Lecture: Economic Growth & Productivity
Lecture script · about 15–20 minutes spoken · Week 4
Opening
Here's a question worth carrying around. Why are some economies so much richer than others? And what does 2 percent growth versus 7 percent growth really mean over a lifetime?
You'll meet this question wherever you end up. A small-business owner wants to know when sales might double. A nursing student hears that a city's output is booming and wonders whether pay per person is rising too. A city planner asks why one region keeps pulling ahead of another. All three are asking about growth, and all three lean on the same few calculations.
Here's where we are. In Week 1, The Macro Perspective, you drew the production possibilities frontier. In Week 2, Measuring Output, you learned to measure an economy with real GDP, which counts stuff made, not higher prices. In Week 3, Measuring Inflation & Unemployment, you turned two levels into a percentage change. In this lecture we put all three together and stretch them across years.
Here's the plan. I'll show you what growth looks like on the frontier, how to compute a growth rate, and how to estimate a doubling time. Then we'll watch small differences pile up, turn total growth into growth per person, measure productivity, and name where growth comes from. Next, in Week 5, Aggregate Demand & Aggregate Supply, you'll see how output swings in the short run around this long-run path.
1. Growth moves the whole frontier
Picture a small town that once had one bakery, one clinic, and a bus that came twice a day. Years later it has three bakeries, a clinic with a new scanner, and buses every half hour. Nobody there is working twice as hard. The town has more equipment, better-trained people, and better ways of doing things. It can produce more of everything at once.
That's the idea. Here's the term. Economic growth is a sustained rise over many years in an economy's real GDP, the amount of final goods and services it can produce; on a production possibilities frontier it shows up as an outward shift of the whole frontier.
Let's go back to the Week 1 frontier. It's illustrative, built for this course. That economy had 24,000,000 labor-hours. A unit of consumer goods took 3 hours, and a unit of capital goods took 6 hours. One combination, 6 units of consumer goods and 3 units of capital goods, sat outside the frontier. It needed 36,000,000 hours, and only 24,000,000 existed.
Now let years pass. The economy gains workers, better machines, and faster methods. The whole frontier moves outward. That combination of 6 and 3, which used to be out of reach, comes within reach.
There's a second way to say this. Potential output is the real output an economy can produce when its labor, capital, and technology are in normal, full use; long-run growth raises it year after year. So growth is a steady march of potential output to the right. Next week, potential output becomes a vertical line on a graph.
Pause and try this. An economy has idle workers, then puts them back to work and produces more. Is that long-run growth?
Think about whether the frontier itself moved.
Here's the answer. No. The economy moved toward its frontier, but the frontier stayed put, and only an outward shift of the frontier is long-run growth.
2. A growth rate divides by where you started
Say your rent goes up by 50 dollars a month. Is that a lot? It depends on where you started. On a 1,000-dollar rent, it's 5 percent. On a 500-dollar rent, it's 10 percent. A growth rate puts every change on the same footing by comparing it with the starting value.
Here's the term. A growth rate is the percentage change in a quantity from one period to the next, found as the new value minus the old value, divided by the old (starting) value, times 100. That's the same move you made for inflation in Week 3.
Let's use the illustrative growth economy, built for this course and measured in billions of dollars of real GDP. Last year real GDP was 800. This year it's 840. First, find the change: 840 minus 800 is 40. Second, divide by the starting value, last year's 800. That's 40 divided by 800, which is 0.05. Third, multiply by 100. That gives 5 percent. In words, this economy produced 5 percent more real output than the year before. And because it's real GDP, that 5 percent is more stuff, not higher prices.
Pause and try this. Someone divides the 40 by 840 and reports about 4.76 percent. What went wrong?
Ask yourself which year the economy started from.
Here's the answer. They divided by the new value instead of the starting value. Dividing 40 by the starting 800 gives the correct 5 percent.
So keep this in your pocket: divide by where you started.
3. The rule of 70 for doubling time
Picture anything growing at a steady rate: a savings account, a town's population, a country's output. A natural question is how long it takes to double. You could multiply year after year until you pass twice the start. That works, but it's slow.
Economists use a shortcut. Doubling time is the number of years a quantity takes to reach twice its starting size when it grows at a steady rate. And the rule of 70 is a shortcut that estimates doubling time as about 70 divided by the growth rate in percent; it is an approximation, close for the small rates economies usually grow at.
Let's run it. At 2 percent, 70 divided by 2 is 35 years. At 5 percent, 70 divided by 5 is 14 years. At 7 percent, 70 divided by 7 is 10 years. At 10 percent, 70 divided by 10 is 7 years. Faster growth, shorter doubling time.
Does the shortcut hold up? Check it at 2 percent. Growing 2 percent a year for 35 years means multiplying by 1.02 a total of 35 times. That product comes out to about 2.0. So 35 years at 2 percent does about double a quantity. The 70 itself is a rounded number. It comes from 69.3, and rounding to 70 makes the division easy to do in your head.
Pause and try this. Someone says an economy growing 2 percent a year doubles in 140 years, because 70 times 2 is 140. What's the slip?
Think about whether faster growth should double sooner or later.
Here's the answer. They multiplied instead of dividing. Faster growth should double sooner, so the rate goes on the bottom: 70 divided by 2 gives 35 years.
4. Compound growth: small differences widen
Picture two savings accounts that start out equal. One grows 2 percent a year and the other grows 7 percent. After one year, the gap is small. After many years, it isn't. Each year's growth gets added to the base, and the next year's growth applies to that bigger base. Growth grows on itself.
That's the term. Compound growth is growth in which each year's increase is added to the base for the next year, so the quantity grows on its earlier growth and small differences in rates widen into large gaps over time.
Here's the illustrative example, built for this course. Start with an economy producing 100, measured in billions of dollars. At 2 percent a year for 10 years, it grows to about 121.90. At 7 percent a year for the same 10 years, it grows to about 196.72. Same start, same 10 years. The rates are 2 percent and 7 percent. The outcomes differ by about 75 in billions of dollars, and the faster economy ends with about 1.6-fold the output.
Now check that against the rule of 70. At 7 percent, 70 divided by 7 says about 10 years to double, so you'd expect about 200 after 10 years. The careful figure, about 196.72, lands close to 200 but not on it. That's a useful honesty note. The rule of 70 is an approximation, so say "about" whenever you use it.
Pause and try this. Using the rule of 70 alone, roughly where would the 7 percent economy be after 10 years?
Recall the doubling time you found for 7 percent.
Here's the answer. About 200, since 70 divided by 7 is 10 years to double. The careful figure, about 196.72, is close but not exact.
5. Per-capita growth and living standards
Picture a pizza at a party. If the pizza gets 10 percent bigger but 10 percent more guests show up, nobody gets a bigger slice. An economy works the same way. Total output can grow fast, but if the number of people grows equally fast, each person's share stays flat.
So economists divide by population. Real GDP per capita is real GDP divided by the population, which gives the amount of output per person and is the usual yardstick for an economy's average living standard. And per-capita growth is the growth rate of real GDP per person, which is approximately the growth rate of total real GDP minus the growth rate of the population.
Here's an illustrative city, built for this course. Its total output grows 3 percent in a year, and its population grows 1 percent. Subtract: 3 minus 1 is 2. Output per person rises about 2 percent a year, so the average resident's share is growing.
Now an illustrative country. Its output grows 2 percent a year, and its population also grows 2 percent. Subtract: 2 minus 2 is 0. Total output grows, but output per person stays about the same. One caveat belongs here too. Per capita is an average. It tells you how much output there is per person, not how that output is shared.
Pause and try this. Which place is raising its average living standard, the city or the country?
Compare what is left after you subtract population growth.
Here's the answer. The city. Its output per person grows about 2 percent a year, while the country's grows about 0 percent, so the country's impressive total growth doesn't raise the average share.
6. Productivity: output per worker
Walk into a print shop where 5 workers turn out posters all day. Then the shop gets a faster press. The same 5 workers now turn out many more posters in the same day. Nobody tried harder. Each worker can produce more.
Here's the term. Productivity is the amount of output produced per worker, or per hour of work; rising productivity is the main source of rising living standards over the long run.
Let's compute it for this illustrative shop, built for this course. Before the new press, 5 workers print 1,000 posters a day. Divide 1,000 by 5, and you get 200 posters per worker. After the new press, the same 5 workers print 1,250. Divide 1,250 by 5, and you get 250 per worker. Now use the growth-rate move from earlier. The change is 250 minus 200, which is 50. Divide 50 by the starting 200 and multiply by 100. That gives 25 percent. Each worker produces a quarter more than before.
Why does this matter for a whole country? Output per person can rise in only two broad ways. More people can work, or each worker can produce more. The first runs into limits fast. The second has no fixed ceiling, and that's why productivity is what lifts output per person over the long run.
Pause and try this. Suppose the shop instead hires 5 more workers and prints 2,000 posters on the old presses. Did productivity rise?
Divide by the number of workers before you decide.
Here's the answer. No. Output doubled, but 2,000 divided by 10 workers is 200 posters per worker, exactly the old figure.
7. The sources of growth: capital, skills, and ideas
Think about three shops. In the first, the owner buys a faster machine. In the second, the workers take a course and learn to set up jobs faster. In the third, the owner finds a smarter way to schedule jobs, so nothing sits idle. Each shop raises output per worker, each in a different way.
Those three ways have names. Physical capital is the stock of equipment, machines, tools, and buildings that workers use to produce goods and services; more and better physical capital lets each worker produce more. Human capital is the education, skills, training, and health that workers bring to their jobs and that raise how much each of them can produce. And technology, in growth economics, is the stock of ideas and methods for turning labor and capital into output, including new products and better ways of organizing work.
Economists tie the three together. An aggregate production function is a description of how an economy's total output depends on its labor, its physical and human capital, and its technology taken together. The Solow growth model is the framework economists use to organize the sources of long-run growth with an aggregate production function, tracing how capital, labor, and technology together set output per worker over time. It's named for the economist R. M. Solow, whose 1956 paper set it out. In this course we name the model and use its organizing idea; we don't derive its equations.
Pause and try this. A farm switches to a new seed that yields more grain per acre. Which source of growth is that?
Ask whether it's a new machine, a new skill, or a new method.
Here's the answer. It's technology. A better way of producing is a new idea, even when no new machine is involved.
Closing
Let me pull it together, in the order we built it. Growth moves the whole frontier outward, and it raises potential output year after year. A growth rate divides the change by where you started, so 800 to 840 is 5 percent. The rule of 70 turns a rate into a doubling time, and it's an approximation, so say "about." Compound growth makes small differences widen, which is why 2 percent and 7 percent end up so far apart. Per-capita growth subtracts population growth, because a bigger economy isn't automatically a richer one per person. Productivity is output per worker, and it's what lifts living standards. And the three sources of growth are physical capital, human capital, and technology, organized by the Solow growth model.
Next in this module come the slide deck, the Readings & Resources page, the lecture tutorial, the practice set, and the quiz. In Week 5, Aggregate Demand & Aggregate Supply, you'll leave the long run for the short run and build the model of why output and prices move together.
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