litres of olive oil, and for more output further along the ray from the origin. The slope of each ray corresponds to the energy–labour ratio. The steeper the ray, the more energy-intensive the technology (meaning that the amount of energy—relative to the number of workers—required to produce a given level of output is greater).

The graph shows that neither technology is necessarily better than the other. The average product of labour is higher with technology B, but it uses far more energy. To decide which one to use, the owner of the firm would need to consider the relative costs of the two inputs. This was a key factor in the choice of technology in the Industrial Revolution, as the following sections of this unit will explain.

**Question 2.5** Choose the correct answer(s)

Figure 2.4 shows the input requirements for different amounts of olive oil, for two technologies (A and B). Suppose there is a third fixed-proportions technology, C, which requires four workers and 360 units of energy to produce 100 litres of olive oil. Based on this information, read the following statements and choose the correct option(s).

- Since technology C is a fixed-proportions technology with constant returns to scale, we multiply the numbers given by 3 to obtain 4 × 3 = 12 workers and 360 × 3 = 1,080 units of energy.
- The average product of labour of technology C is 100/4 = 25, which is lower than that of technology A and B.
- The energy–labour ratio of technology C is 360/4 = 90, which is between that of technology A (80) and B (400).
- Technology B has a higher average product of labour than technology C, but is also more energy-intensive, so the owner’s choice depends on the relative price of the inputs.