How to Calculate the Allocative Inefficiency of a Monopoly
A monopoly is allocatively inefficient because it produces where MR = MC and prices above marginal cost, so the units it never makes form a deadweight loss triangle.
The Monopoly Inefficiency formula
Calculator
Enter a straight-line demand curve and marginal cost to get the monopoly output, the efficient output and the deadweight loss.
The price at which quantity demanded falls to zero.
Where the same demand line meets the quantity axis. It fixes the slope.
Constant cost of producing one more unit.
The triangle over the missing units is worth $625 of surplus that nobody collects.
- Monopoly quantity (MR = MC)
- 25
- Monopoly price
- $70
- Price above marginal cost
- $50
- Allocatively efficient quantity (P = MC)
- 50
- Units not produced
- 25
Marginal revenue meets marginal cost at 25 units, and the monopolist stops there.
The demand curve carries a price of $70 at that quantity, which is what buyers pay.
Price sits $50 above marginal cost, and that gap is the allocative inefficiency: P > MC instead of P = MC.
A competitive market with the same costs would trade 50 units, where the last unit is worth exactly what it costs.
25 units that buyers value above marginal cost never get made, which is the underproduction the graph shows.
How to calculate Monopoly Inefficiency, step by step
- 1Write demand as a straight line. P = choke price − (slope × Q), where the slope equals the choke price divided by the quantity demanded at a price of zero.
- 2Double the slope to get marginal revenue. MR = choke price − (2 × slope × Q). For a straight-line demand curve, marginal revenue starts at the same intercept and falls twice as fast as price.
- 3Set MR = MC to find the monopoly output. Solve for Q, then read the price off the demand curve at that quantity. The price sits above MR, and therefore above marginal cost.
- 4Set P = MC to find the efficient output. Allocative efficiency needs the value of the last unit to buyers to equal what it costs to make, so solve the demand equation for the quantity where price equals marginal cost.
- 5Measure the triangle between the two quantities. Deadweight loss = ½ × (efficient quantity − monopoly quantity) × (monopoly price − MC), the value of the trades that the restricted output gives up.
Worked example: Monopoly Inefficiency
Demand is P = 120 − 2Q, which comes from a choke price of $120 and 60 units demanded at a price of zero, and marginal cost is a constant $20. Marginal revenue is MR = 120 − 4Q, so MR = MC gives 120 − 4Q = 20 and a monopoly output of 25 units. The price comes off demand: P = 120 − 2(25) = $70, which is $50 above marginal cost. The efficient quantity solves 120 − 2Q = 20, giving 50 units. The monopoly leaves 50 − 25 = 25 units unproduced, so deadweight loss = ½ × 25 × 50 = $625.
Monopoly Inefficiency questions
Why is a monopoly allocatively inefficient if it maximizes profit?
Profit maximization sets MR = MC, but buyers pay the price on the demand curve, which sits above MR and so above MC. Units that buyers value at more than they cost to produce go unmade, and that gap is the inefficiency.
Is deadweight loss the same as monopoly profit?
No. Profit is the rectangle between price and average total cost on the units actually sold, and someone collects it. Deadweight loss is the triangle over the units never produced, and nobody collects it.
Does a monopoly always produce less than a competitive market?
With the same cost curves, yes. The competitive outcome sits where price equals marginal cost, and the monopolist stops short of that quantity to keep the price up on the units it does sell.
Why does marginal revenue fall twice as fast as demand?
Selling one more unit forces the price down on every earlier unit as well. For a straight-line demand curve that second effect gives MR the same price intercept and double the slope.
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