Microeconomics: Monopoly Pricing Formula

Monopoly Pricing Formula

• The Monopoly pricing formula is also known as the inverse elasticity rule.
• The formula is derived from the Monopoly problem, which is defined as the Monopoly choosing the quantity that maximizes profit.
• The profit function is computed as the difference between total revenue and total costs.

Demand Curve

• The demand curve is a downward-sloping inverse demand curve.
• The demand curve is negatively sloped, indicating a negative relationship between the price and the quantity demanded.

Cost Function

• The cost function is represented as C(q), which tells the minimum total cost necessary to produce some quantity q.
• The marginal cost is the increase in cost that follows a tiny increase in quantity, represented as C'(q).

Price Elasticity of Demand

• The price elasticity of demand measures the change in quantity demanded of a product in relation to its price change.
• It is represented as η, and is calculated as the ratio of the percentage change in quantity to the percentage change in price.
• The elasticity is measured at a given point of the demand curve.

First Order Condition

• The first order condition is derived by taking the first order derivative of the profit function with respect to the quantity.
• The first order condition tells us what quantity the Monopoly chooses to maximize profit.

Monopoly Pricing Formula Derivation

• The Monopoly pricing formula is derived by solving the first order condition.
• The formula is expressed as (P - C'(q)) / P = 1 / η.

Lerner Index

• The Lerner Index is a measure of market power.
• It is defined as the ratio of the difference between the price and the marginal cost to the price.
• The Lerner Index is inversely related to the price elasticity of demand.

Market Power

• Market power is the capacity of a firm to raise the price above the marginal cost.
• In a perfectly competitive market, firms have no market power, and the price is equal to the marginal cost.
• In a Monopoly market, the firm has market power, and the price is above the marginal cost.

Monopoly Pricing Formula

• The monopoly pricing formula is derived from the profit function, which is the difference between total revenue and total costs.
• The formula is also known as the inverse elasticity rule, and is used to determine the optimal price and quantity for a monopolist.

Demand Curve

• The demand curve is downward-sloping, indicating a negative relationship between price and quantity demanded.
• The demand curve is used to determine the price elasticity of demand.

Cost Function

• The cost function, C(q), represents the minimum total cost necessary to produce a quantity q.
• The marginal cost, C'(q), is the increase in cost that follows a tiny increase in quantity.

Price Elasticity of Demand

• Price elasticity of demand, η, measures the change in quantity demanded in response to a change in price.
• It is calculated as the ratio of the percentage change in quantity to the percentage change in price.
• Elasticity is measured at a given point on the demand curve.

First Order Condition

• The first order condition is derived by taking the first order derivative of the profit function with respect to quantity.
• It determines the quantity that the monopolist chooses to maximize profit.

Monopoly Pricing Formula Derivation

• The monopoly pricing formula is derived by solving the first order condition.
• The formula is expressed as (P - C'(q)) / P = 1 / η.

Lerner Index

• The Lerner Index measures market power, which is the ability of a firm to raise price above marginal cost.
• It is defined as the ratio of the difference between price and marginal cost to price.
• The Lerner Index is inversely related to the price elasticity of demand.

Market Power

• Market power is the ability of a firm to raise price above marginal cost.
• In a perfectly competitive market, firms have no market power, and price is equal to marginal cost.
• In a monopoly market, the firm has market power, and price is above marginal cost.