Monopoly

Market with only one seller.
Market power

Ability of a seller or buyer to affect the price of a good.

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The monopolist completely controls the amount of output offered for sale in the market.
The monopolist must consider the market demand to maximize profit.
Knowledge of demand and cost is crucial for a firm’s economic decision making. Given this, the monopolist can then decide the per unit price and how much to produce.

 

Profit Maximization
• As a firm, a monopolist’s goal is to maximize profit
𝜋 = Total Revenue − Total Cost
• Recall, Total Revenue = price × quantity
• One of the key differences between monopoly and competitive market is that the monopolist is NOT a price taker. 
• In other words, it has market power to influence price. The market price will change along with quantity supplied by the monopolist.

• Demand curve of a monopolist is negatively sloped.
• When the demand curve is downward sloping, the average revenue (price) is greater than marginal revenue (except when output is zero).

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A monopolist seeks to maximize profit

𝜋𝑀 = max 𝑞; 𝜋𝑞 = 𝑇𝑅 − 𝑇𝐶 = 𝑝 𝑞 ⋅ 𝑞 − 𝑐 𝑞
• It is equivalent to marginal cost equals marginal revenue.𝑀𝑅 = 𝑀𝐶
 

Summary
• Monopolist can influence price by choosing different level of quantity.
• Profit is maximized at where 𝑀𝑅 𝑞∗ = 𝑀𝐶 𝑞∗ .
• At profit maximization level, 𝑝∗ > 𝑀𝐶 𝑞∗ .
• An alternative way to represent the question
max 𝑝,𝑞, 𝜋 = 𝑝 ⋅ 𝑞 − 𝑇𝐶 𝑞, s.t.𝑞 = 𝐷 𝑝
• Although a monopolist has large market power, it has to face the constraint of demand.