Solow Model : Dengan Pertumbuhan Populasi

Summary

This video discusses the Solow growth model, focusing on the impact of population growth. It introduces the concept of 'break-even investment,' which compensates for capital depreciation and population growth, ensuring capital per worker remains steady. The presenter explains how higher population growth lowers income per capita in the long run and uses graphical analysis to demonstrate this. Additionally, the video explores the 'Golden Rule' in the Solow model, showing how it changes with population growth, and concludes by discussing how countries with higher population growth tend to have lower income levels.

Takeaways

• 🔍 The video discusses the Solow growth model with the introduction of population growth.
• 👥 Initially, the model assumes a constant population, but now it considers the effects of population growth.
• 📈 Population growth is incorporated using the concept of 'break-even investment,' which adjusts for depreciation and the growing workforce.
• 💼 Break-even investment ensures that capital per worker remains constant despite population growth and depreciation.
• 🧮 The formula for break-even investment is written as Delta (depreciation) plus 'n' (population growth rate) multiplied by capital (K).
• 📉 With population growth, capital per worker decreases unless investments increase to compensate for new workers and depreciation.
• 🛠 The steady-state is reached when investment equals break-even investment, and population growth causes shifts in this equilibrium.
• 💡 Higher population growth leads to lower steady-state levels of income per worker, as demonstrated in the Solow model's predictions.
• 🌍 Empirical data shows a negative correlation between population growth and income per person across different countries.
• 📊 In the Solow model, the 'Golden Rule' steady-state occurs when consumption is maximized, with the marginal product of capital (MPK) equaling depreciation plus population growth.

Q & A

What is the key modification introduced in the Solo Growth Model in this video?

The key modification is the introduction of population growth into the Solo Growth Model, which was previously assumed to be constant.

How does the Solo Model handle population growth?

Population growth is handled by introducing the concept of 'breakeven investment,' which ensures that the capital per worker remains constant, even with population growth and depreciation.

What is 'breakeven investment' in the context of the Solo Model?

Breakeven investment refers to the level of investment required to keep the capital per worker constant. This compensates for both depreciation and the growth of the worker population.

How is the formula for breakeven investment derived?

Breakeven investment is derived as: (δ + n) * K, where δ represents the depreciation rate, n is the population growth rate, and K is the capital per worker.

How does population growth impact capital accumulation in the model?

Population growth increases the amount of investment needed to maintain the same level of capital per worker. The formula for capital accumulation becomes: Investment - (δ + n) * K.

What happens to the steady-state capital level if population growth increases?

If population growth increases, the breakeven investment curve shifts upward, leading to a lower steady-state level of capital per worker.

What does the Solo Model predict about countries with high population growth in the long run?

The Solo Model predicts that countries with higher population growth will tend to have lower levels of income per capita in the long run.

How is the relationship between population growth and income per person illustrated in empirical data?

Empirical data shows a negative relationship between population growth and income per person, meaning countries with higher population growth tend to have lower income per capita.

How does population growth affect the Golden Rule in the Solo Model?

With population growth, the Golden Rule is adjusted so that the marginal product of capital (MPK) equals (δ + n), instead of just δ.

What is the condition for maximizing consumption in the steady-state with population growth?

In the steady-state with population growth, consumption is maximized when MPK - δ = n, ensuring that the difference between MPK and depreciation equals the population growth rate.