# Economic Growth

Business I · Introduction to Economics · https://tryals.app/learn/business-i/economic-growth

## The Force That Compounds

In the short run economies wobble around their trend; in the long run **the trend is everything**. An economy growing 2 percent a year doubles living standards in roughly 35 years; at 7 percent, every decade.

The **rule of 70** does the arithmetic:

$\text{years to double} \approx \frac{70}{\text{growth rate \%}}$

Compound growth is why small differences in rates dwarf every other economic question over a generation. **Physical capital** (machines and infrastructure per worker) faces **diminishing returns**: the tenth truck adds less output than the first.

**Human capital** includes the education, skills, and health embodied in workers. Like physical capital, it also faces diminishing returns eventually.

## Engines and Institutions

**Technology** provides better recipes for combining the same inputs. Unlike capital, ideas do not run into diminishing returns because one blueprint serves everyone at once, making it the engine of **sustained growth**.

| Engine | What it adds | Diminishing returns? |
| --- | --- | --- |
| Physical capital | More machines per worker | Yes |
| Human capital | Skills, education, health | Yes |
| Technology | Better recipes | **No**: one idea serves all |

**Institutions** (property rights, courts, stable money) are the invisible infrastructure making accumulation safe. **Pitfall**: capital can be bought and technology copied, but no one invests where contracts fail.

## Practice questions

6 of this lesson's 14 practice questions, with answers. The full set is in the app.

### 1. A country grows at 2% a year. Using the rule of 70, set the slider to the years its GDP needs to double.

**Answer:** 35 (within ±2)

**Why:** $70/2 = 35$ years, a working lifetime per doubling. At 7% it would be one decade. Over a century, that gap compounds into different civilizations.

Page: https://tryals.app/practice/business-i/economic-growth/a-country-grows-at-2-a-year-using-the-rule-of-70-set-the-slider-to

### 2. Two economies grow at 2% and 3.5%. Over a century, how different are they?

A. Modestly, since 1.5 percentage points is a small annual difference
B. About 1.5 times different, in proportion to the growth gap
C. Identical, since growth rates converge in the long run
D. Enormously; compounding turns 1.5 points into a fourfold gap

**Answer:** D. Enormously; compounding turns 1.5 points into a fourfold gap

**Why:** Doubling every 35 years against every 20 gives roughly three doublings against five, a factor of four. Lucas said that once you start thinking about growth it is hard to think about anything else, and this arithmetic is why.

Page: https://tryals.app/practice/business-i/economic-growth/two-economies-grow-at-2-and-3-5-over-a-century-how-different-are

### 3. Because ideas can be used by everyone simultaneously, technological progress escapes the diminishing returns that limit capital accumulation.

**Answer:** True

**Why:** A blueprint is non-rival: using it doesn’t use it up. That is why sustained long-run growth ultimately rides on technology, not on piling up ever more machines.

Page: https://tryals.app/practice/business-i/economic-growth/because-ideas-can-be-used-by-everyone-simultaneously-technological

### 4. Order these steps of the virtuous growth circle, starting from secure institutions.

**Answer:**

1. Property rights make investment safe
2. Households save and firms build capital
3. Education deepens human capital
4. Innovation raises productivity
5. Higher income funds the next round of all three

**Why:** Institutions unlock accumulation, accumulation feeds innovation, and income closes the loop, growth as a self-reinforcing circle rather than a one-off gift.

Page: https://tryals.app/practice/business-i/economic-growth/order-these-steps-of-the-virtuous-growth-circle-starting-from-secure

### 5. Two countries invest the same in machines and schooling, and one grows much faster. Institutions are usually invoked to explain the gap. How do they act on growth?

A. By determining whether investment pays off for the investor
B. By increasing the quantity of physical capital available
C. By directly producing output the way capital and labour do
D. By raising the birth rate and so the size of the workforce

**Answer:** A. By determining whether investment pays off for the investor

**Why:** Institutions change the return on everything else. That is why they show up as the residual: they do not enter the production function but they determine whether anyone bothers to fill it.

Page: https://tryals.app/practice/business-i/economic-growth/two-countries-invest-the-same-in-machines-and-schooling-and-one

### 6. Order this stylized development path.

**Answer:**

1. Reforms secure property rights and courts
2. Foreign and domestic investment pours in
3. Factories and infrastructure multiply
4. Schooling and skills catch up with the machines
5. Home-grown innovation takes over as the engine

**Why:** The standard escape route: institutions first, capital second, skills third, and finally ideas, the only engine that never hits diminishing returns.

Page: https://tryals.app/practice/business-i/economic-growth/order-this-stylized-development-path