How to Calculate Deadweight Loss?
What is deadweight loss?
Deadweight loss definition
Deadweight loss can be identified as the losing of economic efficiency when optimal output level is not achieved. How to calculate deadweight loss? To calculate the deadweight loss, we can multiply price change and quantity change as results of the price distortion and divide by two
Deadweight loss formula
The formula for deadweight loss is as follows
Deadweight loss = 1/2 x Change in price x Change in quantity
In the deadweight loss formula, change in price and change in quantity means,
Change in price – Change of the market price in a market distortion when compared to before market distortion.
Change in quantity – Change of the market quantity in a market distortion when compared to before market distortion.
How to calculate the deadweight loss? – Deadweight loss example
We will give an example of deadweight loss. Let’s calculate deadweight loss
Suppose the original price and quantity of a product are $12 and 120 units, respectively. If the government imposes a tax of $2 per unit, the new price and quantity will be $14 and 80 units, respectively. Calculate deadweight loss
Deadweight loss = 1/2 x Change in price x Change in quantity
Deadweight Loss= 1/2 ×($14−$12)×(120−80) = 1/2 x $2 x 40 = $40
Causes for deadweight loss
Deadweight loss can be occurred because of market distortions such as,
Price ceiling
Price floor
Tax
Subsidy
Imperfect market structures such as monopoly, oligopoly, monopolistic competition
Let’s consider how to calculate deadweight loss at each market distortion above mentioned.
How to calculate deadweight loss in a monopoly?
In the monopoly market, there is only one firm that produces a product with no close substitutes. So, a monopoly firm controls the supply of the whole market and so that it has monopoly power to control the market price. Hence, a monopolistic market is a non-competitive market.
As a results of charging higher prices than competitive equilibrium, a monopoly firm loses the economic efficiency. So that, there is a deadweight loss.
To calculate deadweight loss of monopoly, you need to know the monopoly price and quantity, the marginal cost, and the demand curve. The deadweight loss monopoly formula is:
Monopoly deadweight loss formula
Deadweight Loss=1/2 × (Monopoly Price − Marginal Cost) × (Competitive Quantity − Monopoly Quantity)
How to calculate deadweight loss on a monopoly graph?
According to the above graph, in point E, MR=MC. At the point E, this monopoly firm earn the maximum profit. In this example, this monopolistic firm operates at the point Q1. (Where MR= MC). So, the price level equals P1 where the relevant price to Q1 production is. So, this monopolistic firm produces at the excess capacity in other words produces a lower amount of output than the optimum amount of output.
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Excess Capacity – Complete Lesson with FAQ
In the above monopoly graph in point “D”, price equals to the marginal cost. So, at point “D”, this firm can produce the economically efficient output level (Q2).
At the point A of monopoly graph, price is higher than the marginal cost (MC). The fact that monopoly prices are higher than marginal costs shows that the monopoly solution violates a fundamental requirement for economic efficiency,
As we discussed above, this firm produce less than economically efficient output level. So, there is a dead weight loss (DWL). Dead weight loss in monopoly means, lost of the social wellbeing as a result of not producing economically efficient output level. In above monopoly graph, DWL equals to BDE area.
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Monopoly Graph, Characteristics, Types, Examples and Causes
How to calculate deadweight loss with a price ceiling
A ceiling price implies that the government has fixed the maximum permitted price for a specific good and in price ceiling graph, it is set below the market equilibrium. Price ceiling creates shortage (The demand exceeds the supply). As a results of the price ceiling, there will be a economic inefficiency in other words, a deadweight loss. Because some consumers will not able to buy the good at the ceiling price and so that they have to pay a higher price.
To calculate the deadweight loss with a price ceiling, you need to know the equilibrium price and quantity, the price ceiling, and the supply and demand curves. The deadweight loss formula of price ceiling is as follows.
Deadweight loss formula of price ceiling
Deadweight Loss = 1/2 (black market Price − Price Ceiling) × (market equilibrium quantity − Quantity supplied under price ceiling)
How to calculate deadweight loss on a price ceiling graph?
Price ceiling of $0.2 on the face mask is less than the market equilibrium price of $0.4. We will draw the impact of price ceiling on a graph as follows.
Deadweight loss of price ceiling
A deadweight loss is a cost to society created by market inefficiency, which occurs when supply and demand are out of equilibrium. In this price ceiling example, deadweight loss from price ceiling is presented in the pink coloured area. Also, the difference between economic surplus presents the deadweight loss of price ceiling.
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Price Ceiling Definition, Graph, Examples and Effects
Let’s calculate the deadweight loss of above example using the deadweight loss formula of price ceiling
Deadweight Loss = 1/2 (black market Price − Price Ceiling) × (market equilibrium quantity − Quantity supplied under price ceiling)
Deadweight Loss = 1/2 (0.8− 0.2) × (2 – 1) = 0.3
How to calculate deadweight loss from tax?
A tax means the compulsory levies are imposed by the government on business organizations and individuals. Most countries in the world impose taxes on the people. Taxation can be identified as the major source of income for many governments. Beyond the imposition of taxes, the government receives non-tax income such as dividends income, interest income, and so on.
To calculate the deadweight loss from tax, you need to know the original equilibrium price and quantity, the tax per unit, and the new equilibrium price and quantity after the tax.
Deadweight loss formula with tax
The formula for deadweight loss from tax is:
Deadweight Loss= 1/2 × Tax per Unit × (Original Quantity − New Quantity)
How to calculate deadweight loss on a tax graph?
Assume that above graph presents the USA apartments market. Before the USA government imposes taxes on apartments, the equilibrium price is $200,000, and the equilibrium quantity is 350,000 apartments.
Assume that after the government imposes a unit tax of $125000 on apartments. As a result of it, the supply curve has been shifted leftward (Shifted from S to S + Tax). Now market equilibrium price has been increased to $300,000 and the market equilibrium quantity has been decreased to 250,000 apartments. As results of the tax implementation, the market price has increased and quantity has decreased.
Let’s calculate deadweight loss using the deadweight loss formula
Deadweight Loss= 1/2 × Tax per Unit × (Original Quantity − New Quantity)
Deadweight Loss= 1/2 × 125,000 × (350,000 − 250,000) = 62,500,000,000
