D2.Eco.13.9-12: Technology, Capital, Human Capital and Growth

Overview

Lesson Procedure

70-85 minutes of class time across 5 phases.

1. Warm-Up5-10 minutes
2. Direct Instruction20-25 minutes
3. Guided Practice15-20 minutes
4. Independent Practice15 minutes
5. Closure15 minutes

1. Warm-Up5-10 minutes

   Warm-Up Prompt

   "A country can spend one extra billion dollars on one of three things: new machines for its factories, a research lab, or training for young workers. Which would you choose if you wanted the country to be richer in 5 years? In 40 years? Are your two answers the same?"

   Take a quick vote for each time horizon and record it. Students often pick machines for 5 years and are split for 40 years. Do not settle the question. Tell students that the indicator names exactly these three: capital goods, technology and human capital. Today they will learn how economists measure each one's part in growth, and they will return to the vote at the end.

2. Direct Instruction20-25 minutes

   Key terms for D2.Eco.13.9-12 (working definitions)

   Term	Meaning	Example
   Economic growth	A sustained rise in real GDP, the total output of goods and services adjusted for price changes	Real GDP rising 2% a year
   Standard of living	The material well-being of a typical person, often measured by real GDP per person	More goods, services and leisure per person
   Capital goods	Long-lasting goods used to produce other goods and services: equipment, structures and software	A container crane, a factory, design software
   Human capital	The knowledge, skills, experience and health that make workers more productive	An apprenticeship, a nursing degree
   Technology	Knowledge about how to produce: new methods, products and ways of organizing work	A new seed variety, a faster routing method
   Capital intensity (capital deepening)	The amount of capital services per hour worked	More machines per worker
   Total factor productivity (TFP)	Output divided by an index of combined labor and capital inputs: the part of growth not explained by measured inputs	Output rises 3% while combined inputs rise 2%
   Diminishing returns	Each additional unit of one input adds less output than the one before, when other inputs stay the same	A fifth machine for one worker adds little

   Part 1: From productivity to living standards. Review the identity from the middle school version of this indicator: real GDP per person = (real GDP / hours worked) x (hours worked / population). Hours per person cannot rise forever, so sustained growth in living standards comes mainly from output per hour. Read Source 1 together, paragraphs 1-3: it lists what raises output per hour.

   1Productivity is not the same as production or output.
   Productivity can increase or decrease when output increases.
   For example, working more hours increases total output, not necessarily output per hour.

   [...]

   2What affects labor productivity?
   A change in labor productivity reflects the change in output that is not explained by the change in hours worked.
   Output per hour can increase over time due to:
   Technological advances
   Improved worker skills
   Improved management practices
   Economies of scale in production
   Increases in the amount of non-labor inputs used

   3What affects multifactor productivity?
   A change in multifactor productivity reflects the change in output that is not explained by the change in measured inputs.
   Many of the same factors that affect labor productivity affect multifactor productivity, but NOT increases in other measured inputs, such as capital.

   4Example
   A farmer buys a new tractor and can cultivate 400 acres of land rather than 200 acres if he works the same number of hours. Measured labor productivity will double, although this increase is due to using the new tractor. Labor productivity measures only compare output to labor hours.

   5In a multifactor productivity measure, the new tractor is included in the combined input index. Multifactor productivity will not double because measured inputs have also increased. MFP may still rise if output increases more than combined inputs.

   Teacher note on Source 1: paragraph 2 lists "Technological advances" (technology), "Improved worker skills" (human capital) and "Increases in the amount of non-labor inputs used" (capital goods), plus management and scale. Paragraph 3 explains why economists also use total factor productivity: it leaves out gains that come only from adding capital. Paragraphs 4 and 5 are for the quiz.

   Part 2: A simple model. Economists often write output as Y = A x K^0.3 x (h x L)^0.7, where K is capital, L is hours of work, h is skill per hour (human capital) and A is technology. The exponents are typical shares of income paid to capital and to labor, used here only as a model. Work the examples below, then show Diagram 2.

   • Diminishing returns to capital (model)

     Let A = 1, h = 1 and L = 100, so Y = K^0.3 x 100^0.7. Find output when K = 100, 200 and 300. How much does each extra 100 units of capital add?

     Result: Y(100) = 100.0; Y(200) = 100 x 2^0.3 = 123.1; Y(300) = 100 x 3^0.3 = 139.0. The first 100 units add 23.1, the next 100 add only 15.9. More capital raises output, but by less each time.

   • Technology (model)

     Same economy with K = 200. Technology A rises 10%, from 1 to 1.1. What happens to output?

     Result: Y = 1.1 x 123.1 = 135.4, exactly 10% more. A rise in A raises output at every level of capital: it shifts the whole curve up instead of moving along it, so it does not run into diminishing returns.

   • Human capital (model)

     Same economy with A = 1 and K = 100. Training raises skill per hour h by 10%, from 1 to 1.1. What happens to output?

     Result: Y = 100^0.3 x (1.1 x 100)^0.7 = 100 x 1.1^0.7 = 106.9, a 6.9% rise with the same hours and the same machines.

   • Growth accounting (real data)

     Use the BLS table. From 1987 to 2025, labor productivity grew 2.03% a year. What share came from capital intensity, from labor composition and from total factor productivity?

     Result: Capital intensity: 0.86 / 2.03 = 42%. Labor composition: 0.31 / 2.03 = 15%. TFP: 0.85 / 2.03 = 42%. Capital goods and the TFP residual each explain a bit over two-fifths; better-skilled and more experienced workers explain about one-seventh.

   • From productivity to living standards (real data)

     Real GDP per person rose from $37,628 in 1987 to $70,021 in 2025 (2017 dollars), 1.65% a year. About how many years does it take to double at that rate?

     Result: Rule of 70: 70 / 1.65 = 42 years (exactly: ln 2 / ln 1.0165 = 42.4). Over 38 years, real GDP per person grew 70,021 / 37,628 = 1.86 times.

   Sources of U.S. labor productivity growth, private nonfarm business sector (real data). Average annual growth in percent; the three contributions are in percentage points. Computed by SVHS from BLS total factor productivity series MPU4910062 (labor productivity), MPU4910152 (contribution of capital intensity), MPU4910182 (contribution of labor composition) and MPU4910012 (total factor productivity), index values downloaded October 3, 2026. Real GDP per person: BEA, NIPA Table 7.1, chained 2017 dollars ($37,628 in 1987, $55,561 in 2007, $62,677 in 2019, $70,021 in 2025). Because each rate compounds, the three contributions add up to labor productivity growth only approximately.

   Period	Labor productivity	From capital intensity (capital goods per hour)	From labor composition (skills and experience)	Total factor productivity (technology and other)	Real GDP per person
   1987-2007	2.27	0.97	0.31	0.98	1.97
   2007-2019	1.55	0.68	0.30	0.56	1.01
   2019-2025	2.23	0.85	0.32	1.04	1.86
   1987-2025	2.03	0.86	0.31	0.85	1.65

   Part 3: Read the table with care. TFP is measured as a residual: whatever output growth is left after counting capital and labor. Technology is its largest part, but it also picks up better management, shifts of workers to more productive firms and measurement errors. Software and research and development count as capital (intellectual property products), so some technology shows up in the capital column too. The three causes in the indicator also work together: a new machine is often useless without trained workers and the know-how to run it.

3. Guided Practice15-20 minutes

   Reading a BLS news release. Context note: every March, BLS publishes total factor productivity (TFP) for the previous year. Source 2 is the release of March 19, 2026, for 2025. "Intellectual property products" are software, research and development, and creative originals; "labor composition" is the BLS measure of the skills and experience of the workforce. Read paragraphs 1, 2, 5 and 6 together; paragraphs 3 and 4 are for the quiz.

   1Total factor productivity is calculated by dividing an index of real output by an index of combined units of labor input and capital input. Total factor productivity annual measures differ from BLS quarterly labor productivity (output per hour worked) measures because TFP includes the influences of capital input and shifts in the composition of workers. Measures for the most recent year of this release are preliminary estimates. See the Technical Notes for additional information.

   2Combined Inputs in the private nonfarm business sector: 2019-25
   Combined input growth is made up of growth in three components: capital input, hours worked, and labor composition. Capital input, which includes equipment, structures, and intellectual property products, grew 2.7 percent in 2025, consistent with the last 4 years of growth.

   [...]

   3Labor composition, which estimates the effect of shifts in the age, education, and sex of the workforce, tends to be a relatively stable measure with average annual growth of 0.5 percent over the 2019-25 period. However, the measure was uncharacteristically volatile during the pandemic and subsequent recovery. The labor composition index tends to increase faster during a recession and the early stages of the recovery, because younger and less-educated workers are more likely to lose their jobs. Labor composition grew 2.8 percent in 2020 as businesses shed less skilled workers but then declined 0.8 percent the following year as the economy reopened. More recently, growth in labor composition has stabilized and grew 0.6 percent in both 2024 and 2025. (See table A.)

   4Total Factor Productivity Trends – 1990-2025
   Productivity is often viewed as a long-run measure as changes in the production process that lead to productivity growth take time to implement. TFP grew 1.0 percent in the private nonfarm business sector over the current business cycle, 2019-25. This growth outpaced the 0.6-percent TFP growth in the previous business cycle which spanned from 2007-19. The growth in output in the 2019-25 period of 2.7 percent is higher than the 2007-19 growth in output of 2.1 percent. Combined inputs growth in 2019-25 is the same as the previous business cycle, 1.6 percent. (See table A.)

   5Labor Productivity Trends
   Changes in the use of capital and worker skills impact output per hour worked, also known as labor productivity. Labor productivity growth can be approximated as the sum of three components: the contribution of capital intensity, the contribution of labor composition, and the remaining gains that are attributed to total factor productivity. In 2025, private nonfarm business labor productivity increased 2.2 percent, less than the 3.0 percent growth in 2024. (See table B.)

   6The deceleration in labor productivity growth in 2025 can be attributed to slower growth from TFP and the contribution of capital intensity. In 2024, TFP was the largest contributor to labor productivity growth at 1.5 percent. However, in 2025, TFP’s contribution decreased by almost half to 0.8 percent, which accounted for most of the labor productivity decline. Additionally, the contribution of capital intensity in 2025 decreased slightly from the 1.1 percentage point growth in 2024 to 0.9 percentage point growth in 2025. The contribution of labor composition to labor productivity for private nonfarm business increased slightly from 0.3 percentage point in 2024 to 0.4 percentage point in 2025.

   1. Definition. Prompt: in paragraph 1, how is TFP calculated, and why is it different from labor productivity? Teacher note: real output divided by combined labor and capital input; labor productivity counts only hours, so it rises when capital is added, while TFP does not.
   2. Capital. Prompt: in paragraph 2, what three kinds of capital does BLS count? Which of them could be called technology? Teacher note: equipment, structures and intellectual property products; software and research and development blur the line between capital goods and technology.
   3. The three-part rule. Prompt: paragraph 5 says labor productivity growth "can be approximated as the sum of three components." Match each to a cause in the indicator. Teacher note: capital intensity is capital goods, labor composition is human capital, and TFP is mostly technology.
   4. Check the sum. Prompt: use paragraph 6 to add the three 2025 contributions and compare with labor productivity growth in 2025. Teacher note: 0.9 + 0.4 + 0.8 = 2.1, against reported growth of 2.2 percent; the gap is rounding, because the release gives each number to one decimal.
   5. Connect to living standards. Prompt: if labor productivity grows about 2% a year for a working lifetime of 40 years, how much more does an hour of work produce at the end? Teacher note: 1.02⁴⁰ = 2.21, so more than twice as much.
4. Independent Practice15 minutes

   Investing in people, 1862. Context note: the Morrill Act, sponsored by Representative Justin Morrill of Vermont and signed by President Abraham Lincoln on July 2, 1862, gave each state federal land (or "land scrip", certificates for land elsewhere) to sell, and the money funded colleges. The National Archives notes that over 10 million acres provided by these grants were expropriated (taken) from the tribal lands of Native nations, and that the Second Morrill Act of 1890 required states either to show that admission was not restricted by race or to fund separate land-grant colleges for Black students, which led to several historically Black land-grant universities. "Mechanic arts" meant engineering and skilled trades; "the industrial classes" meant working people such as farmers and mechanics.

   1AN ACT Donating Public Lands to the several States and Territories which may provide Colleges for the Benefit of Agriculture and Mechanic Arts.

   2Be it enacted by the Senate and House of Representatives of the United States of America in Congress assembled, That there be granted to the several States, for the purposes hereinafter mentioned, an amount of public land, to be apportioned to each State a quantity equal to thirty thousand acres for each senator and representative in Congress to which the States are respectively entitled by the apportionment under the census of eighteen hundred and sixty: Provided, That no mineral lands shall be selected or purchased under the provisions of this Act.

   [...]

   3SEC. 4. And be it further enacted, That all moneys derived from the sale of the lands aforesaid by the States to which the lands are apportioned, and from the sales of land scrip hereinbefore provided for, shall be invested in stocks of the United States, or of the States, or some other safe stocks, yielding not less than five per centum upon the par value of said stocks; and that the moneys so invested shall constitute a perpetual fund, the capital of which shall remain forever undiminished, (except so far as may be provided in section fifth of this act,) and the interest of which shall be inviolably appropriated, by each State which may take and claim the benefit of this act, to the endowment, support, and maintenance of at least one college where the leading object shall be, without excluding other scientific and classical studies, and including military tactics, to teach such branches of learning as are related to agriculture and the mechanic arts, in such manner as the legislatures of the States may respectively prescribe, in order to promote the liberal and practical education of the industrial classes in the several pursuits and professions in life.

   Questions for Source 3:

   1. Paragraph 2: how much land did each state receive, and how was the amount set?
   2. Paragraph 3: what is the "leading object" of the colleges the act funds?
   3. Paragraph 3: whose education does the act aim to promote, and of what kind?
   4. Is the Morrill Act an investment in technology, capital goods or human capital? It may be more than one; explain with evidence.
   5. Who bore costs of this investment that the act itself does not mention? Use the context note.

   Teacher key for 1-3. (1) Thirty thousand acres for each senator and representative the state had under the 1860 census apportionment. (2) To teach branches of learning related to agriculture and the mechanic arts, without excluding scientific and classical studies, and including military tactics. (3) "the industrial classes", in "the several pursuits and professions in life"; the education is to be "liberal and practical". Questions 4 and 5 are open; score the evidence and reasoning.

5. Closure15 minutes

   Choosing a plan. Students read Source 4, an invented scenario, which they will also use in Activity 2 and in quiz questions 14-17.

   1Invented scenario, written for this page. Quillon is an invented country of 12 million people. Its real GDP per person is $18,000 a year, and for the past decade it has grown about 2 percent a year. The national budget office can spend $3 billion on a ten-year growth program and must choose one of three plans. Each plan costs $3 billion, and all amounts are in constant dollars. The estimated effects below come from the budget office and are uncertain.

   2Plan A, technology: fund a national research agency and extend high-speed internet to every rural district, so that farms and small firms can adopt new methods. Estimated effect: total factor productivity grows 0.6 percentage point a year faster, starting after about five years, and the gain does not fade.

   3Plan B, capital goods: build a modern container port and lend money to firms for new machinery. Estimated effect: the contribution of capital intensity rises 0.8 percentage point a year for ten years, starting at once. After that the boost fades, because machines wear out and each additional machine adds less output than the one before.

   4Plan C, human capital: expand the technical colleges and pay for apprenticeships for 200,000 young workers. Estimated effect: the contribution of labor composition rises 0.4 percentage point a year, starting after three years, for as long as the trained workers stay in the workforce.

   5Each plan has critics. A business association says the research in Plan A may take decades to pay off. A labor federation says Plan B helps the owners of firms first. A group of economists says Plan C will do little unless there are jobs that use the new skills.

   Exit ticket (index card): "Name one real example from your own community of each cause in the indicator: a technology, a capital good and an investment in human capital. For one of them, explain in one sentence how it raises output per hour." Return to the warm-up vote and ask whether anyone would change their 40-year answer.

   Teacher notes. (1) The BLS numbers are revised, and the most recent year is preliminary, so newer downloads may differ slightly. (2) TFP is not a direct measure of technology; it is a residual. Present it as "technology and other influences". (3) The Morrill Act built a lasting system of colleges, and the land that paid for it was in large part taken from Native nations; both facts belong in the discussion. (4) Quillon is invented so that students can weigh real trade-offs without taking a side on any current budget or policy debate. Score the reasoning, not the plan chosen.

Differentiation Strategies

Assessment Guidance

1. Question 1 of 20 · Multiple Choice

   Which of these is an investment in human capital?

   AA railroad lays a second track beside its first one BAn airline pays to train its mechanics CA lab invents a battery that lasts twice as long DA port buys three new cranes for unloading ships

2. Question 2 of 20 · Multiple Choice

   Use Source 1, paragraph 4. Why does the farmer's measured labor productivity double?

   AHe works twice as many hours as before on the farm BFarm prices doubled during that same year CHe learned new farming skills at a college DThe tractor doubles the land worked per hour

3. Question 3 of 20 · Multiple Choice

   Use Source 1, paragraph 5. Why will multifactor productivity not double in the tractor example?

   AThe tractor counts as an input, so inputs rose BThe farmer worked fewer hours than he did before CMultifactor productivity counts only labor hours DOutput did not really increase in the example

4. Question 4 of 20 · Multiple Choice

   Use the BLS table. In 1987-2007, what share of labor productivity growth came from capital intensity?

   AAbout 43% BAbout 14% CAbout 1% DAbout 57%

5. Question 5 of 20 · Multiple Choice

   Use the BLS table. From 1987-2007 to 2007-2019, labor productivity growth slowed. Which contribution fell by the most percentage points?

   ACapital intensity BLabor composition CTotal factor productivity DAll three fell by the same amount

6. Question 6 of 20 · Multiple Choice

   Use the BLS table. At the 2007-2019 rate of growth of real GDP per person (1.01% a year), about how many years would real GDP per person take to double?

   AAbout 69 years BAbout 38 years CAbout 36 years DAbout 7 years

7. Question 7 of 20 · Multiple Choice

   In a model economy, output is Y = 10 x √K with labor fixed. Raising capital from K = 16 to K = 25 adds 10 units of output. How much output does raising it from K = 25 to K = 34 add?

   A10.0 B8.3 C58.3 D9.0

8. Question 8 of 20 · Multiple Choice

   In the model Y = A x K^0.3 x L^0.7, technology A rises 5% and capital K rises 10% in the same year, with L unchanged. By about what percent does output rise?

   A15.0% B8.0% C5.0% D2.9%

9. Question 9 of 20 · Multiple Choice

   In the model Y = A x K^0.3 x (h x L)^0.7, a training program raises skill per hour h by 20%, with A, K and L unchanged. By about what percent does output rise?

   A20.0% B6.0% C13.6% D14.0%

10. Question 10 of 20 · Multiple Choice

    Use Source 2, paragraph 3. Why did labor composition grow 2.8 percent in 2020?

    AMany workers went back to school BFirms trained their workers online CHours worked rose sharply that year DLess skilled workers were laid off

11. Question 11 of 20 · Multiple Choice

    Use Source 2, paragraph 4. Why does BLS say productivity "is often viewed as a long-run measure"?

    AIts data are released only once a decade BIt cannot change from one year to the next CProduction changes take time to set up DIt measures only very old industries

12. Question 12 of 20 · Multiple Choice

    Use Source 3, paragraph 3 (section 4). What must the states do with the money from selling the land?

    ASpend all of it at once on new college buildings BLend it to farmers so they can buy machinery CReturn all of it to the federal Treasury DKeep it as a fund and spend only the interest

13. Question 13 of 20 · Multiple Choice

    Use Source 3, paragraph 2. Under section 1, how much land would a state with 2 senators and 9 representatives receive?

    A330,000 acres B270,000 acres C30,000 acres D60,000 acres

14. Question 14 of 20 · Multiple Choice

    Use Source 4. If Quillon's real GDP per person keeps growing 2 percent a year, about how large will it be in 35 years?

    A$30,600 B$36,000 C$18,360 D$72,000

15. Question 15 of 20 · Short Answer

    Use Source 4. Suppose Plan B raises Quillon's growth of real GDP per person from 2.0% to 2.8% a year for ten years. What would real GDP per person be after ten years with and without Plan B? Then explain, using Source 4, why the boost does not last.

    Show model answer

16. Question 16 of 20 · Short Answer

    Use Source 4. If all of Plan C's $3 billion went to the apprenticeships, how much would it spend per apprentice? About what percent of one year of Quillon's total real GDP is the $3 billion? Then explain how Plan C raises growth, and respond to its critics.

    Show model answer

17. Question 17 of 20 · Short Answer

    Use Source 4. Assume the base growth rate is 2% a year. Plan A raises it to 2.6% from year 6 through year 30. Plan B raises it to 2.8% for years 1-10, after which growth returns to 2%. Which plan gives the higher real GDP per person after 10 years, and which after 30 years? Show the calculations and explain the difference.

    Show model answer

18. Question 18 of 20 · Short Answer

    Use Source 3, paragraph 3. Section 4 requires that the fund's capital "shall remain forever undiminished" and that only the interest be spent. Why would a Congress that wanted long-run economic growth design the act this way? Connect your answer to human capital.

    Show model answer

19. Question 19 of 20 · Multiple Choice

    Go back to the tractor example in Source 1. Suppose the farmer's output doubles (from 200 to 400 acres) while his combined inputs of labor and capital rise 60%. What happens to multifactor productivity?

    AIt doubles BIt does not change CIt rises 25% DIt rises 40%

20. Question 20 of 20 · Short Answer

    Write a short explanation (6-8 sentences) of why advances in technology, investment in capital goods and investment in human capital each increase economic growth and the standard of living. Use at least one number from the BLS table and evidence from two different sources on this page.

    Show model answer

These standards connect to D2.Eco.13.9-12: prerequisites to review first, parallel standards at the same level, and next steps that build on it.

Standard text: National Council for the Social Studies (NCSS), The College, Career, and Civic Life (C3) Framework for Social Studies State Standards: Guidance for Enhancing the Rigor of K-12 Civics, Economics, Geography, and History (Silver Spring, MD: NCSS, 2013). NCSS was not involved in the production of this lesson and does not endorse it.