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

ECON MATHS

7 Feb 202121:14

EducationalLearning

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TLDRIn this video on mathematical economics, Halal explains how to solve a numerical problem involving consumer surplus, producer surplus, and deadweight loss due to a price floor. Using given inverse demand and supply functions, he calculates the equilibrium price and quantity. He then determines the consumer and producer surpluses without a price floor, followed by the surpluses and total surplus with a price floor of 120. Finally, he explains how to calculate the deadweight loss resulting from the price floor, providing a comprehensive step-by-step solution.

Takeaways

📚 The video discusses a numerical problem in mathematical economics involving the impact of a price ceiling on a market.
📉 The inverse market demand and supply functions are given as p = 200 - 2q for demand and p = 50 + q for supply.
⚖️ Equilibrium in the market is found by setting the demand and supply functions equal to each other, resulting in a price of 100 and a quantity of 50.
🛒 Consumer surplus is calculated as the area above the equilibrium price and below the demand curve, resulting in 2500 units.
🚚 Producer surplus is the area below the equilibrium price and above the supply curve, which amounts to 1250 units.
🔢 Total surplus is the sum of consumer and producer surpluses, which equals 3750 units without the price floor.
🚫 The government imposes a price floor at 120, which disrupts the market equilibrium.
📈 With the price floor at 120, the new quantity demanded is 40 units, and the corresponding price from the supply function is 90.
💰 The new consumer surplus after the price floor is imposed is 1600 units, which is less than the original surplus.
📦 Producer surplus increases to 2000 units due to the price floor, as it is now the area below the price floor and above the supply curve.
📉 Total surplus after the price floor is 3600 units, which is different from the total surplus before the price floor.
🗑 Deadweight loss, a measure of market inefficiency, is calculated as the area of the triangle formed by the price floor and the equilibrium quantity, resulting in a loss of 150 units.

Q & A

What is the purpose of the video?
-The purpose of the video is to demonstrate how to calculate total surplus, consumer surplus, producer surplus, and deadweight loss in a market when a price ceiling is imposed, using the given inverse market demand and supply curves.
What are the given inverse market demand and supply functions?
-The inverse market demand function is given as p = 200 - 2q, and the inverse market supply function is given as p = 50 + q.
What is the equilibrium price and quantity before the imposition of the price floor?
-The equilibrium price before the imposition of the price floor is 100, and the equilibrium quantity is 50 units.
How is the consumer surplus calculated in this scenario?
-The consumer surplus is calculated as the area of the triangle formed above the equilibrium price (100) and below the demand curve, which is 1/2 * base (50) * height (100), resulting in 2500.
How is the producer surplus calculated in the initial equilibrium?
-The producer surplus is the area of the triangle formed below the equilibrium price (100) and above the supply curve, which is 1/2 * base (50) * height (50), resulting in 1250.
What is the total surplus before the price floor is imposed?
-The total surplus before the price floor is the sum of consumer surplus (2500) and producer surplus (1250), which equals 3750.
What price floor is imposed by the government in the scenario?
-The government imposes a price floor of 120.
What is the new quantity demanded when the price floor of 120 is imposed?
-When the price floor of 120 is imposed, the new quantity demanded is 40 units, as calculated by substituting the price floor into the demand function.
What is the new price corresponding to the quantity of 40 units after the price floor is imposed?
-The new price corresponding to the quantity of 40 units after the price floor is imposed is 90, as calculated by substituting the quantity into the supply function.
How is the consumer surplus affected by the imposition of the price floor?
-The consumer surplus after the imposition of the price floor is the area of the triangle formed above the price floor (120) and below the demand curve, which is 1/2 * base (40) * height (80), resulting in 1600.
What is the producer surplus after the price floor is imposed?
-The producer surplus after the price floor is imposed is the area of the quadrilateral formed below the price floor (120) and above the supply curve, which is 1200 for the rectangle plus 800 for the triangle, totaling 2000.
What is the total surplus after the price floor is imposed?
-The total surplus after the price floor is imposed is the sum of the new consumer surplus (1600) and the new producer surplus (2000), which equals 3600.
How is the deadweight loss calculated after the price floor is imposed?
-The deadweight loss is calculated as the area of the triangle formed below the equilibrium quantity (50) and above the quantity after the price floor (40), which is 1/2 * base (30) * height (10), resulting in 150.

Outlines

00:00

📊 Introduction to Surplus Calculation

In this video on the mathematical economics series, Halal will solve a numerical problem on finding total surplus, consumer surplus, producer surplus, and deadweight loss due to the imposition of a price ceiling. The given inverse market demand and supply curves are used to solve the problem. The demand function is p = 200 - 2q and the supply function is p = 50 + q. The government imposes a price floor at 120, and we need to find the equilibrium price and quantity, consumer surplus, producer surplus, total surplus without the price floor, and the effect of the price floor on these surpluses and the resulting deadweight loss.

05:00

📈 Equilibrium Price and Quantity Calculation

First, we find the equilibrium price and quantity by equating the demand and supply functions: 200 - 2q = 50 + q. Solving for q gives us an equilibrium quantity of 50. Substituting q = 50 into the supply function, we get an equilibrium price of 100. These are the equilibrium price and quantity without the imposition of a price floor.

10:03

💰 Calculating Consumer Surplus

Consumer surplus is the area above the equilibrium price and below the demand curve. The area of this triangle is calculated as 1/2 * base * height. The base is 50, and the height is 100 (200 - 100). Therefore, the consumer surplus is 2500.

15:03

🏭 Calculating Producer Surplus

Producer surplus is the area below the equilibrium price and above the supply curve. The area of this triangle is 1/2 * base * height. The base is 50, and the height is 50 (100 - 50). Therefore, the producer surplus is 1250. The total surplus without the price floor is the sum of consumer surplus and producer surplus, which equals 3750.

20:04

📉 Effect of Price Floor on Surpluses

With a price floor of 120, we calculate the new quantities and surpluses. Substituting p = 120 into the demand function, we get a quantity of 40. Substituting q = 40 into the supply function, we get a price of 90. The new consumer surplus is the area of the triangle above the price floor and below the demand curve, calculated as 1600. The producer surplus is the area below the price floor and above the supply curve, calculated as 2000. The total surplus after the imposition of the price floor is 3600.

🔻 Calculating Deadweight Loss

Deadweight loss is the area of the triangle between the supply and demand curves, from the new quantity to the equilibrium quantity. The base of this triangle is 30 (120 - 90), and the height is 10 (50 - 40). The area of this triangle is 150, representing the deadweight loss due to the price floor. This concludes the analysis of the effects of the price floor on consumer surplus, producer surplus, total surplus, and deadweight loss.

📚 Summary and Additional Resources

To summarize, we started with the given demand and supply functions, found the equilibrium price and quantity, calculated the surpluses without the price floor, and then analyzed the effects of the price floor on these surpluses and the resulting deadweight loss. For more detailed explanations and additional resources on calculating surpluses using integration methods, viewers are encouraged to check other videos in the mathematical economics series.

Mindmap

Keywords

💡Total Surplus

Total surplus refers to the combined economic value created in a transaction, which is the sum of consumer surplus and producer surplus. In the video, total surplus is calculated before and after the imposition of a price floor to illustrate the economic impact of such a policy. The script explains that total surplus initially is the sum of consumer surplus (2500) and producer surplus (1250), equating to 3750, and then recalculates it post-policy to 3600, indicating a change due to government intervention.

💡Consumer Surplus

Consumer surplus is the difference between what consumers are willing to pay for a good and what they actually pay, represented by the area between the demand curve and the market price. The video script describes consumer surplus as the area above the equilibrium price and below the demand curve, initially calculated as 2500. After the price floor is imposed, the new consumer surplus is the area of a different triangle (aef), recalculated to be 1600, showing a decrease due to the policy change.

💡Producer Surplus

Producer surplus is the difference between the market price and the minimum price producers are willing to accept for a good, depicted as the area below the supply curve and above the market price. In the script, initial producer surplus is the area below the equilibrium price and above the supply curve, calculated as 1250. After the price floor imposition, the new producer surplus includes a rectangle and a triangle (edhf and gdh), with the total recalculated to be 2000, indicating an increase due to the price floor.

💡Price Floor

A price floor is a government-imposed minimum price that a good or service can be sold for, which is above the equilibrium price. The script uses the price floor as a scenario to analyze its effects on consumer surplus, producer surplus, and total surplus. The imposition of a price floor at 120 leads to a new equilibrium quantity of 40 and a price of 90, resulting in changes in surpluses and a deadweight loss.

💡Equilibrium Price and Quantity

Equilibrium price and quantity are the values at which the supply and demand for a product equalize, meaning the quantity supplied equals the quantity demanded. The script calculates the initial equilibrium price as 100 and quantity as 50 by setting the demand and supply functions equal to each other. These values serve as a benchmark to compare against the effects of the price floor.

💡Deadweight Loss

Deadweight loss is the decrease in economic efficiency due to market interventions such as price floors or ceilings. It is represented by the area of a triangle formed by the market equilibrium and the price control. The script calculates the deadweight loss as the area of triangle fhc, resulting in a loss of 150 after the price floor is imposed, indicating a net loss in economic welfare.

💡Inverse Demand and Supply Functions

Inverse demand and supply functions express the relationship between price and quantity in a way that allows for direct calculation of price based on quantity demanded or supplied. The video uses the inverse demand function p = 200 - 2q and the inverse supply function p = 50 + q to find equilibrium and to analyze the effects of the price floor. These functions are essential for understanding how changes in quantity affect price.

💡Market Intervention

Market intervention refers to any action by a government or other authority that alters the natural operation of a market. The script discusses market intervention through the imposition of a price floor, which changes the market's equilibrium and has various economic consequences, such as the redistribution of surplus and the creation of deadweight loss.

💡Law of Demand

The law of demand states that, all else being equal, as the price of a good increases, the quantity demanded decreases, and vice versa. The script implies this law when describing the demand curve as sloping downwards, indicating that higher prices result in less quantity demanded, which is a fundamental concept in the analysis of the price floor's impact.

💡Supply and Demand Curves

Supply and demand curves graphically represent the relationship between the price of a good and the quantity that producers are willing to supply and consumers are willing to demand. The script uses these curves to illustrate the initial market conditions and the changes that occur after the price floor is imposed, showing how the curves shift and the new equilibrium is established.

Highlights

Introduction to solving a numerical on finding total surplus, consumer surplus, producer surplus, and deadweight loss due to the imposition of a price ceiling.

Given inverse market demand function: p = 200 - 2q, and supply function: p = 50 + q.

Government imposes a price floor at 120.

Finding equilibrium price and quantity without the price floor: equilibrium occurs where demand equals supply.

Equilibrium quantity calculated as q = 50.

Equilibrium price determined as p = 100.

Consumer surplus is the area above the equilibrium price and below the demand curve, calculated as 2500.

Producer surplus is the area below the equilibrium price and above the supply curve, calculated as 1250.

Total surplus without the price floor is the sum of consumer and producer surplus, totaling 3750.

After imposing the price floor at 120, the new quantity demanded is found to be q = 40.

New equilibrium price with the price floor determined as p = 90.

Consumer surplus with the price floor is the area above the price floor and below the demand curve, calculated as 1600.

Producer surplus with the price floor is the area below the price floor and above the supply curve, calculated as 2000.

Total surplus with the price floor is 3600, less than the original total surplus.

Deadweight loss due to the price floor is the area of the triangle between the demand and supply curves, calculated as 150.

Summary of the process: equating demand and supply functions to find equilibrium, calculating surpluses and deadweight loss before and after imposing the price floor.

Discussion on the meaning of price floor, consumer surplus, and producer surplus, with additional resources for further learning.

Transcripts

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