Calculating the area of Deadweight Loss (welfare loss) in a Linear Demand and Supply model

Jason Welker
29 Sept 201507:36
EducationalLearning
32 Likes 10 Comments

TLDRThis educational video teaches viewers how to calculate the area of deadweight loss in a market when it's not at equilibrium. Starting with equilibrium price and quantity, the script demonstrates how to find consumer and producer surplus, then shifts to a non-equilibrium scenario at a higher price. It illustrates the decrease in consumer surplus and increase in producer surplus, leading to a total welfare calculation. The script concludes by showing the loss in total welfare, equating to a deadweight loss, and offers an alternative method for calculating this loss using the areas of two triangles.

Takeaways
  • 📈 The video explains how to calculate the area of deadweight loss in a market with a linear demand and supply graph when the market price deviates from the equilibrium price.
  • 📚 Viewers should be familiar with deriving demand and supply equations from data and graphing them before watching this video.
  • 📉 The script provides a step-by-step guide to plotting demand and supply curves on a graph using derived equations.
  • 💰 The equilibrium price and quantity for olives in the example are $5 and 20,000 kilograms, respectively.
  • 🔍 To find consumer and producer surplus at equilibrium, the script describes calculating the area of two triangles formed by the demand and supply curves.
  • 📊 Consumer surplus is the area above the equilibrium price and under the demand curve, while producer surplus is the area below the equilibrium price and above the supply curve.
  • 📉 At a price higher than equilibrium (e.g., $7), consumer surplus decreases, and producer surplus increases, affecting total welfare.
  • 🧩 The script breaks down the calculation of producer surplus into a rectangle and a triangle to simplify the process.
  • 📌 At a price of $7, total welfare is calculated by adding the reduced consumer surplus ($10) to the increased producer surplus ($50), resulting in $60.
  • 🔑 Deadweight loss is determined by comparing total welfare at disequilibrium to that at equilibrium, resulting in a loss of $20,000 in the example.
  • 📝 An alternative method to find deadweight loss is by calculating the area of the two triangles representing the loss of consumer and producer surplus.
Q & A

  • What is the main topic of the video script?

    -The main topic of the video script is how to calculate the area of deadweight loss in a market when there is a deviation from the equilibrium price and quantity in a linear demand and supply graph.

  • What are the prerequisites for understanding the video content?

    -The prerequisites for understanding the video content include familiarity with deriving demand and supply equations from data, graphing those equations, and understanding how to calculate consumer and producer surplus in a linear demand and supply model.

  • What is the equilibrium price and quantity of olives according to the graph in the script?

    -The equilibrium price of olives is $5, and the equilibrium quantity is 20,000 kilograms.

  • How is consumer surplus represented on a demand and supply graph?

    -Consumer surplus is represented by the area above the equilibrium price and below the demand curve on a demand and supply graph.

  • What is the formula for calculating the area of consumer surplus when the market is at equilibrium?

    -The area of consumer surplus at equilibrium is calculated as the area of a triangle, which is 0.5 * base * height, where the base is the equilibrium quantity and the height is the difference between the demand price and the equilibrium price.

  • How is producer surplus represented on a demand and supply graph?

    -Producer surplus is represented by the area below the equilibrium price and above the supply curve on a demand and supply graph.

  • What happens to consumer surplus when the market price is higher than the equilibrium price?

    -When the market price is higher than the equilibrium price, the area of consumer surplus decreases because consumers are willing and able to buy fewer goods at the higher price, resulting in less consumer surplus.

  • How does the producer surplus change when the market price is higher than the equilibrium price?

    -Producer surplus can increase when the market price is higher than the equilibrium price because producers are able to sell their goods at a higher price, but the increase may be offset by a decrease in the quantity demanded.

  • What is the total welfare when the market is at equilibrium, according to the script?

    -The total welfare when the market is at equilibrium is $80, which is the sum of consumer surplus ($40) and producer surplus ($40).

  • How is the deadweight loss calculated when the market is in disequilibrium?

    -Deadweight loss is calculated by finding the difference in total welfare between the equilibrium and disequilibrium states. It represents the loss of total welfare due to the market not being at its most efficient point.

  • What is the total welfare at the disequilibrium price of $7 in the script?

    -The total welfare at the disequilibrium price of $7 is $60, which is the sum of consumer surplus ($10) and producer surplus ($50).

  • How much is the deadweight loss when the market price is $7, as per the script?

    -The deadweight loss when the market price is $7 is $20,000, which is the difference between the total welfare at equilibrium ($80,000) and the total welfare at the disequilibrium price ($60,000).

Outlines
00:00
📊 Calculating Deadweight Loss in Market Disequilibrium

This paragraph introduces the concept of calculating deadweight loss in a market scenario where the price deviates from the equilibrium. The script explains the prerequisites, such as understanding the derivation of demand and supply equations and the ability to graph them. It sets the stage for a detailed explanation of how to calculate consumer and producer surplus and the total welfare at equilibrium, using the example of olives. The equilibrium price and quantity are identified as $5 and 20,000 kilograms, respectively. The paragraph concludes with a teaser for the upcoming calculation of deadweight loss when the market is not at equilibrium.

05:03
📉 Impact of Price Changes on Consumer and Producer Surplus

The second paragraph delves into the effects of a non-equilibrium market price on consumer and producer surplus. It uses the example of olives priced at $7 instead of the equilibrium $5. The script explains how higher prices reduce consumer surplus and increase producer surplus, but with fewer producers able to sell due to decreased demand. The calculation of consumer surplus at the higher price is straightforward, resulting in a decrease to $10. For producer surplus, the script describes a more complex calculation involving both a rectangle and a triangle, resulting in an increase to $50. The total welfare at the higher price is $60, which is less than the equilibrium welfare of $80, indicating a loss in total welfare of $20,000. The paragraph also introduces the concept of deadweight loss as the inefficiency resulting from market disequilibrium, which is calculated by subtracting the new total welfare from the equilibrium welfare.

Mindmap
Keywords
💡Deadweight Loss
Deadweight loss is an economic concept referring to the inefficiency that occurs when the quantity of a good or service demanded and supplied deviates from the equilibrium level, resulting in a loss of total welfare. In the video's context, it is calculated by comparing the total welfare at equilibrium to the welfare at a non-equilibrium price, such as $7, and finding the difference, which represents the loss in total welfare due to market inefficiency.
💡Linear Demand and Supply Graph
A linear demand and supply graph is a graphical representation of the relationship between the price of a good and the quantity demanded or supplied, with demand and supply depicted as straight lines. The video script discusses how to plot these curves and use them to analyze market equilibrium and disequilibrium, specifically focusing on the impact of a price change on consumer and producer surplus.
💡Equilibrium Price and Quantity
The equilibrium price and quantity are the values at which the supply and demand for a product meet, resulting in a market balance where the quantity demanded equals the quantity supplied. In the script, the equilibrium price for olives is given as $5 and the equilibrium quantity as 20,000 kilograms, serving as the reference point for calculating changes in welfare.
💡Consumer Surplus
Consumer surplus is the difference between what consumers are willing to pay for a good and what they actually pay, typically represented by the area under the demand curve but above the market price. The video explains that at equilibrium, consumer surplus is $40, and it decreases to $10 when the price rises to $7, illustrating the impact of price changes on consumer welfare.
💡Producer Surplus
Producer surplus is the difference between the price at which producers are willing to sell a good and the actual market price, usually shown as the area below the supply curve but above the market price. The script details how to calculate producer surplus at different prices, noting an increase from $40 at equilibrium to $50 at a price of $7.
💡Disequilibrium
Disequilibrium in economics occurs when the market price is not equal to the equilibrium price, leading to quantities demanded and supplied that do not match. The video script explores the effects of a price set at $7, which is a disequilibrium price, on consumer and producer surplus and the resulting deadweight loss.
💡Total Welfare
Total welfare is the combined measure of consumer and producer surplus in a market, representing the overall economic benefit derived from transactions. The script calculates total welfare at equilibrium as $80 and then at a disequilibrium price of $7 as $60, highlighting the decrease in welfare due to market inefficiency.
💡Demand and Supply Equations
Demand and supply equations are mathematical representations of the relationship between price and quantity demanded or supplied. The script mentions deriving these equations from data and plotting them on a graph, which is essential for visualizing and analyzing market dynamics.
💡Market Inefficiency
Market inefficiency refers to a situation where the allocation of resources does not maximize social welfare. The script uses the example of a market at a price of $7 to demonstrate how a departure from the equilibrium price can lead to a deadweight loss, indicating a less efficient market outcome.
💡Right Triangles
In the context of the script, right triangles are used to represent the areas of deadweight loss graphically. The area of these triangles is calculated to quantify the loss in total welfare when the market is in disequilibrium, with the script providing an alternative method for calculating deadweight loss by directly finding the area of these triangles.
💡Supply Schedule
A supply schedule is a table or list that shows the quantity of a good that producers are willing to supply at various prices. The script uses the supply schedule to determine the quantity supplied at different prices, which is crucial for calculating producer surplus and understanding market dynamics.
Highlights

Introduction to calculating the area of deadweight loss in a linear demand and supply graph when the market is not at equilibrium.

Assumption that viewers are familiar with deriving demand and supply equations and graphing them.

Presentation of a demand and supply schedule for olives with price ranges and corresponding quantities.

Derivation of demand and supply equations from the data provided in the schedule.

Graphical representation of the derived demand and supply curves on a graph.

Identification of the equilibrium price and quantity for olives as $5 and 20,000 kilograms respectively.

Explanation of calculating consumer and producer surplus at equilibrium as areas of triangles.

Calculation of total welfare in the market at equilibrium as the sum of consumer and producer surplus.

Impact of market disequilibrium on consumer and producer surplus, with a shift in price from $5 to $7.

Reduction in consumer surplus due to a higher market price.

Increase in producer surplus due to the higher selling price, despite reduced quantity sold.

Calculation of the new consumer surplus at the non-equilibrium price of $7.

Complex calculation of producer surplus involving both a rectangle and a triangle area.

Determination of total welfare at the disequilibrium price, showing a decrease from the equilibrium state.

Introduction to the concept of deadweight loss as a measure of market inefficiency.

Methodology to calculate deadweight loss by comparing total welfare at equilibrium and disequilibrium.

Visual representation of deadweight loss as two triangles on the graph.

Alternative method to calculate deadweight loss by directly finding the area of the two triangles.

Conclusion emphasizing the importance of understanding deadweight loss in economic analysis.

Special acknowledgment of a student's achievement in the class.

Transcripts

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Related Tags
EconomicsDeadweight LossMarket EquilibriumConsumer SurplusProducer SurplusDemand SupplyGraphical AnalysisEconomic EfficiencyPrice ControlsWelfare EconomicsSupply Schedule