Deadweight Loss

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:

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.

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.

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 (Q_d) is less than the quantity supplied (Q_s). 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 (Q_e). This creates an area of deadweight loss, as seen in Figure 2.

Fig. 2 - Price Floor with Deadweight Loss

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 (Q_s) is less than the quantity demanded (Q_d). 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 (P_m) 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 P_d. This creates a deadweight loss because the output (Q_m) is less than the socially optimal level (Q_e).

Fig. 4 - Deadweight Loss in Monopoly

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 (P_c - P_s). P_c is the price that consumers have to pay, and the producers will receive an amount of P_s after the tax is paid. The tax creates a deadweight loss because it reduces the quantity of the goods being bought and sold from Q_e to Q_t. 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.

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.

1. 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.
2. Determine the equilibrium price: This is the price (\(P_{eq}\)) at which supply and demand would be equal without any market interventions.
3. 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.
4. 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 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.

What would happen if the government imposed a tax on drinking glasses? Let's check out an example.