An exercise on understanding monopoly with an example

Here let us focus on applying the marginal principle to determine the profit-maximizing price of a monopolist.

Problem Statement

Suppose SpaceX is a monopoly for launching satellites from the USA.

• The demand curve for space launches is given by Q = 8 - P, where Q is the number of satellites, and P is the price in millions of USD.

• The total cost in millions of USD for launching a satellite is 3 + 2Q.

The questions are:

1. What would be the profit-maximizing quantity and price for SpaceX? Also, calculate the profits.

2. How would the answer change if the cost was given by 10 + 2Q instead of 3 + 2Q?

Solution Approach

The problem is solved using two methods:

Method 1: Profit Maximization

• The profit expression is written as: Profit = Revenue - Total Cost.

• Revenue is calculated as Price × Quantity, and the total cost is given.

• The profit expression is a quadratic equation, and the profit-maximizing quantity is found using the properties of the quadratic equation.

• The corresponding price and profits are calculated.

• The analysis is repeated for the second cost scenario (10 + 2Q).

Method 2: Marginal Principle

• Marginal revenue (MR) and marginal cost (MC) are calculated.

• The marginal principle is applied: Produce a quantity Q such that MR ≥ MC, provided that profits are non-negative.

Key Takeaways

• A monopolist is a price maker.

• The quantity and price decisions for a monopolist are interrelated through the inverse demand curve.

• The profit-maximizing quantity is determined by the marginal principle.

• It is crucial to ensure that profits are non-negative at the profit-maximizing quantity.