Linear Demand Marginal Revenue Calculator

Model linear demand. Calculate marginal revenue, total revenue, and price. Review elasticity before output decisions. Use exports for clear records after each submitted run.

Calculator Inputs

Formula Used

For inverse linear demand:

P = a - bQ

Total revenue is price multiplied by quantity:

TR = P × Q = aQ - bQ²

Marginal revenue is the derivative of total revenue:

MR = d(TR)/dQ = a - 2bQ

Revenue is maximized where MR = 0:

Q = a / (2b), P = a / 2

With direct demand Q = c - dP, the calculator converts it to P = c/d - Q/d before solving.

How to Use This Calculator

  1. Choose the demand input type.
  2. Enter inverse demand values, direct demand values, or two demand points.
  3. Enter the quantity you want to test.
  4. Add fixed and variable cost if profit signals are needed.
  5. Set the quantity step for a discrete revenue check.
  6. Press Calculate to show the result above the form.
  7. Use CSV or PDF buttons to save the calculated result.

Example Data Table

Demand Curve Quantity Price Total Revenue Marginal Revenue Signal
P = 120 - 2Q 10 100 1,000 80 Revenue rises with more output.
P = 120 - 2Q 30 60 1,800 0 Total revenue is maximized.
P = 120 - 2Q 40 40 1,600 -40 Revenue falls with more output.

Understanding Marginal Revenue

Marginal revenue shows the extra revenue from selling one more unit. For a linear demand curve, price falls as quantity rises. That change matters. The seller must lower price on all units, not only the next unit. So marginal revenue drops faster than price.

This calculator uses the inverse demand form P = a - bQ. Here, a is the price intercept. It is the price when quantity is zero. The value b is the demand slope size. It tells how much price falls for each extra unit. Total revenue equals price times quantity. After substitution, total revenue becomes aQ - bQ². The derivative of that expression gives marginal revenue.

Why Linear Demand Is Useful

A linear curve is simple, but it is powerful. It gives clear revenue signals. It also helps students, analysts, and small businesses test output choices. When marginal revenue is positive, another unit adds revenue. When it is zero, total revenue is at its highest point. When it is negative, more output lowers total revenue.

The calculator also shows elasticity. Elasticity explains how sensitive buyers are to price. On the upper part of a linear demand curve, demand is elastic. In the middle, elasticity is one. On the lower part, demand is inelastic. Marginal revenue turns zero at unit elasticity.

Using Cost Fields

Marginal revenue is not the same as profit. Profit also depends on cost. This page includes fixed cost and variable cost fields. These fields estimate total cost, profit, and marginal profit. Marginal profit compares marginal revenue with variable cost. If marginal profit is positive, the selected output may still add profit. If it is negative, the next unit may reduce profit.

Better Decisions From One Line

Linear demand models are often used before deeper forecasting. They are easy to explain. They also show the link between price, quantity, total revenue, and elasticity. Use the result as a planning guide. Check real market data before making final pricing decisions. A clean demand line helps you see the tradeoff quickly.

Because every input stays visible, you can compare scenarios. Change slope, quantity, or cost. Then run the model again. Small changes often reveal the best output range and safer pricing limits for demand planning today.

FAQs

What is marginal revenue from a linear demand curve?

It is the extra revenue earned from selling one more unit when price follows a straight-line demand equation.

Which demand forms can I enter?

You can enter P = a - bQ, Q = c - dP, or two price and quantity points. The page converts each form into inverse demand.

Why is marginal revenue lower than price?

A seller on a downward demand curve must reduce price to sell more units. That lower price affects all sold units, so MR drops faster.

When is total revenue maximized?

Total revenue is maximized where marginal revenue equals zero. For P = a - bQ, that quantity is a divided by 2b.

What does negative marginal revenue mean?

It means selling more output reduces total revenue. The tested quantity is beyond the revenue maximizing output level.

Does this calculator include costs?

Yes. Fixed cost and variable cost fields estimate total cost, profit, and marginal profit. Marginal revenue itself still comes from demand.

How do the download buttons work?

CSV exports a spreadsheet-ready file. PDF exports a simple report with equations, results, interpretation, and warnings.

Why can the result show a negative price?

A linear equation can be extended beyond its realistic range. If price is negative, choose a lower quantity or review the demand data.

Related Calculators

Paver Sand Bedding Calculator (depth-based)Paver Edge Restraint Length & Cost CalculatorPaver Sealer Quantity & Cost CalculatorExcavation Hauling Loads Calculator (truck loads)Soil Disposal Fee CalculatorSite Leveling Cost CalculatorCompaction Passes Time & Cost CalculatorPlate Compactor Rental Cost CalculatorGravel Volume Calculator (yards/tons)Gravel Weight Calculator (by material type)

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.