Consumer Welfare: Compensating Variation & Equivalent Variation

Economics in Many Lessons

26 Jun 201806:57

EducationalLearning

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TLDRThis educational video explores the concepts of compensating and equivalent variation in consumer welfare. It uses a hypothetical scenario where a person moves from City A to City B, demonstrating how to calculate the additional income needed (compensating variation) to maintain the same utility level despite price changes. The video also explains how much income reduction (equivalent variation) would decrease utility by the same amount as the price increase. The example involves a utility function with perfect complements and a budget constraint, illustrating the calculations clearly.

Takeaways

📚 The video discusses consumer welfare, focusing on compensating variation and equivalent variation in the context of moving from City A to City B.
🔍 The utility function for a person in City A is given as a perfect complements utility function, with income and prices for goods X and Y specified.
💰 The budget constraint in City A is derived from the income and prices of goods X and Y, leading to the determination of the quantities of goods that maximize utility.
🔄 The person's utility in City A is calculated using the quantities of goods purchased, resulting in a specific utility level.
🏙️ Moving to City B, the price of good Y increases, but the utility function and income remain unchanged, necessitating a new budget constraint.
📈 The compensating variation is defined as the additional money needed to offset the price increase and maintain the same utility level.
🔢 Through calculations, it is determined that an additional $1,250 is required in City B to achieve the same utility as in City A.
🔧 The equivalent variation is the amount of income reduction that would result in the same utility decrease as the price increase in City B.
📉 The equivalent variation calculation shows that an income of $4,000 in City A with lower prices would provide the same utility as $5,000 in City B with higher prices.
🤔 The video emphasizes the concept of utility maximization and how price changes can be offset by income adjustments to maintain consumer welfare.
📚 The video concludes by summarizing the calculations and concepts, aiming to provide a clear understanding of compensating and equivalent variations.

Q & A

What is the main topic of the video?
-The main topic of the video is consumer welfare, specifically focusing on compensating variation and equivalent variation in the context of a hypothetical move from City A to City B.
What is a perfect complements utility function?
-A perfect complements utility function is a type of utility function where two goods are consumed in fixed proportions, meaning one good is consumed twice as much as the other.
What are the prices of goods X and Y in City A?
-In City A, the price of good X is $1 and the price of good Y is $2.
What happens to the price of good Y when the person moves to City B?
-When the person moves to City B, the price of good Y increases to $3, while the price of good X remains unchanged at $1.
How is the budget constraint in City A derived?
-The budget constraint in City A is derived by setting the income equal to the price of good X times the units of good X plus the price of good Y times the units of good Y.
What is the definition of compensating variation?
-Compensating variation is the amount of money that needs to be given to a consumer to completely offset a price increase, so that the consumer's utility remains unchanged.
What is the utility function evaluated at the optimal consumption levels in City A?
-The utility function evaluated at the optimal consumption levels in City A is 2500 units, where the consumer buys 2500 units of good X and 1250 units of good Y.
How much additional income would the consumer need in City B to maintain the same utility level as in City A?
-The consumer would need an additional $1250 in City B to maintain the same utility level as in City A, given the higher price of good Y.
What is the definition of equivalent variation?
-Equivalent variation is the amount of money that needs to be taken away from a consumer to lower their utility by the same amount as a price increase.
What is the utility level in City B when the consumer's income is $5000 and the prices are adjusted?
-The utility level in City B when the consumer's income is $5000 and the prices are adjusted is 2000 units, with the consumer buying 2000 units of good X and 1000 units of good Y.
What would be the consumer's income in City A to provide the same utility as in City B with the higher prices?
-The consumer's income in City A would need to be $4000 to provide the same utility as in City B with the higher prices, assuming the lower prices of goods X and Y.

Outlines

00:00

💼 Consumer Welfare and Price Changes Analysis

This paragraph introduces the video's focus on consumer welfare, specifically compensating and equivalent variations. It discusses a hypothetical scenario where a person moves from City A to City B, with an unchanged utility function and income, but a price change for good-y. The compensating variation is defined as the amount needed to offset the price increase and maintain the same utility level. The utility function for a consumer with a perfect complements utility function is maximized by setting units of goods x and y in a specific ratio, given the budget constraint. The example provided calculates the compensating variation required for the consumer to maintain the same level of utility in City B as in City A, due to the increased price of good-y.

05:03

💸 Calculating Equivalent Variation in Price Sensitivity

The second paragraph delves into the concept of equivalent variation, which is the amount of income reduction that would result in the same utility level decrease as caused by the price increase. It uses the same utility function and budget constraint approach but starts with the assumption of City B's price structure and income. The calculation shows the income level that would provide the same utility as the higher prices in City B, if the consumer had lower prices in City A. The equivalent variation is determined by the difference in income that would yield the same utility under different price scenarios. The paragraph concludes by reiterating the idea that different combinations of income and prices can result in the same level of utility, emphasizing the sensitivity of consumer utility to price changes.

Mindmap

Keywords

💡Consumer Welfare

Consumer welfare refers to the overall well-being of consumers, often measured by their satisfaction and utility derived from the consumption of goods and services. In the video, consumer welfare is the central theme, as it discusses how changes in prices and income can affect a consumer's utility and the compensating and equivalent variations needed to maintain that utility.

💡Compensating Variation

Compensating variation is an economic concept that describes the amount of money that would need to be given to a consumer to offset a price increase and maintain the same level of utility. In the video, it is calculated to determine how much additional income a person would need in City B to compensate for the higher price of good-y and remain on the same indifference curve as in City A.

💡Equivalent Variation

Equivalent variation is the amount of money that would need to be taken away from a consumer to reduce their utility by the same amount as a price increase. The video explains this concept by showing how a decrease in income in City A, with lower prices, would provide the same utility as an income of $5,000 with higher prices in City B.

💡Utility Function

A utility function in economics represents the preferences of a consumer and is used to determine the maximum satisfaction that can be derived from a given quantity of goods. In the video, the utility function is given by a perfect complements function, which is used to find the optimal consumption bundle that maximizes utility under a given budget constraint.

💡Perfect Complements

Perfect complements are goods that are consumed in fixed proportions, meaning that the consumption of one good is entirely dependent on the consumption of the other. The video script uses a utility function with perfect complements, where the quantity of good-x is always twice that of good-y, to illustrate the consumer's preferences and optimal consumption choices.

💡Budget Constraint

A budget constraint is the limit on consumption that a consumer faces due to their income and the prices of goods. In the video, the budget constraint is used to determine the maximum quantity of goods that can be purchased with a given income, and it changes when the consumer moves from City A to City B due to a change in the price of good-y.

💡Indifference Curve

An indifference curve on a utility graph represents all the combinations of goods that provide the consumer with the same level of satisfaction. The video discusses how compensating and equivalent variations are used to keep the consumer on the same indifference curve despite price changes.

💡Price Increase

A price increase refers to a rise in the cost of a good or service. In the context of the video, the price of good-y increases when the consumer moves from City A to City B, which affects the consumer's utility and necessitates the calculation of compensating and equivalent variations.

💡Income

Income is the total monetary earnings of an individual or household, which is used to purchase goods and services. The video assumes that the consumer's income remains unchanged when moving from City A to City B, allowing for a direct comparison of the effects of price changes on utility.

💡Maximizing Utility

Maximizing utility is the process of choosing the optimal consumption bundle that provides the highest possible satisfaction given a consumer's preferences and constraints. The video demonstrates this process by setting the quantities of goods in the utility function equal to each other and solving the budget constraint to find the quantities of goods that maximize utility.

Highlights

The video discusses consumer welfare in the context of compensating and equivalent variations.

The scenario involves a hypothetical move from City A to City B with a change in the price of good-y.

The person's utility function is given as a perfect complements utility function.

Income and the price of good-x remain constant, while the price of good-y increases in City B.

Compensating variation is defined as the amount needed to offset the price increase and maintain the same utility level.

The utility function is maximized by setting the ratio of goods x to y equal to each other.

In City A, the consumer buys 2,500 units of good-x and 1,250 units of good-y, resulting in a utility of 2,500 units.

For City B, the utility function is set to match the utility in City A, and the budget constraint is adjusted for the new prices.

In City B, the consumer would need an additional $1,250 to maintain the same utility level with the higher price of good-y.

Equivalent variation is the amount of money to take from the consumer to lower their utility by the same amount as the price increase.

The utility in City B is maximized with the new price structure, resulting in a lower utility level.

To achieve the same utility as in City B with lower prices, the consumer's income would need to be reduced to $4,000.

The equivalent variation is the difference in income, which is $1,000.

The video concludes by comparing the utility levels under different price and income scenarios.

The compensating variation and equivalent variation concepts are illustrated through a practical example.

The video provides a clear explanation of how changes in prices affect consumer welfare and the economic measures to quantify these effects.

The importance of understanding the impact of price changes on consumer utility is emphasized.

Transcripts

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Takeaways

Q & A

What is the main topic of the video?

What is a perfect complements utility function?

What are the prices of goods X and Y in City A?

What happens to the price of good Y when the person moves to City B?

How is the budget constraint in City A derived?

What is the definition of compensating variation?

What is the utility function evaluated at the optimal consumption levels in City A?

How much additional income would the consumer need in City B to maintain the same utility level as in City A?

What is the definition of equivalent variation?

What is the utility level in City B when the consumer's income is $5000 and the prices are adjusted?

What would be the consumer's income in City A to provide the same utility as in City B with the higher prices?