Marginal Revenue Calculator
Calculate marginal revenue MR = ΔTR/ΔQ from two revenue-quantity points or from price and elasticity.
Includes profit-max guidance with MR=MC rule.
What marginal revenue means
Marginal revenue (MR) is the change in total revenue from selling one more unit. The basic formula:
MR = ΔTR / ΔQ
Where ΔTR is the change in total revenue and ΔQ is the change in quantity sold. If selling one more widget raises total revenue by 12 dollars, marginal revenue is 12 dollars per widget.
For firms in perfectly competitive markets, MR equals the market price. Each additional unit sells at the going price, and the firm is too small to push that price down. For firms with any market power (monopolies, oligopolies, monopolistic competition), MR is strictly less than price. To sell one more unit, they have to lower price across all units, so the gain on the extra unit is partially offset by lost revenue on units they could have sold at the higher price.
Two ways to compute it
You can find MR two ways. The first is direct: take two quantity-revenue pairs and compute MR = (TR₂ − TR₁) / (Q₂ − Q₁). The second uses price and demand elasticity:
MR = P × (1 + 1/E_d)
Where E_d is the price elasticity of demand (a negative number for normal goods). This is the elasticity form and it carries a deep insight: marginal revenue is positive only when demand is elastic (|E_d| greater than 1). In the inelastic region (|E_d| less than 1), marginal revenue is negative, meaning that lowering price to sell more actually reduces total revenue. At unit elasticity (E_d = −1), marginal revenue is exactly zero and total revenue is at its peak.
The profit-maximization rule
The single most important use of marginal revenue is the profit-maximization condition for any firm:
Produce the quantity where MR = MC
Where MC is marginal cost. Below that quantity, the firm gains more revenue than it spends on the next unit, so producing more raises profit. Above that quantity, the next unit costs more to produce than the revenue it brings in, so producing less raises profit. The MR = MC point is where marginal profit equals zero, and total profit is at its maximum.
For perfectly competitive firms, MR equals P, so the rule becomes P = MC. For monopolies, MR is less than P, so the rule is MR = MC, which means the monopoly produces less than the competitive quantity and charges a higher price.
Why MR < P for monopolies (with numbers)
Suppose a small theater sells 100 tickets at 20 dollars (TR = 2,000) and discovers it can sell 110 tickets if it drops the price to 19 dollars (TR = 2,090). The marginal revenue from those extra 10 tickets:
MR = (2,090 − 2,000) / (110 − 100) = 90 / 10 = 9 dollars per ticket
Even though the new price is 19 dollars, marginal revenue is only 9 dollars, because the price drop affected all 110 tickets, not just the extra 10. The theater lost 100 dollars on the original 100 tickets (1 dollar each) while gaining 190 dollars on the new 10 tickets (19 dollars each). Net: 90 dollars across 10 marginal units = 9 dollars per unit.
This 50 percent gap between price and marginal revenue is normal for firms facing downward-sloping demand. The gap is what allows the Lerner Index (L = (P − MC) / P) to measure market power: at the profit-maximizing MR = MC point, L equals −1/E_d.
Elasticity intuition
| Elasticity range | MR sign | What it means for the firm |
|---|---|---|
| Elastic (E_d below −1) | Positive | Lowering price increases total revenue |
| Unit elastic (E_d = −1) | Zero | Total revenue is at its peak |
| Inelastic (−1 < E_d < 0) | Negative | Lowering price reduces total revenue |
A monopoly will never produce in the inelastic part of the demand curve, because MR is negative there. By cutting output to reach the elastic region, the firm raises both price and total revenue. Drug companies pricing insulin operate at very inelastic E_d (around −0.2 to −0.5), which is why their pricing power is so high. Airlines tend to operate around unit elastic for leisure passengers and inelastic for business passengers.
Linear demand curve quick fact
For a linear demand curve P = a − bQ:
- Total revenue: TR = P × Q = a Q − b Q²
- Marginal revenue: MR = a − 2 b Q
This says MR has the same intercept as the demand curve (at Q = 0) but twice the slope. On a graph, if you draw a linear demand curve, the marginal revenue curve starts at the same point on the price axis and falls twice as fast, crossing zero at half the quantity where demand crosses zero. This is a standard graph in microeconomics textbooks.
When MR equals price
Perfectly competitive firms face a horizontal demand curve at the market price. They can sell any quantity they want at price P without affecting P. For these firms, MR = P at every quantity. This is why the profit-max rule simplifies to P = MC for competitive firms: every unit’s revenue is exactly the market price.
In oligopoly with kinked demand (Sweezy model), MR has discontinuities. In monopolistic competition, MR is below P but the gap is small. In monopoly, the gap is large. The size of the gap measures market power directly.
Common confusions
People often confuse marginal revenue with profit margin. Marginal revenue is per unit, in dollars. Profit margin is per dollar of revenue, in percent. A high-volume low-margin firm (Walmart) and a low-volume high-margin firm (Tiffany) can have similar absolute profits but very different marginal revenue structures.
Another confusion: people sometimes think MR has to be positive for the firm to operate. False. A firm can have MR less than zero on some units if it has already committed to producing them and wants to clear inventory. The MR = MC rule guides the choice of how many units to commit to, but once you have inventory, dumping is a separate calculation involving sunk costs.