First‑Degree Price Discrimination Revenue Calculator

Calculator

Intercept a (choke price)

Slope b (> 0)

Marginal Cost Type

Constant MC c

k (> 0)

e (> 0)

Constant MC c (> 0)

qmin (integration lower bound)

Note: For e ≥ 1 the integral from zero diverges. The calculator integrates from qmin to the efficient quantity.

Enter willingness‑to‑pay values (one per line; higher first recommended)

Constant MC per unit c

What Is First‑Degree Price Discrimination Revenue?

First degree price discrimination revenue is the total income a seller collects when each buyer is charged exactly their willingness to pay for every unit purchased. Instead of a single posted price, the seller tailors prices to individuals or infinitesimal units, extracting the entire consumer surplus. In a continuous model, revenue equals the integral of the inverse demand curve from zero to the traded quantity. Under perfect discrimination, the efficient quantity occurs where marginal cost intersects demand, because no deadweight loss remains. Profit then equals revenue minus total cost, which is the area between the demand curve and the marginal cost curve up to that efficient quantity. Real world examples include personalized tuition discounts, car dealership negotiations, airline yield management with rich segmentation, and auctions with bidder specific reserve prices. Although textbook perfection is rare, modern data and targeting tools let firms approximate it. Measuring this revenue requires a demand specification and cost information. This calculator implements linear and isoelastic models and also aggregates discrete valuations to estimate revenue, profit, and welfare impacts. Use it to compare strategies and constraints.

FAQs

It assumes perfect price discrimination, so the seller can observe willingness to pay and charge accordingly. Quantity is set where demand meets marginal cost; consumer surplus is zero.

Revenue equals the area under P(Q)=a−bQ from zero to Q*. Algebraically it is a·Q* minus one half b·Q*². Q* solves demand equal to marginal cost.

Under first‑degree price discrimination, the monopolist produces the efficient quantity where demand equals marginal cost because there is no pricing distortion creating deadweight loss.

Yes. Select linear marginal cost to model rising costs c(Q)=c0+c1Q. The tool adjusts Q*, revenue, and profit accordingly using closed‑form expressions.

Inverse isoelastic demand blows up as Q→0. For e≥1 the integral from zero diverges, so the calculator integrates from a positive qmin you can control.

Enter per‑unit willingness‑to‑pay values. The tool sums values above marginal cost, yielding quantity sold, total revenue, cost, profit, and the marginal buyer’s price.

Then no units are produced under efficiency. Quantity, revenue, and profit are zero because producing would destroy value relative to cost.

By definition of perfect discrimination, the seller captures the entire surplus, leaving consumers with zero surplus. With imperfect targeting, some surplus may remain.

Calculator

What Is First‑Degree Price Discrimination Revenue?

FAQs

What assumptions does this calculator make?

How is revenue computed in the linear model?

When is Q* equal to the efficient output?

Can marginal cost vary with quantity?

Why can isoelastic revenue be sensitive?

How do discrete valuations work?

What if all valuations are below cost?

Is consumer surplus always zero here?

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