Exercises: Factors of growth and income distribution

Explain what economic growth is and which measure is typically used to quantify it. For a country, what difference does it make to grow by $2\ \%$ compared to $5\ \%$?

Name the factors that explain an economy's growth and classify these examples: building a highway, training workers, inventing new management software, and having courts that enforce contracts.

Explain what labor productivity is (output per worker or per hour). One bakery produces $200$ loaves per hour per worker and another, $120$: which is more productive and what three reasons could explain the difference (machinery, training, organization)?

Distinguish between physical capital and human capital, and classify: a factory robot, a welding course, a delivery van, and the accumulated experience of a surgeon. Which of the two types of capital does the person "carry with them"?

What are a country's institutions (laws, courts, registries, the stability of the rules) and why do they count as a factor of growth? Imagine two identical countries except that in one of them contracts are not enforced: what happens to investment?

Explain the difference between economic growth and recession. The term "technical recession" is used when GDP falls for two consecutive quarters: what does that mean and how would it be noticeable in the news and around you?

The GDP of a country increases from $100,000$ million dollars to $104,000$ million in one year.

1. a) Calculate its annual growth rate.
2. b) If the population grew by $1\ \%$, did income per capita also grow? Justify your answer.

The countries Arta and Briga have the same GDP, $200,000$ million dollars, but Arta has $5$ million inhabitants and Briga has $10$ million.

1. a) Calculate the income per capita of each country.
2. b) Explain why GDP per capita is a better measure than total GDP for comparing living standards.

One factory with $50$ workers produces $10,000$ parts a month; another, with $80$ workers, produces $14,000$ parts.

1. a) Calculate productivity per worker for each factory.
2. b) If the first produces more per worker thanks to better machinery, which factors of growth does the comparison illustrate? Relate it to physical capital and technology.

A country's GDP rises from $100,000$ million to $102,000$ million and, the following year, to $104,040$ million.

1. a) Calculate the growth rate for each year.
2. b) Explain why growing $2\ \%$ two years in a row is not exactly growing $4\ \%$: what is the effect that explains this called?

Growing $1\ \%$ a year for $30$ years multiplies income by roughly $1.35$; growing $3\ \%$ a year multiplies it by $2.43$.

1. a) Interpret the difference: what does it mean for the standard of living of grandchildren compared with grandparents in each case?
2. b) Explain why small differences in the growth rate matter so much in the long run (the compounding effect).

A country increases its output by $4\ \%$ in a year, but its workers grow by only $1\ \%$ and its capital (machinery, infrastructure) by another $1\ \%$.

1. a) Where can the rest of the growth come from (technology, organization, training)? What name does that "unexplained" part receive?
2. b) Explain why that source is the most valuable one for growing in a sustained way.

The Department of the Treasury has an extraordinary budget allocation to reboot the economy and is torn between two opposing measures:

• Proposal A: Distribute a direct check of 1.000 dollars to each citizen to boost immediate consumption.

• Proposal B: Finance a ten-year plan to modernize Career and Technical Education (CTE) and apprenticeship programs and provide advanced technical qualifications.

1. a) Economically justify why Proposal B has a greater capacity than Proposal A to shift the PPF (Production Possibility Frontier) to the right in the long run. Model the complete causal chain connecting human capital accumulation with potential GDP growth, explaining its effect on labor productivity, unit labor costs, and aggregate demand.
2. b) If Proposal B generates more solid and sustainable growth, predict why governments often have incentives to opt for Proposal A. What political business cycle failure explains this time lag, and what institutional mechanism would you design to shield training investment from electoral cycles?

The manufacturing industry of a country automates its assembly lines by replacing operational jobs with robots and artificial intelligence systems. Productivity per hour worked grows by 30%, but 25,000 low-skilled workers lose their jobs in the process.

1. a) Analyze the tension between the "displacement effect" (destruction of routine jobs) and the "compensation/productivity effect" (cost reduction, job creation in complementary activities, and an increase in real income). Predict what will happen in the short versus long term with structural unemployment and wage dispersion if the market is left to self-regulate.
2. b) Faced with this shock, the labor union demands a ban on replacing labor, and the employers' association demands full freedom to fire workers. Design a viable economic policy alternative that combines the absorption of technical change with the protection of employability, justifying the specific measures in which investment in human capital should materialize.

An international report compares two economies in the year 2024:

• Emerging Country: Per capita income of 10.000, dollars with a sustained GDP per capita growth rate of 6.0% per year.

• Advanced Country: Per capita income of 40.000, dollars with a sustained GDP per capita growth rate of 2.0% per year.

1. a) Using the rule of 72 (estimated doubling time: $72 / \text{rate}$), calculate how many years it will take for the Emerging Country to double its income for the first time and estimate in how many decades it will manage to catch up with the Advanced Country's per capita income (assuming both maintain their average growth rates constant).
2. b) In practice, many developing countries stall their convergence after reaching middle-income levels. Explain two economic reasons that justify why convergence is not automatic (the so-called "middle-income trap") and predict how a deterioration in legal certainty or property rights would affect the timeline calculated in the previous section.

Two neighboring regions start from an identical economic situation and receive the same amount of federal development funds per capita (1,500 dollars annually) for a decade, invested entirely in transport infrastructure (highways and high-speed rail). Ten years later, Region Alpha has increased its GDP per capita by 28% and has attracted logistics and industrial companies, while Region Beta has barely grown by 3% and its infrastructure registers minimal usage.

1. a) Interpret this divergence based on the theory of the determinants of economic growth: why does the accumulation of physical capital generate strongly diminishing returns if complementary factors such as human capital or a pre-existing business ecosystem are not present? Develop two technical arguments.
2. b) As the head of state economic planning, design a plan to redirect the funds for Region Beta. Justify which three areas you would reallocate the budget items to in order to transform spending into a real multiplier of long-term productivity.