Monopoly's Deadweight Loss

Introduction

Welcome back! In our last lesson, we determined the monopolist's profit-maximizing strategy: produce the quantity where marginal revenue equals marginal cost (MR=MC), and then charge the highest price consumers are willing to pay for that quantity, as given by the demand curve.

This strategy maximizes the monopolist's profit, but does it maximize the welfare of society as a whole? To answer this, we need a benchmark. In economics, the "efficient" outcome is the one that maximizes total surplus—the sum of the benefits to consumers (consumer surplus) and producers (producer surplus). As we've seen, this efficient outcome occurs in a perfectly competitive market.

Today, we will analyze the social cost of monopoly by comparing its outcome to the perfectly competitive benchmark. You will learn to calculate the deadweight loss (DWL), which is the value lost to society because the monopolist produces less than the socially optimal quantity of a good.

1. Revisiting Surpluses and the Competitive Benchmark

Before we can measure the inefficiency of a monopoly, let's quickly formalize the concepts of consumer surplus, producer surplus, and the efficient outcome in a perfectly competitive market.

• Consumer Surplus (CS): The difference between the maximum price consumers are willing to pay and the price they actually pay, summed over all units sold. On a graph, it's the area below the demand curve and above the price line.
• Producer Surplus (PS): The difference between the price producers receive and their marginal cost of production, summed over all units sold. On a graph, it's the area above the marginal cost (supply) curve and below the price line.
• Total Surplus: The sum of consumer and producer surplus (TS = CS + PS).

In a perfectly competitive market, equilibrium occurs where the supply curve (S) and demand curve (D) intersect. Since the market supply curve in a competitive industry is the sum of the individual firms' marginal cost curves, the competitive equilibrium is where Price = Marginal Cost. This equilibrium quantity is considered allocatively efficient because it maximizes total surplus.

Let's use a worksheet to see this in action.

As you saw in the reading, in the competitive market:

• Equilibrium Quantity (Qc) = 4 units
• Equilibrium Price (Pc) = $16
• Total Surplus = CS ($16) + PS ($32) = $48

This $48 represents the maximum possible social welfare in this market. Now, let's see what happens when it becomes a monopoly.

2. The Inefficiency of Monopoly

From our last lesson, you know a monopolist doesn't produce where P=MC. It produces where MR=MC, resulting in a lower quantity (Qm) and a higher price (Pm).

Because Qm is less than the efficient quantity Qc, several units for which consumers were willing to pay more than the marginal cost of production are simply not made. The potential surplus from these un-produced units is lost to everyone—it doesn't go to consumers or the producer. This lost value is the deadweight loss.

The graph below illustrates how the total surplus is divided in a monopoly and identifies the deadweight loss.

Notice three things are happening compared to the competitive outcome:

1. Consumer surplus is smaller.
2. Producer surplus is larger. The monopolist captures some of the former consumer surplus.
3. The purple triangle appears. This is the deadweight loss—the part of the total surplus that is lost entirely due to the monopoly's output restriction.

3. Calculating the Deadweight Loss

Now for the main goal: calculating the value of this deadweight loss. Since the DWL is a triangle on the graph, we can find its value using the formula for the area of a triangle:

$$\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}$$

The key is to correctly identify the base and height of the DWL triangle.

A very clear way to identify this triangle is to locate three specific points on the graph:

1. The monopolist's production point (where MR = MC).
2. The competitive market equilibrium point (where Demand = MC).
3. The point on the demand curve at the monopoly quantity.

Let's watch a short video that walks through this identification and calculation process on a graph.

A Full Analytical Example

The graphical method is excellent for understanding the concept. Given your analytical background, let's work through a problem starting from the underlying equations, which allows for a more precise calculation.

This next video does exactly that. It starts with demand and cost functions, finds the monopoly price and quantity, finds the competitive quantity, and then calculates the deadweight loss.

Let's break down the calculation from that video:

• Monopoly Outcome: Qm = 40, Pm = $110.
• Competitive Outcome (where P = MC):
  • Inverse Demand (P): $130-0.5Q$
  • Marginal Cost (MC): $2Q+10$
  • Set P = MC: $130-0.5Q=2Q+10⟹120=2.5Q⟹Q_c=48$.
• Identify the DWL Triangle:
  • Height: The reduction in quantity: $Q_c-Q_m=48-40=8$.
  • Base: The "price wedge" at the monopoly quantity. This is the difference between what consumers were willing to pay for unit #40 (which is Pm = $110) and the marginal cost of producing unit #40.
    • We find MC at Q=40 by plugging it into the MC equation: $MC(40)=2(40)+10=90$.
    • Base = $P_m-MC(Q_m)=110-90=20$.
• Calculate the Area: $$\text{DWL}=\frac{1}{2}\times \text{base}\times \text{height}=\frac{1}{2}\times 20\times 8=\$80$$

This $80 represents the total value of economic welfare that is lost because the monopolist restricts output from 48 to 40 units.

4. Tying It All Together

Let's return to the EconEdLink worksheet to see the full comparison side-by-side and solidify the concept of how surplus is transferred and lost.

As the worksheet confirms, when the market changes from perfect competition to monopoly:

• Total surplus falls from $48 to $45.
• The deadweight loss is the difference: $3.
• Consumer surplus falls by $7 (from $16 to $9). Of this $7, $6 is transferred to the monopolist as producer surplus, and $1 vanishes as part of the deadweight loss. The other $2 of deadweight loss comes from a reduction in the original producer surplus.

Conclusion

In this lesson, we have quantified the social cost of monopoly. While a monopolist may earn high economic profits, it does so by creating an outcome that is inefficient from society's perspective.

Here are the key takeaways:

• The socially efficient level of output occurs in a competitive market where Price = Marginal Cost, maximizing total surplus.
• A monopolist produces less than the efficient quantity, charging a higher price.
• Deadweight loss is the reduction in total surplus that results from the monopolist's output restriction.
• We can calculate the deadweight loss by finding the area of the triangle between the demand and marginal cost curves, spanning the gap between the monopoly quantity and the competitive quantity.

This analysis applies to a single-price monopolist. But what if a firm could charge different prices to different buyers? In our next lesson, we will explore price discrimination, a strategy monopolists can use to increase their profits, and we will analyze its surprising effects on output and economic welfare.