Enter Values
Monopoly Formulas
MR = MC → Qm = (a - MC) / 2b
a = Demand intercept |
b = Demand slope |
MC = Marginal cost |
MR = Marginal revenue
Model Assumptions
- Linear demand curve (P = a - bQ)
- Constant marginal cost (horizontal MC curve)
- Single-product monopolist (no bundling)
- No price discrimination (uniform pricing)
- No regulatory constraints
- Fixed cost affects profit but not the efficient benchmark quantity in this model
- For educational purposes. Not financial advice. Market conventions simplified.
Monopoly Results
Monopoly Profit
$1,600.00
Monopoly Q
40.00
Monopoly P
$60.00
Competitive Q
80.00
Competitive P
$20.00
Consumer Surplus
$800.00
Producer Surplus ?
$1,600.00
Total Surplus
$2,400.00
Deadweight Loss
$800.00
Lerner Index
0.6667
Output Reduction
50.0%
Price Markup
200.0%
Monopoly Diagram
Formula Breakdown
Profit Maximization: MR = MC → a - 2bQ = MC
Step-by-step calculation with your inputs
Monopoly vs Competition
| Measure | Monopoly | Competitive / Efficient |
|---|---|---|
| Price | Pm = (a + MC) / 2 | Pc = MC |
| Quantity | Qm = (a - MC) / 2b | Qc = (a - MC) / b |
| Output | Restricted | Efficient |
| DWL | Welfare loss | Zero DWL |
Understanding Monopoly Pricing & Welfare
What is a Monopoly?
A monopoly is a market structure where a single firm is the sole producer of a good with no close substitutes. Unlike competitive firms that are price takers, a monopolist is a price maker who faces the entire market demand curve.
Key Monopoly Equations
Inverse Demand: P = a - bQ
Marginal Revenue: MR = a - 2bQ
Profit Max: MR = MC → Qm = (a - MC) / 2b
Monopolist produces half the competitive output for linear demand
Marginal Revenue: MR = a - 2bQ
Profit Max: MR = MC → Qm = (a - MC) / 2b
Monopolist produces half the competitive output for linear demand
Monopoly vs Perfect Competition
Monopoly
One seller, price maker
Produces where MR = MC. Price exceeds MC, creating deadweight loss. Output is restricted to maximize profit.
Perfect Competition
Many sellers, price takers
Produces where P = MC. No deadweight loss. Efficient allocation of resources with maximum total surplus.
Deadweight Loss & Welfare
The social cost of monopoly is the deadweight loss from underproduction, not the monopolist's profits. The DWL triangle represents transactions that would benefit both buyers and sellers but don't occur because the monopolist restricts output.
- DWL = 0.5 × (Pm - MC) × (Qc - Qm)
- Monopoly transfers surplus from consumers to the producer
- But the DWL is lost to everyone — it benefits no one
Lerner Index: L = (P - MC) / P measures market power. L = 0 means perfect competition; L → 1 means extreme monopoly power. For a profit-maximizing monopolist, L = 1/|ε| (inverse of demand elasticity).
Frequently Asked Questions
A monopolist maximizes profit by producing where marginal revenue (MR) equals marginal cost (MC). Because a monopolist faces a downward-sloping demand curve, MR is always less than price. The monopolist finds the profit-maximizing quantity where MR = MC, then charges the highest price consumers will pay for that quantity by reading up to the demand curve. This results in a price above MC, unlike perfect competition where P = MC.
Deadweight loss (DWL) is the reduction in total economic surplus caused by producing less than the socially efficient quantity. A monopolist restricts output below the competitive level to charge a higher price. The lost surplus — transactions that would benefit both buyers and sellers but don't occur — is the deadweight loss. It's represented by the triangle between the demand curve and MC curve, from the monopoly quantity to the competitive quantity.
Under perfect competition, firms produce where P = MC, resulting in the efficient quantity Qc = (a − MC)/b. A monopolist produces where MR = MC, yielding Qm = (a − MC)/(2b) — exactly half the competitive output for linear demand. The monopoly price Pm = (a + MC)/2 is always higher than Pc = MC. This output restriction transfers surplus from consumers to the monopolist and creates deadweight loss.
The Lerner Index L = (P − MC)/P measures a firm's market power — its ability to price above marginal cost. It ranges from 0 (perfect competition, P = MC) to approaching 1 (extreme market power). For a profit-maximizing single-price monopolist at the chosen quantity, L equals the inverse of the absolute price elasticity of demand: L = 1/|ε|. A higher Lerner Index indicates greater market power and larger welfare distortions.
Yes. A monopolist maximizes profit (or minimizes loss) at MR = MC, but if fixed costs are high enough, total profit can be negative even at the optimal output. The monopolist earns positive producer surplus (variable profit) of (Pm − MC) × Qm but loses money overall when FC exceeds this amount. In the long run, a monopolist operating at a loss would exit the market unless it expects future profitability or faces exit barriers.
Monopoly is an extreme form of market power where a single firm is the sole seller in a market. Market power, more broadly, is any firm's ability to influence the price of its product — to charge above marginal cost. Firms in monopolistic competition and oligopoly also have market power, but less than a pure monopolist. The Lerner Index quantifies the degree of market power regardless of market structure.
Disclaimer
This calculator is for educational purposes only and assumes a simple linear demand curve with constant marginal cost. Real-world monopolies involve more complex cost structures, regulatory environments, and demand functions. This tool should not be used for business decisions.
