Why Technology Adoption Matters
A technology can raise productivity only when it is put to effective use. A firm may adopt software, equipment, or a production method that already exists, then adjust its routines and workforce to make it work well. As more firms use and adapt that technology, its productivity effects can spread beyond the original users. The pace and impact of this diffusion depend on firms’ decisions and circumstances.
This tutorial focuses on diffusion: the spread of existing technologies among firms and industries. It distinguishes adopting a technology from adapting it to a firm’s operations, then shows how changing adoption rates can affect average output per hour. These ideas are aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus.
Adoption is not the same as invention. An adopting firm can gain from a technology developed elsewhere, even if it does not create a new technology itself. Nor does purchasing a machine or installing software guarantee a productivity gain. The firm must use it effectively. For example, new scheduling software may require staff training and changes to work assignments before it improves output per hour.
The earlier material on complementarity among capital, skills, and technology is relevant here: technologies may produce larger gains when used with suitable equipment and worker capabilities. The point in this tutorial is that firms differ in whether, when, and how well they make those changes. These differences help explain why a technology’s arrival does not immediately produce a uniform increase in productivity.
Adoption Across Firms
Firms may adopt at different times because the expected benefits, costs, and implementation challenges are not the same for every firm. A technology may suit one firm’s production process particularly well, while another would need substantial changes to use it. A firm may also delay adoption while it learns about the technology or waits for uncertainty about its performance to diminish.
A decision to adopt can be framed as a comparison of expected benefits and costs. Benefits might include lower labor requirements, fewer errors, or greater output from the same inputs. Costs can include purchase or setup costs, training, disruption during installation, and ongoing operating expenses. A firm considers whether the expected value of the resulting net benefits justifies the costs. This is a decision framework, not a guarantee that every expected benefit will occur.
Worked Example: A Firm’s Adoption Decision
A hypothetical packaging firm is considering a production system that costs $40,000 to install. The firm expects net operating savings of $15,000 at the end of each of the next three years. Assume the savings are certain, occur at each year-end, there are no other costs or benefits, and the firm discounts future amounts at an effective annual rate of 5%. Should it adopt based on these assumptions?
Method. Compare the installation cost with the present value of the net savings. Because each saving occurs at a year-end, discount it by the corresponding number of years.
The present value of the first year’s saving is $15,000 / 1.05 = $14,285.71. The second year’s saving has present value $15,000 / (1.05)2 = $13,605.44. The third year’s saving has present value $15,000 / (1.05)3 = $12,957.56.
The net present value is positive, so the firm should adopt under the stated assumptions. The conclusion depends on those assumptions: if savings are uncertain, delayed, or accompanied by additional costs, the calculation would need to reflect them. The common mistake is to add the three undiscounted savings and compare $45,000 directly with $40,000. That ignores the timing of the savings and overstates their value at the present date. All dollar amounts above are rounded to the nearest cent.
How Adoption Changes Average Productivity
Consider a simple setting in which firms produce output using labor, and productivity is measured as output per hour. Suppose there are two groups: firms that have adopted a technology and firms that have not. If the groups’ output per hour is known, aggregate productivity can be calculated as a weighted average. The relevant weights are the groups’ shares of total hours, not necessarily their shares of the number of firms.
The formula follows directly from the definition of output per hour. Let total hours be \(H\), so adopters supply \(sH\) hours and non-adopters supply \((1-s)H\) hours. Their total output is \(sH p_A+(1-s)H p_N\). Dividing total output by total hours \(H\) gives \(s p_A+(1-s)p_N\). If the technology changes adopters’ output per hour, or if firms change their hours, those effects must be included in the relevant productivity values or weights.
Worked Example: A Rising Adoption Share
Suppose adopters in a hypothetical service industry produce 120 completed jobs per labor hour, while non-adopters produce 90. Initially, adopters account for 40% of industry labor hours. Later, they account for 70%. Assume the two groups’ output per hour stays fixed and the total hours used by the industry do not change. Calculate average productivity at each date and its percentage increase.
Method. Use the labor-hour-weighted average. Initially, the adopter share is 0.40 and the non-adopter share is \(1-0.40=0.60\). Average productivity is \(0.40(120)+0.60(90)=48+54=102\) jobs per hour.
Later, the adopter share is 0.70 and the non-adopter share is \(1-0.70=0.30\). Average productivity is \(0.70(120)+0.30(90)=84+27=111\) jobs per hour. The increase is \(111-102=9\) jobs per hour. Relative to the initial average, the increase is \(9/102=0.088235\ldots\), or 8.82% to two decimal places.
The result can also be checked by noting that adopters are 30 jobs per hour more productive than non-adopters. The adoption share rises by 0.30, so the weighted average rises by \(0.30(30)=9\) jobs per hour. A common mistake is to calculate the percentage increase in the adoption share and report that as the productivity increase. Here the adoption share rises from 40% to 70%, but productivity rises by 8.82%, not 75%. The two quantities have different starting values and meanings.
Adoption and Adaptation Both Matter
Wider adoption can raise average productivity if adopters are more productive than non-adopters. But the productivity of adopters can also change as they gain experience and adapt the technology. For instance, employees may learn more efficient procedures, or managers may reorganize tasks around the new equipment. In this case, the average can rise because the adopter group grows, because adopters become more productive, or both.
Worked Example: Separating Wider Adoption From Adaptation
A hypothetical economy has two industries. Industry A accounts for 60% of total labor hours and industry B accounts for 40%; assume those shares remain fixed. Before adoption, productivity is 100 units per hour in A and 80 in B. Initially, 25% of A’s hours and 50% of B’s hours are in firms using a technology that raises productivity by 20% relative to each industry’s non-adopters. Later, the adoption shares rise to 50% in A and 75% in B. By then, adopters have adapted the technology, and their productivity is 25% above non-adopters’ productivity. Calculate the initial and later economy-wide averages, and separate the change due to wider adoption from the change due to adaptation.
Initial industry averages. In A, adopters produce \(100(1.20)=120\) units per hour, so the industry average is \(0.25(120)+0.75(100)=30+75=105\). In B, adopters produce \(80(1.20)=96\), so the industry average is \(0.50(96)+0.50(80)=48+40=88\). The economy-wide average is \(0.60(105)+0.40(88)=63+35.2=98.2\) units per hour.
Effect of wider adoption alone. First raise the adoption shares to their later values but keep the original 20% productivity advantage. Industry A’s average becomes \(0.50(120)+0.50(100)=110\). Industry B’s average becomes \(0.75(96)+0.25(80)=72+20=92\). The economy-wide average is \(0.60(110)+0.40(92)=66+36.8=102.8\). Thus wider adoption adds \(102.8-98.2=4.6\) units per hour.
Effect of adaptation. Now use the later 25% productivity advantage and the later adoption shares. In A, adopters produce \(100(1.25)=125\), so the average is \(0.50(125)+0.50(100)=62.5+50=112.5\). In B, adopters produce \(80(1.25)=100\), so the average is \(0.75(100)+0.25(80)=75+20=95\). The economy-wide average is \(0.60(112.5)+0.40(95)=67.5+38=105.5\). Adaptation adds \(105.5-102.8=2.7\) units per hour after the adoption change.
The total increase is \(105.5-98.2=7.3\) units per hour, equal to the 4.6-unit adoption contribution plus the 2.7-unit adaptation contribution under this calculation order. As a check, the percentage increase in the economy-wide average is \(7.3/98.2=0.074338\ldots\), or 7.43% to two decimal places. The common mistake is to average the two industries equally. Their labor-hour shares are 60% and 40%, so equal weighting would not represent economy-wide output per hour.
Why Diffusion Is Uneven
Diffusion often takes time because adoption requires information, resources, and changes to business practices. A firm may need to test whether an existing technology suits its tasks, pay implementation costs, train workers, or reorganize production. Even after adoption, performance may improve gradually as workers and managers learn how best to use it. These are general mechanisms, not a claim that all technologies follow the same path.
A common description of diffusion is an S-shaped pattern: adoption may begin slowly, accelerate as knowledge and experience spread, and slow again as the pool of remaining non-adopters shrinks. This is a possible pattern, not a rule that applies to every technology or industry. A technology can spread quickly if it is easy to implement, or slowly if its use requires substantial adjustment.
Diffusion can also occur through channels other than direct adoption. Firms may learn from suppliers, customers, workers who move between employers, or other firms’ demonstrated practices. A business may adopt a production method while another adopts related software or equipment. In each case, what matters for measured productivity is the output produced relative to the inputs used, not the mere presence of a technology.
What Diffusion Does—and Does Not—Show
The weighted-average calculations isolate the contribution of adoption under specified assumptions. Actual economy-wide productivity can also change because firms alter their labor hours, output, or mix of products, and because the productivity of non-adopters changes. The distribution of hours across firms and industries matters as well. For example, a shift of labor toward firms with higher output per hour can raise the aggregate average even if each firm’s own productivity stays constant. Conversely, adoption can become widespread without a large measured aggregate gain if adopters account for few hours or achieve only small productivity improvements.
This distinction is useful when interpreting productivity evidence. An increase in adoption rates is not itself a measurement of productivity growth. To assess its contribution, one needs information on which firms adopted, how many hours they account for, their productivity relative to non-adopters, and whether those differences persist after accounting for other changes. In practice, measured differences between adopters and non-adopters do not automatically prove that adoption caused all of the difference; the firms may have differed in other ways before adopting.
Check Your Understanding
Work through each problem, paying attention to whether the weights refer to firms or to labor hours.
- In a hypothetical repair network, adopters complete 104 service calls per hour and non-adopters complete 80. Adopters initially account for 25% of hours and later account for 50%, with group productivity unchanged. Find the average at each date and the percentage increase. (Answer: 86 initially, 92 later, an increase of 6.98%.)
- A hypothetical firm pays $28,000 now for a system expected to produce net savings of $10,000 at each of the next three year-ends. Assume certain savings, no other costs or benefits, and an effective annual discount rate of 4%. Find the net present value and state the decision under these assumptions. (Answer: NPV = \(-\$249.09\); do not adopt under the stated assumptions.)
- In one industry, non-adopters produce 60 units per hour and adopters initially produce 72. The adoption share of total labor hours rises from 20% to 60%. Calculate the average productivity before and after the increase, assuming the productivity gap is unchanged. (Answer: 62.4 initially and 67.2 after adoption expands.)
- Two industries account for 70% and 30% of total hours. Their initial productivities are 50 and 90 units per hour, respectively. Calculate the economy-wide average. Explain why averaging the two industry productivities equally would be inappropriate. (Answer: 62 units per hour; equal weighting ignores the industries’ different shares of total hours.)
- In a hypothetical industry, non-adopters produce 100 units per hour. Initially, 30% of hours are in adopter firms whose productivity is 20% higher. Later, 60% of hours are in adopter firms, whose productivity has adapted to be 25% higher. Find the initial and later average productivities and the total percentage increase. (Answer: 106 initially, 115 later, an increase of 8.49%.)