What it means
Traditional growth models treated technology as something separate from investment. Kaldor argued in the 1950s that the two are linked, because new machinery embodies the latest ideas, so a business that invests more also tends to become more productive.
This was a break from earlier models that treated technology as arriving from outside, like weather. The technical progress function captures this with a curve.
On one axis is the growth rate of capital per worker, and on the other is the growth rate of output per worker. The curve slopes upward, showing that faster investment brings faster productivity gains.
The curve is usually drawn as bending over, meaning that gains become smaller as investment speeds up. That reflects the intuition that doubling the investment does not double the rewards, since good opportunities are used first and later projects add less.
In practice, a company can see this when its fifth machine adds less than its first. A related idea is learning by doing, associated with Kenneth Arrow, which says that productivity improves as workers gain experience from producing and using new equipment.
Both ideas explain why countries and companies that invest steadily in modern equipment tend to see their productivity rise over time. Together, the two ideas suggest that skills and equipment improve side by side.
For business readers the practical point is that capital spending is not only about adding capacity. A new production line, a better software system or an automated warehouse can also raise output per employee, which should be reflected when appraising an investment.
Ignoring this effect can make useful projects look unattractive on paper. There are limits.
The function is a stylised relationship, not a precise law, and its shape differs between industries, countries and periods. Managers should treat it as a way of thinking about investment and productivity, not a forecasting formula.
In practice
Real-world examples.
Example
A manufacturer replaces ageing machines with computer-controlled ones. Capital per worker rises by 8%, and the plant finds that output per worker rises by 4.2%, a sign that the new technology came with the equipment. That result is close to what a simple relationship between investment and productivity would predict.
Example
A logistics company invests $12,000,000 in automated sorting. After a year, the number of parcels handled per employee has risen by a quarter, a gain that would not have come from simply hiring more staff. Management credits the new equipment for the gain, and the finance team uses the figure to test whether the project meets its return target.
Example
A government economist compares two regions. The region with steadier investment in modern equipment shows stronger productivity growth, which supports the idea behind the function. The pattern is not proof, since education and policy also differ, but it fits the idea that investment carries new technology with it.
Formula
Calculation
A simple linear form is: Growth of output per worker = a + b x Growth of capital per worker
Suppose, for illustration, a = 1% (productivity gain unrelated to new investment) and b = 0.4. If capital per worker grows by 5% a year, productivity growth is 1% + 0.4 x 5% = 1% + 2% = 3% a year. If an employee produces $100,000 of output a year, that growth lifts it to $100,000 x 1.03 = $103,000 the next year.Case study
Seen in the real world.
Kestrel Textiles is an illustrative, fictional clothing maker deciding whether to modernise its looms. Its finance manager, Amira, first estimated the gain simply from extra capacity, which gave a poor return.
She then added the productivity effect: newer machines would cut waste and need fewer operators per unit. Using a simple technical progress relationship, she estimated that a 10% rise in capital per worker could lift output per worker by about 4%.
In this fictional story, adding the productivity gain turned a marginal project into an attractive one, and the board approved the investment. Amira cautioned that the 4% was an estimate and set up tracking to check it after installation. After the first year, the actual gain was 3.5%, a little below her estimate, so Amira adjusted her assumptions for the next project. The board valued the habit of checking forecasts against results.
Watch out
Common mistakes.
- Assuming technology improves by itself, apart from any investment in equipment, skills or research. Research budgets, equipment purchases and training all have to be paid for.
- Treating the function as a precise law instead of a simplified relationship that varies by industry.
- Counting the productivity gain in an investment appraisal without any plan to measure it afterwards.
Questions
People also ask.
Who developed the technical progress function?
Nicholas Kaldor is the economist most closely associated with it, and it appeared in his work on economic growth in the 1950s. Later economists refined and criticised it.
How does it differ from the production function?
A production function links inputs to output, while the technical progress function adds that new capital also improves productivity.
Why does it matter to business?
It reminds managers that investment can raise productivity as well as capacity, which should be reflected in project appraisal. It also helps explain why under-investing in equipment can leave a company falling behind rivals in output per employee.
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