Deadweight Loss Formula

What is the Deadweight Loss Formula?

Deadweight loss formula refers to the calculation of resources that are wasted due to inefficient allocation or excess burden of cost to society due to market inefficiency. When the two fundamental forces of Economy Supply and Demand are not balanced it leads to Deadweight loss.

Market inefficiency is a situation where consumption (demand) or allocation (supply) of goods and services will be high or low which in turn leads to Deadweight loss.

The formula is given below –

DEADWEIGHT LOSS
Deadweight Loss Formula = 0.5 * (P2 – P1) * (Q1 – Q2)

Where,

  • P1 – Original price of goods/service
  • P2 – New Price of goods/service
  • Q1 – Original Quantity
  • Q2 – New Quantity

Explanation

The deadweight loss can be derived using the following steps.

Step 1: First you need to determine the Price (P1) and Quantity (Q1) using supply and demand curves as shown in the graph, then the new price(P2) and quantity(Q2) have to be found.

Step 2: The second step is deriving the value of deadweight loss by applying the formula in which 0.5 is multiplied with a difference of new price and old price (P2-P1), as well as new quantity and old quantity (Q1-Q2).

Deadweight Loss  = 0.5*(P2-P1)*(Q1-Q2)
Deadweight Loss Formula

Factors Leading to Deadweight Loss

  • Price Ceiling
  • Pricing Floor
  • Monopoly
  • Taxation
  • Government Intervention

Calculate Deadweight Loss with Examples

Below are the examples -.

You can download this Deadweight Loss Formula Excel Template here – Deadweight Loss Formula Excel Template

Example #1 (With Pricing Floor)

Let us consider A is working as labor in D’s company for a wage of Rs.100/day, if the Government has set pricing floor for wage as Rs.150/day which leads to a situation where either A will not work for wage below Rs.150 or the company will not pay above Rs.100, hence leading to loss of tax from revenue from both of them, which is a deadweight loss to the government.

Example #2 (With Taxation)

Let’s consider the cinema ticket sold by a theater is Rs.120 and it would sell around 500 tickets per show. Now the government has increased Entertainment tax to 28% so the tickets which are not sold are considered deadweight loss as some set of people wouldn’t spend much on a show.

Solution:

Use the given data for calculation of deadweight loss:

Given Data Example 2

Now the Government has increased the Entertainment tax to 28% which has to lead to an increase in which and decrease in tickets sold, the price increase is calculated as below.

Tax increased by the government to 28% which is calculated as = 120 * 28 / 100 = 34(rounded off)

Hence, New Price will be=120+34=155 (rounded off to nearer amount)(P2)

And the New Quantity is=450(Q2)

Calculation of deadweight loss can be done as follows:

Deadweight loss Example 2-1

Deadweight Loss = 0.5* (154-120)*(500-450) = 0.5 * (34)*(50)

Example 2-2

Value of Deadweight Loss is = 840

Therefore the DeadWeight loss for the above scenario is 840.

Example #3 (With Monopoly)

In the below example a single seller spends Rs.100 to create a unique product and sells it to Rs.150 and 50 customers purchase it. Once he decides to increase the selling price to Rs.200 the demand for quantity reduces to 30 units hence he loses the customers who are below the purchasing power which is considered as Deadweight loss.

Solution:

Use the given data for calculation of deadweight loss:

Given data Example 3

Calculation of deadweight loss can be done as follows:

Deadweight loss Example 3-1

Deadweight Loss = 0.5 * (200 – 150) * (50 – 30)= 0.5 * (50) * (20)

Deadweight loss Example 3-2

Value of Deadweight Loss is = 500

Therefore the DeadWeight loss for the above scenario is 500.

Deadweight Loss Calculator

You can use this deadweight loss Calculator.

P1
P2
Q1
Q2
Deadweight Loss Formula
 

Deadweight Loss Formula = 0.5 * (P2 - P1) * (Q1 - Q2)
0.5 * (0 - 0) * (0 - 0) = 0

Relevance and Uses

The deadweight loss can be calculated for any deficiency that is occurred due to imbalanced market equilibrium, tax or any other factors as mentioned above.

Deadweight loss is used to calculate the value of the deadweight loss at various stages, let us consider if the Government imposes more tax which affects production and purchase in a market which in turn reduces the Government Tax revenue. In this case, the Government can judge the market from calculating Deadweight loss, higher the value relative loss in revenue.

Recommended Articles

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