Production [Macro Economics]

Macro Economics 

- Chapter 4. Model of Production 

What is a Production Model?

A production model is a mathematical framework that helps explain how a country produces goods and services. At its core, it focuses on two main inputs:

• Labor (L) – the people doing the work

• Capital (K) – tools, machines, and buildings used for production

Economists use a production function to show the relationship between these inputs and output (Y).

One of the most common forms is the Cobb-Douglas production function:

Where:

• Y = Output

• K = Capital

• L = Labor

• A = Productivity (also known as Total Factor Productivity or TFP)

• α = Share of capital in output, typically around 1/3

Why Capital and Labor Alone Don’t Explain Everything

You might think that richer countries simply have more capital or labor. But that’s only part of the story.

This model shows diminishing returns to capital. That means adding more machines or buildings doesn’t lead to proportionally more output—unless the country is also improving how it uses them.

What really sets countries apart? Productivity (A)—how efficiently labor and capital are used.

What is Total Factor Productivity (TFP)?

TFP measures the efficiency of production. If two countries have the same capital and labor but one produces more, the difference comes down to TFP.

Here’s why TFP matters:

• Poor countries often have low TFP even if they invest in capital.
• Rich countries tend to use better technology, have more skilled workers (human capital), and enjoy stronger institutions.

In fact, research shows that about two-thirds of the income gap between rich and poor countries is due to differences in productivity—not just inputs.

The Rule of Diminishing Marginal Products

As you keep adding more capital or labor while holding the other constant, the extra output you get from each new unit starts to decline. This is called:

• Diminishing marginal product of capital (MPK)

• Diminishing marginal product of labor (MPL)

That’s why simply increasing the number of factories or machines won’t close the income gap unless you also boost efficiency. 

The rental rate and wage rate are taken as given under perfect competition.

• Hire capital until MPK = r. 

• Hire labor until MPL = w.

Equilibrium in the Model

In a perfectly competitive market, firms pay workers based on MPL and rent capital based on MPK. The economy reaches an equilibrium where:

• All labor and capital are fully used
• Firms make zero profit (all income goes to capital or labor)
• Output = Income = Spending

This creates a clean, simplified model of how real economies work—though, of course, it leaves out complications like government policy, trade, and market imperfections.

Why Doesn’t Capital Flow to Poor Countries?

If capital is more productive in poor countries, why doesn’t it naturally flow there?

The answer lies in TFP differences. Without strong institutions, property rights, or efficient use of resources, returns on capital remain low even where it’s scarce. This explains why investors often avoid riskier, lower-productivity economies.

What Drives Productivity?

Here’s what makes TFP higher in rich countries:

1. Human Capital – Skilled labor from better education and training
2. Technology – Advanced tools and production methods
3. Institutions – Stable governments, legal systems, and market access
4. Efficient Resource Allocation – Resources used where they’re most productive

Poor governance or corruption can lead to misallocation, where capital and labor are wasted or underutilized.

Strengths and Weaknesses of the Model

Strengths:

• Simple and intuitive
• Explains how output depends on inputs and efficiency
• Matches real-world data when TFP is included

Weaknesses:

• Cannot predict why countries differ in TFP
• Oversimplifies the economy (e.g., assumes one good, perfect markets)
• Doesn’t factor in trade, policy, or short-term fluctuations

Still, for a first step in understanding global income differences, the production model is a powerful tool.

Key Takeaways

• A production model explains how GDP is generated from labor, capital, and productivity.
• TFP is the most important factor in explaining why some countries are richer than others.
• Human capital, technology, institutions, and resource allocation are major drivers of productivity.
• Capital alone is not enough—how it’s used matters more.

If you want to understand global inequality, economic growth, or development strategy, you’ll want to start here—with the production model.

[Reference]

[1] Charles I. Jones, Macroeconomics, 5th Edition, Norton.