Have you ever baked cupcakes for a bake sale but could not sell all of the cookies? Say you baked 200 cookies, but only 176 were sold. The leftover 24 cookies sat out in the sun and went hard, and the chocolate melted, so they were inedible by the end of the day. Those 24 leftover cookies were a deadweight loss. You overproduced cookies, and the leftovers did not benefit you or the consumers.
This is a rudimentary example, and there is much more to deadweight loss. We will explain to you what the deadweight loss is and how to calculate it using deadweight loss formula. We have also prepared for you different examples of deadweight loss caused by taxes, price ceilings and price floors. And don't worry we have a couple of calculation examples too! Does deadweight loss seem interesting to you? It sure is for us, so stick around and let's dive right in!
What is Deadweight Loss?
Deadweight loss is a term used in economics to describe a situation where the overall society or economy loses out due to market inefficiencies. Imagine a scenario where a mismatch occurs between what buyers are willing to pay for a good or service and what sellers are willing to accept, creating a loss that no one benefits from. This lost value, which could have been enjoyed under a perfectly competitive market scenario, is what economists refer to as "deadweight loss"
Deadweight Loss Definition
The definitions of deadweight loss is as follows:
In economics, deadweight loss is defined as the inefficiency resulting from a divergence between the quantity of a product or service produced and the quantity consumed, including government taxation. This inefficiency signifies a loss that no one recovers, and thus, it's termed as a 'deadweight'.
A deadweight loss is also called efficiency loss. It is the result of the market's misallocation of resources so that they cannot satisfy society's needs in the best way. This is any situation where the supply and demand curves do not intersect at the equilibrium.
Let's say the government imposes a tax on your favorite brand of sneakers. This tax increases the cost for the manufacturer, who then passes it onto the consumers by hiking the price. As a result, some consumers decide not to buy the sneakers because of the increased price. The tax revenue the government gains does not make up for the satisfaction lost by the consumers who could no longer afford the sneakers, or the income the manufacturer lost due to fewer sales. The shoes that weren't sold represent a deadweight loss – a loss of economic efficiency where neither the government, consumers, nor manufacturers benefit.
The consumer surplus is the difference between the highest price that a consumer is willing to pay for a good and the market price of that good. If there is a large consumer surplus, the maximum price that consumers are willing to pay for a good is much higher than the market price. On a graph, the consumer surplus is the area below the demand curve and above the market price.
Similarly, the producer surplus is the difference between the actual price a producer receives for a good or service and the lowest acceptable price that the producer is willing to accept. On a graph, the producer surplus is the area below the market price and above the supply curve.
Consumer Surplus is the difference between the highest price that a consumer is willing to pay for a good or service and the actual price that the consumer pays for that good or service.
Producer Surplus is the difference between the actual price a producer receives for a good or service and the lowest acceptable price that the producer is willing to accept.
Deadweight loss can also be caused by market failures and externalities. To learn more, check out these explanations:
- Market Failure and the Role of Government
- Externalities
- Externalities and Public Policy
Deadweight Loss Graph
Let us look at a graph illustrating a situation with deadweight loss. To understand deadweight loss, we must first identify the consumer and producer surplus on the graph.
Fig. 1 - Consumer and Producer Surplus
Figure 1 shows that the red shaded area is the consumer surplus and the blue shaded area is the producer surplus. When there is no inefficiency in the market, meaning the market supply is equal to the market demand at E, there is no deadweight loss.
Deadweight Loss from Price Floors and Surpluses
In Figure 2 below, consumer surplus is the red area, and producer surplus is the blue area. The price floor creates a surplus of goods in the market, which we see in Figure 2 because the quantity demanded (Qd) is less than the quantity supplied (Qs). In effect, the higher price mandated by the price floor reduces the quantity of a good being bought and sold to a level below the equilibrium quantity in the absence of the price floor (Qe). This creates an area of deadweight loss, as seen in Figure 2.
Fig. 2 - Price Floor with Deadweight Loss
Notice that the producer surplus now incorporates the section from Pe to Ps that used to belong to the consumer surplus in Figure 1.
Deadweight Loss from Price Ceiling and Shortages
Figure 3 below shows a price ceiling. The price ceiling causes a shortage because the supply does not keep up with the demand when producers cannot charge enough per unit to make it worthwhile to produce more. This shortage is seen in the graph as the quantity supplied (Qs) is less than the quantity demanded (Qd). Like in the case of a price floor, a price ceiling also, in effect, reduces the quantity of a good being bought and sold. This creates an area of deadweight loss, as seen in Figure 3.
Fig. 3 - Price Ceiling and Deadweight Loss
Deadweight Loss: Monopoly
In a monopoly, the firm produces until the point where its marginal cost (MC) is equal to its marginal revenue (MR). Then, it charges a corresponding price (Pm) on the demand curve. Here, the monopolist firm faces a downward-sloping MR curve that is below the market demand curve because it has control over the market price. On the other hand, firms in perfect competition are price-takers and would have to charge the market price of Pd. This creates a deadweight loss because the output (Qm) is less than the socially optimal level (Qe).
Fig. 4 - Deadweight Loss in Monopoly
Want to learn more about monopolies and other market structures? Check out the following explanations:
- Market Structures
- Monopoly
- Oligopoly
- Monopolistic Competition
- Perfect Competition
Deadweight Loss from Tax
A per-unit tax can create a deadweight loss too. When the government decides to place a per-unit tax on a good, it makes a difference between the price that consumers have to pay and the price that producers receive for the good. In Figure 5 below, the per-unit tax amount is (Pc - Ps). Pc is the price that consumers have to pay, and the producers will receive an amount of Ps after the tax is paid. The tax creates a deadweight loss because it reduces the quantity of the goods being bought and sold from Qe to Qt. It reduces both consumer and producer surplus.
Fig. 5 - Deadweight Loss with a Per-unit Tax
Deadweight Loss Formula
The deadweight loss formula is the same as for calculating the area of a triangle because that is all the area of deadweight loss really is.
Simplified formula for deadweight loss is:
\(\hbox {Deadweight Loss} = \frac {1} {2} \times \hbox {base} \times {height}\)
Where base and height are found as follows:
\begin{equation} \text{Deadweight Loss} = \frac{1}{2} \times (Q_{\text{s}} - Q_{\text{d}}) \times (P_{\text{int}} - P_{\text{eq}}) \end{equation}
Where:
- \(Q_{\text{s}}\) and \(Q_{\text{d}}\) are the quantities supplied and demanded, respectively, at the price with the market intervention (\(P_{\text{int}}\)).
Let's calculate an example together.
Fig. 6 - Calculating Deadweight Loss
Take Figure 6 above and calculate the deadweight loss after the government has imposed a price floor preventing prices from decreasing towards market equilibrium.
\(\hbox {DWL} = \frac {1} {2} \times (\$20 - \$10) \times (6-4)\)
\(\hbox {DWL} = \frac {1} {2} \times \$10 \times 2 \)
\(\hbox{DWL} = \$10\)
We can see that after the price floor has been set at $20, the quantity demanded decreases to 4 units, indicating that the price floor has reduced the quantity demanded.
How to Calculate Deadweight Loss?
Calculating deadweight loss requires an understanding of the supply and demand curves in a market and where they intersect to form an equilibrium. Previously we used the formula, this time we go through the whole process step by step.
- Identify the quantities supplied and demanded at the intervention price: At the price level where the market intervention occurs \(P_{int}\), identify the quantities that would be supplied and demanded, denoted \(Q_{s}\) and \(Q_{d}\), respectively.
- Determine the equilibrium price: This is the price (\(P_{eq}\)) at which supply and demand would be equal without any market interventions.
- Calculate the difference in quantities and prices: Subtract the quantity demanded from the quantity supplied (\(Q_{s} - Q_{d}\)) to get the base of the triangle representing the deadweight loss. Subtract the equilibrium price from the intervention price (\(P_{int} - P_{eq}\)) to get the height of the triangle.
- Calculate the deadweight loss: The deadweight loss is then calculated as half of the product of the differences calculated in the previous step. This is because the deadweight loss is represented by the area of a triangle, which is given by \(\frac{1}{2} \times base \times height\).
\begin{equation}
\text{Deadweight Loss} = \frac{1}{2} \times (Q_{\text{s}} - Q_{\text{d}}) \times (P_{\text{int}} - P_{\text{eq}})
\end{equation}
Where:
- \(Q_{\text{s}}\) and \(Q_{\text{d}}\) are the quantities supplied and demanded, respectively, at the price with the market intervention (\(P_{\text{int}}\)).
- \(P_{\text{eq}}\) is the equilibrium price, where the supply and demand curves intersect.
- The \(0.5\) is there because the deadweight loss is represented by the area of a triangle, and the area of a triangle is given by (\\frac{1}{2} \times \text{base} \times \text{height}\).
- The \(\text{base}\) of the triangle is the difference in the quantities supplied and demanded (\(Q_{\text{s}} - Q_{\text{d}}\)), and the \( \text{height}\) of the triangle is the difference in the prices (\(P_{\text{int}} - P_{\text{eq}}\)).
Please note that these steps assume that the supply and demand curves are linear and that the market intervention creates a wedge between the price received by sellers and the price paid by buyers. These conditions generally apply for taxes, subsidies, price floors, and price ceilings.
Deadweight Loss Units
The unit of the deadweight loss is the dollar amount of the reduction in total economic surplus.
If the height of the deadweight loss triangle is $10 and the base of the triangle (change in quantity) is 15 units, the deadweight loss would be denoted as 75 dollars:
\(\hbox{DWL} = \frac {1} {2} \times \$10 \times 15 = \$75\)
Deadweight Loss Example
A deadweight loss example would be the cost to society of the government imposing a price floor or a tax on goods. Let's first work through an example of the resulting deadweight loss of a government-imposed price floor.
Let's say that the price of corn has been dropping in the U.S. It has gotten so low that government intervention is required. The price of corn before the price floor is $5, with 30 million bushels sold. The U.S. Government decides to impose a price floor of $7 per bushel of corn.
At this price, farmers are willing to supply 40 million bushels of corn. However, at $7, consumers will only demand 20 million bushels of corn. The price where farmers would only supply 20 million bushels of corn is $3 per bushel. Calculate the deadweight loss after the government imposes the price floor.
Fig. 7 - Price Floor Deadweight Loss Example
\(\hbox {DWL} = \frac {1} {2} \times (\$7 - \$3) \times \hbox{(30 million - 20 million)}\)
\(\hbox {DWL} = \frac {1} {2} \times \$4 \times \hbox {10 million}\)
\(\hbox {DWL} = \hbox {\$20 million}\)
What would happen if the government imposed a tax on drinking glasses? Let's check out an example.
At the equilibrium price of $0.50 per drinking glass, the quantity demanded is 1,000. The government places a $0.50 tax on the glasses. At the new price, only 700 glasses are demanded. The price consumers pay for a drinking glass is now $0.75, and the producers now receive $0.25. Because of the tax, the quantity demanded and produced is less now. Calculate the deadweight loss from the new tax.
Fig. 8 - Tax Deadweight Loss Example
\(\hbox {DWL} = \frac {1} {2} \times \$0.50 \times (1000-700)\)
\(\hbox {DWL} = \frac {1} {2} \times \$0.50 \times 300 \)
\(\hbox {DWL} = \$75 \)
Deadweight Loss - Key takeaways
- Deadweight loss is the inefficiency in the market due to overproduction or underproduction of goods and services, causing a reduction in the total economic surplus.
- Deadweight loss can be caused by several factors such as price floors, price ceilings, taxes, and monopolies. These factors disrupt the equilibrium between supply and demand, leading to an inefficient allocation of resources.
- The formula for calculating deadweight loss is \(\hbox {Deadweight Loss} = \frac {1} {2} \times \hbox {height} \times \hbox {base} \)
- Deadweight loss represents a reduction in total economic surplus. It is an indicator of lost economic benefits for both consumers and producers due to market inefficiencies or interventions. It also demonstrates the cost to society from market distortions such as taxes or regulations.
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