First-Degree Price Discrimination: Profit & Consumer Surplus

What is Perfect Price Discrimination?

Price discrimination is the practice of selling the same good at different prices to different buyers. First-degree, or perfect, price discrimination is the most extreme form, where a monopolist charges each consumer the absolute maximum price they are willing to pay for each unit of the good.

For this to be possible, three conditions must be met:

1. Market Power: The firm must be a price-maker (e.g., a monopoly).
2. Information: The firm must know the maximum willingness to pay (the reservation price) of every individual consumer for every unit they might buy.
3. Prevention of Arbitrage: The firm must be able to prevent consumers who buy at a lower price from reselling the product to those willing to pay a higher price.

While perfect information makes this a largely theoretical concept, real-world examples can approximate it. For instance, in your hobby of designing custom lingerie, a bespoke piece is created for a single client. The price is often negotiated based on the specific design, materials, and the client's perceived desire and budget, allowing you to capture a value close to their maximum willingness to pay—a much different scenario than selling a standard-sized bikini top off the rack for a single price.

From Single Price to Perfect Price Discrimination

Let's first recall the single-price monopolist's decision. They produce where marginal revenue equals marginal cost ($MR=MC$) and set a uniform price for all consumers. This leaves some consumers with consumer surplus (they would have been willing to pay more) and creates a deadweight loss (some mutually beneficial trades don't happen).

A perfect price discriminator behaves differently. Because they can charge a different price for every single unit sold, they don't need to lower the price on all previous units to sell one more. The revenue from an additional unit is simply the price it is sold for. Therefore, for a perfect price discriminator, the demand curve itself becomes the marginal revenue curve.

This leads to a new profit-maximization rule: keep selling units as long as the price for the next unit (given by the demand curve) is greater than or equal to the marginal cost of producing it. The optimal quantity, $q^{\ast }$, is found where the demand curve intersects the marginal cost curve.

This is the same condition for allocative efficiency found in perfect competition. However, the distribution of the surplus is radically different.

The following video provides an excellent graphical introduction, comparing the welfare outcomes of a single-price monopolist to one practicing perfect price discrimination.

As the video demonstrates, the key outcomes are:

• Consumer Surplus is Zero: Since every consumer pays exactly their maximum willingness to pay, no surplus is left for them.
• Producer Surplus is Maximized: The producer captures everything: the original producer surplus, the original consumer surplus, and the original deadweight loss.
• No Deadweight Loss: The market produces the allocatively efficient quantity, maximizing total surplus. The monopolist, however, captures all of it.

Quantitative Analysis of Perfect Price Discrimination

While graphs provide the intuition, your exam will require you to perform calculations using specific functions for demand and cost. Let's formalize the process.

Producer surplus (PS) is the area between the price received and the marginal cost curve. Under perfect price discrimination, the "price received" is not a single line but the entire demand curve. Thus, producer surplus is the area between the demand curve and the marginal cost curve, up to the optimal quantity $q^{\ast }$.

For a statistician, it's useful to know that this "area" is formally expressed as an integral. Producer surplus is the integral of the difference between the inverse demand function $P(q)$ and the marginal cost function $MC(q)$ from zero to the optimal quantity $q^{\ast }$:

You don't need to perform integration for the CB2 exam; you'll typically be working with linear functions where you can calculate the areas of triangles and rectangles, but this formal definition clarifies exactly what we are measuring.

The following video works through two excellent numerical examples that are very similar to what you might see on your exam.

Worked Example

Let's work through a fresh example to solidify the method. Suppose a monopolist faces the following market conditions:

• Inverse Demand: $P=150-2Q$
• Marginal Cost: $MC=30$

We want to find the quantity produced, consumer surplus, and producer surplus under perfect price discrimination.

Step 1: Find the profit-maximizing quantity.
The firm produces up to the point where price equals marginal cost.

The firm will produce 60 units.

Step 2: Calculate Consumer Surplus (CS).
By definition, under perfect price discrimination, there is no consumer surplus.

Step 3: Calculate Producer Surplus (PS).
Producer surplus is the area between the demand curve and the marginal cost curve, from $Q=0$ to $Q=60$. With a linear demand curve and constant marginal cost, this area is a triangle.

• Base of the triangle: The quantity produced, which is $60$.
• Height of the triangle: The difference between the demand curve's price intercept and the marginal cost.
  • The price intercept (where $Q=0$) is $P=150$.
  • The marginal cost is $30$.
  • Height = $150-30=120$.

Now, we use the formula for the area of a triangle, $\frac{1}{2}\times \text{base}\times \text{height}$.

The producer surplus is £3,600. This entire amount also represents the total economic surplus, as the firm has captured everything.

Conclusion

In this lesson, we have dissected the mechanics of first-degree price discrimination. We established that this strategy, while theoretical, provides a crucial benchmark for understanding how a firm with market power can maximize its profit by capturing all available economic surplus.

Key Takeaways:

• Definition: First-degree price discrimination involves charging each consumer their maximum willingness to pay for every unit.
• Optimal Quantity: The firm produces where $P=MC$, resulting in an allocatively efficient output level (no deadweight loss).
• Consumer Surplus: Consumer surplus is completely eliminated and transferred to the producer.
• Producer Surplus Calculation: Producer surplus is the total area between the demand curve and the marginal cost curve, up to the efficient quantity. With linear functions, this is often the area of a triangle.

We have explored the most absolute form of price discrimination. In practice, firms rarely have the perfect information required for it. In our next lesson, we will examine third-degree price discrimination, a far more common strategy where firms divide their customers into distinct groups and charge a different price to each group. This will build directly on our understanding of market segmentation but apply it in a more realistic context.