Slutsky Equation (5): Rate of Change (Varian 8.5)

Summary

In this video, Iris France explores the velocity equation in economics, focusing on how changes in the price of a good impact its consumption. The discussion delves into the substitution effect and income effect, explaining how price changes influence consumer decisions and purchasing behavior. France introduces a term for the negative income effect and reworks the velocity equation, offering insight into the relationship between price changes, income, and consumption. This equation is highlighted as a key tool for understanding market dynamics, particularly in the context of future lessons on binding and sound in Chapter 9.

Takeaways

• 😀 The video explains the velocity equation, focusing on how changes in price affect consumption and how these effects are decomposed.
• 😀 The main effects discussed are the substitution effect and the income effect, which together influence changes in consumption patterns.
• 😀 The substitution effect arises when the price of a good changes, and the consumer substitutes their original bundle with a new one, maintaining their purchasing power.
• 😀 The income effect comes into play when the consumer’s income is adjusted back to its original level after the substitution effect, resulting in a further change in consumption.
• 😀 The total effect on consumption is the sum of the substitution effect and the income effect, showing how both factors work together to affect choices.
• 😀 The concept of negative income effect (Δx₁n) is introduced, which is visually represented as the difference between the new bundle (Y) and the restored bundle (Z).
• 😀 The velocity equation is adjusted to account for changes in price (Δp₁) and changes in income (Δm) through specific notations for compensated income and consumption bundles.
• 😀 The equation shows how changes in consumption (Δx₁) can be explained in terms of changes in price and income effects using different terms like Δx₁s (substitution effect) and Δx₁n (negative income effect).
• 😀 The final velocity equation simplifies the relationship between price and consumption, breaking it down into substitution and negative income effects as key components.
• 😀 The velocity equation will be useful in future topics, particularly in Chapter 9, where more complex economic concepts like binding and sound will be explored.
• 😀 The video emphasizes that the velocity equation is a tool for understanding the relationship between price, income, and consumption in economic models.

Q & A

What is the main topic of the video?

The video focuses on explaining the velocity equation and its relationship to changes in price and consumption, specifically discussing the rate of change in variant 8.5.

What happens when the price of a good (e.g., hu1) changes?

When the price of hu1 changes, the consumption of hu1 will change as well. The change in consumption can be decomposed into the substitution effect and the income effect.

What is the substitution effect?

The substitution effect refers to the change in consumption resulting from a price change, where a person’s income is adjusted to allow the previous consumption bundle to remain affordable. The consumer then switches to a new consumption bundle (bundle y) as a result of the price change.

What is the income effect?

The income effect occurs after the substitution effect, where the consumer’s income is restored to its original level, allowing them to purchase the new bundle (bundle y). The difference between the original bundle and the new bundle reflects the income effect.

How are the substitution effect and income effect related to each other?

The total effect of a price change is the sum of the substitution effect and the income effect. The substitution effect represents the change due to price adjustments, while the income effect accounts for the change once income is restored.

What is the negative income effect and how is it visualized?

The negative income effect, denoted as delta x1n, is the difference between the consumption bundles y and z, but in the opposite direction. Visually, it is represented by the distance between points y and z, indicating the decrease in consumption due to income adjustment.

How is the total effect rewritten in terms of the negative income effect?

The total effect can be rewritten as the substitution effect minus the negative income effect. This formula helps to better understand how price changes and income adjustments impact consumption.

What is the equation that represents the relationship between the change in price and the change in income?

The relationship between the change in price (delta p1) and income change (delta m) is expressed by the equation delta p1 = delta m / x1. This equation shows how income changes are related to price changes in the velocity equation.

How is the velocity equation modified in the video?

In the video, the velocity equation is modified by substituting delta p1 with delta m divided by x1. The equation is then rewritten to avoid fractions, resulting in the form: delta x1 / delta p1 = delta x1s / delta p1 - delta x1n / delta m * x1.

Why is the modified velocity equation important?

The modified velocity equation is important because it will be helpful in understanding concepts related to binding and sound in Chapter 9. This equation provides a clearer way to analyze price and income changes.