Consumer Surplus, Producer Surplus,& Deadweight Loss before and after imposing the price ceiling?

ECON MATHS

23 Aug 202120:22

EducationalLearning

32 Likes 10 Comments

TLDRThis video script tackles a supply and demand problem involving sandwiches with unique functions, where supply is 500p - 1000 and demand is 11000 - 1000p. It explains the concept of a price ceiling and calculates consumer and producer surplus before and after imposing a $4 price cap. The equilibrium price is found to be $8, leading to a surplus of $13,500. After the price ceiling, surpluses are recalculated, resulting in a new consumer surplus of $6,500, producer surplus of $1,000, and a deadweight loss of $6,000, illustrating the impact of price controls on market efficiency.

Takeaways

📈 The video discusses a problem involving supply and demand functions for sandwiches with specific equations given for supply and demand.
💡 A price ceiling, also known as a price cap, is defined as the maximum price at which goods can be sold, acting as a form of price control.
🔍 The equilibrium price and quantity are calculated by setting the supply function equal to the demand function, resulting in an equilibrium price of $8.
📊 The equilibrium quantity is found by substituting the equilibrium price back into either the supply or demand function, yielding a quantity of 3,000 sandwiches.
🤔 Consumer surplus is calculated as the area below the demand curve and above the equilibrium price, amounting to 4,500 in this scenario.
🛒 Producer surplus is determined by the area above the supply curve and below the equilibrium price, which is 9,000 for this example.
🔢 The total surplus, which is the sum of consumer and producer surplus, is calculated to be 13,500 before the imposition of a price ceiling.
🚫 When a price ceiling of $4 is imposed, it results in a market inefficiency, causing a shortage and a change in both consumer and producer surpluses.
📉 The new consumer surplus after the price ceiling is a combination of the area of a triangle and a rectangle, totaling 6,500.
📈 The new producer surplus shrinks to 1,000 due to the price ceiling, as the area of the triangle representing it decreases.
💔 Deadweight loss, representing the cost to society from market inefficiency, is calculated as the area of a triangle, resulting in a loss of 6,000.

Q & A

What is the supply function for sandwiches in the given problem?
-The supply function for sandwiches is given as 500p - 1000, where p is the price and q is the quantity.
What is the demand function for sandwiches in the given problem?
-The demand function for sandwiches is given as 11,000 - 1,000p, where p is the price and q is the quantity.
What is a price ceiling and how is it described in the script?
-A price ceiling, also called a price cap, is the highest point at which goods can be sold. It is a type of price control, setting the maximum amount sellers can charge for a good.
How do you find the equilibrium price and quantity before the imposition of the price ceiling?
-To find the equilibrium price and quantity, set the quantity supplied equal to the quantity demanded and solve for the price. Then, substitute the equilibrium price back into either function to find the equilibrium quantity.
What are the equilibrium price and quantity for sandwiches before the price ceiling is imposed?
-The equilibrium price is $8, and the equilibrium quantity is 3,000 sandwiches.
How is the consumer surplus calculated before the imposition of the price ceiling?
-Consumer surplus is the area below the demand curve and above the equilibrium price, which is calculated as 0.5 * (11 - 8) * 3,000, resulting in a consumer surplus of $4,500.
How is the producer surplus calculated before the imposition of the price ceiling?
-Producer surplus is the area above the supply curve and below the equilibrium price, which is calculated as 0.5 * (8 - 2) * 3,000, resulting in a producer surplus of $9,000.
What is the total surplus before the imposition of the price ceiling?
-The total surplus before the imposition of the price ceiling is the sum of the consumer surplus and producer surplus, which is $4,500 + $9,000 = $13,500.
What happens to the quantity supplied and demanded when a price ceiling of $4 is imposed?
-When a price ceiling of $4 is imposed, the quantity supplied is 1,000 sandwiches, and the quantity demanded is greater than the quantity supplied, leading to a shortage.
How is the new consumer surplus calculated after the imposition of the price ceiling?
-The new consumer surplus is the area below the demand curve and above the price ceiling, which is composed of a triangle and a rectangle. It is calculated as 0.5 * (11 - 10) * 1,000 + 6 * 1,000, resulting in a consumer surplus of $6,500.
How is the new producer surplus calculated after the imposition of the price ceiling?
-The new producer surplus is the area above the supply curve and below the price ceiling, which is calculated as 0.5 * (4 - 2) * 1,000, resulting in a producer surplus of $1,000.
What is the deadweight loss due to the imposition of the price ceiling?
-The deadweight loss is the cost to society created by market inefficiency, calculated as the area of the triangle formed between the demand and supply curves at the new quantity supplied. It is calculated as 0.5 * (10 - 4) * (3,000 - 1,000), resulting in a deadweight loss of $6,000.

Outlines

00:00

📚 Introduction to Price Ceiling and Supply-Demand Analysis

The video begins by introducing a problem regarding supply and demand functions for sandwiches, posed by a friend on a Telegram channel. The supply function is given as 500p - 1000, and the demand function as 11,000 - 1,000p, where p is the price and q is the quantity. A price ceiling of $4 is imposed, and the task is to calculate the consumer surplus, producer surplus, and deadweight loss before and after this price control measure. The concept of a price ceiling is explained as the maximum price at which goods can be sold, acting as a form of price control. The video then proceeds to find the equilibrium price and quantity before the price ceiling is imposed, using the supply and demand equations to solve for p and q, resulting in an equilibrium price of $8 and quantity of 3,000 units.

05:02

📈 Calculating Intercepts and Surpluses Before Price Ceiling

The second paragraph delves into the process of calculating the intercepts of the supply and demand curves to understand the market conditions before the price ceiling. The supply curve intercept is found to be at a price of $2, and the demand curve intercept at $11. Using these intercepts, along with the equilibrium price and quantity, the video calculates the consumer surplus as the area of a triangle formed by the demand curve, equilibrium price, and quantity. The consumer surplus is determined to be 4,500 units of currency. Similarly, the producer surplus is calculated as the area between the supply curve and the equilibrium price, resulting in a producer surplus of 9,000 units. The total surplus, which is the sum of consumer and producer surplus, is then presented as 13,500 units.

10:02

🛑 Impact of Price Ceiling on Market Surpluses

In the third paragraph, the video discusses the impact of the imposed price ceiling of $4 on the market. It explains that at this price, the quantity supplied would be 1,000 units, as calculated using the supply function with p=4. However, the quantity demanded would greatly exceed the supplied amount, leading to a shortage. The video then calculates the new consumer surplus under the price ceiling, which is a combination of the area of a triangle and a rectangle, resulting in a new consumer surplus of 6,500 units. The producer surplus is recalculated as well, shrinking to 1,000 units due to the price ceiling's effect on the market dynamics.

15:02

📉 Deadweight Loss and Market Inefficiency

The fourth paragraph focuses on the concept of deadweight loss, which is the cost to society created by market inefficiency when supply and demand are out of equilibrium due to price controls like the price ceiling. The video identifies the deadweight loss as the area of a triangle formed by the difference between the equilibrium quantity and the quantity supplied at the price ceiling, and the difference between the equilibrium price and the price ceiling. The calculation results in a deadweight loss of 6,000 units, indicating the inefficiency and loss of total surplus caused by the price ceiling.

20:04

🙌 Conclusion and Call to Action

The final paragraph wraps up the video by summarizing the effects of the price ceiling on consumer and producer surpluses and the resulting deadweight loss. It emphasizes the importance of understanding the intercepts of supply and demand functions and the calculation of surpluses in analyzing market outcomes. The video concludes with a call to action, encouraging viewers to share and subscribe for more informative content.

Mindmap

Keywords

💡Supply and Demand Functions

Supply and demand functions are mathematical representations that show the relationship between the price of a good and the quantity of the good that producers are willing to supply and consumers are willing to demand. In the video, the supply function is given as 500p - 1000 and the demand function as 11,000 - 1,000p, where p is the price and q is the quantity. These functions are fundamental to understanding how the market operates and are central to the analysis of the price ceiling's impact.

💡Price Ceiling

A price ceiling is a government-imposed limit on the price at which a good or service can be sold. It is a form of price control that prevents sellers from charging more than the specified maximum price. In the video, a price ceiling of four dollars is imposed on sandwiches, which leads to a change in market dynamics and affects consumer and producer surpluses.

💡Consumer Surplus

Consumer surplus is the difference between what consumers are willing to pay for a good and what they actually pay. It is often represented graphically as the area below the demand curve and above the market price up to the quantity transacted. In the video, the calculation of consumer surplus before and after the price ceiling is imposed is a key part of understanding the market's efficiency.

💡Producer Surplus

Producer surplus is the difference between the price at which producers are willing to sell a good and the actual price they receive. It is depicted as the area above the supply curve and below the market price up to the quantity sold. The video discusses how the producer surplus changes when a price ceiling is imposed, indicating the impact on sellers.

💡Equilibrium Price and Quantity

The equilibrium price and quantity are the values at which the quantity demanded by consumers equals the quantity supplied by producers. In the script, the equilibrium price is calculated to be eight dollars, and the equilibrium quantity is three thousand units, which is a critical point for understanding the market's natural state before intervention.

💡Intercept

In the context of the video, the intercept of a supply or demand curve is the point where the curve crosses the price or quantity axis. The intercept helps in determining the maximum price consumers are willing to pay or the maximum quantity producers are willing to supply without any cost. The script uses intercepts to calculate consumer and producer surpluses.

💡Shortage

A shortage occurs when the quantity demanded exceeds the quantity supplied at a given price. In the video, when a price ceiling of four dollars is imposed, it results in a shortage because the quantity demanded is greater than the quantity supplied at that price level.

💡Deadweight Loss

Deadweight loss is the inefficiency caused by a divergence between the equilibrium quantity and the quantity actually transacted due to market interventions like price ceilings or floors. The video calculates the deadweight loss as the area of a triangle representing the lost consumer and producer surplus due to the price ceiling.

💡Market Inefficiency

Market inefficiency refers to a situation where the allocation of goods and services does not reflect the optimal distribution from an economic perspective. In the video, the imposition of a price ceiling leads to market inefficiency, as indicated by the deadweight loss and the discrepancy between the quantity demanded and supplied.

💡Total Surplus

Total surplus is the sum of consumer surplus and producer surplus, representing the total economic welfare in a market. The video calculates the total surplus before the imposition of the price ceiling and compares it to the situation after the ceiling is imposed to demonstrate the impact on overall market welfare.

Highlights

Introduction of a problem involving supply and demand functions for sandwiches with a given supply function of 500p - 1000 and a demand function of 11000 - 1000p.

Explanation of the concept of a price ceiling, which is the maximum price at which goods can be sold.

Method to find equilibrium price and quantity by equating supply and demand functions before price ceiling imposition.

Calculation of equilibrium price at $8 and quantity at 3000 units using the supply and demand equations.

Description of how to calculate consumer surplus as the area below the demand curve and above the equilibrium price.

Identification of the intercepts of the supply and demand curves to facilitate surplus calculations.

Calculation of consumer surplus before the price ceiling as the area of a triangle with a base of 3000 and height of 3.

Explanation of producer surplus as the area above the supply curve and below the equilibrium price.

Calculation of producer surplus before the price ceiling as the area of a triangle with a base of 6 and height of 3000.

Determination of total surplus as the sum of consumer and producer surplus before the price ceiling imposition.

Imposition of a $4 price ceiling and its impact on the market, leading to a shortage and a change in supply and demand dynamics.

Calculation of the new quantity supplied at the price ceiling of 1000 units when the price is $4.

Analysis of the new consumer surplus after the price ceiling, including the area of a triangle and a rectangle.

Reduction in producer surplus to the area of a triangle formed by the price ceiling and the supply curve.

Introduction of the concept of deadweight loss as a result of market inefficiency due to the price ceiling.

Calculation of deadweight loss as the area of a triangle resulting from the price ceiling's impact on supply and demand equilibrium.

Summary of the changes in consumer and producer surplus and the introduction of deadweight loss due to the price ceiling.

Emphasis on the importance of understanding the intercepts of supply and demand functions for accurate surplus calculations.

Transcripts

Browse More Related Video

Consumers 'surplus Producers' Surplus , Total surplus, deadweight loss with price floor

Animation on How to Price Ceilings with Calculations

Rent control and deadweight loss | Microeconomics | Khan Academy

Price Ceiling: Consumer Surplus, Producer Surplus, & Deadweight loss

What is Consumers Surplus and Producer Surplus?

Price floors and surplus

Related Tags

Economics Price Ceiling Supply & Demand Consumer Surplus Producer Surplus Market Efficiency Economic Analysis Quantity Calculation Equilibrium Price Deadweight Loss Policy Impact