The Relationship between Average and Marginal Revenue Curves

Introduction:
The relationship between average revenue (AR) and marginal revenue (MR) curves is an important aspect of microeconomics. Understanding this relationship is crucial for firms to make pricing and production decisions in order to maximize their profits. The AR and MR curves are derived from the demand curve and depict the revenue generated by a firm at different levels of output.

Average Revenue (AR):
- Average revenue is the total revenue earned by a firm divided by the quantity of output sold.
- It represents the revenue per unit of output.
- AR can be calculated by dividing the total revenue (TR) by the quantity sold (Q), i.e., AR = TR/Q.

Marginal Revenue (MR):
- Marginal revenue is the additional revenue earned by a firm from selling one more unit of output.
- It represents the change in total revenue resulting from a change in output by one unit.
- MR can be calculated by finding the change in total revenue when output increases by one unit, i.e., MR = ΔTR/ΔQ.

Relationship between AR and MR Curves:
- The AR curve is always downward sloping due to the law of demand. As the firm increases its output, it has to lower the price to attract more buyers, resulting in a decrease in AR.
- The MR curve is also downward sloping, but it lies below the AR curve. This is because the firm can only increase its revenue by selling additional units at a lower price, which decreases the average revenue for all units sold.
- The MR curve intersects the x-axis (quantity axis) at a point where MR is zero. This occurs when the firm reaches the revenue-maximizing level of output.
- The AR curve and MR curve will coincide when AR is constant, such as in a perfectly competitive market, where the firm is a price taker and faces a horizontal demand curve.

Key Points:
- Average revenue is the total revenue divided by the quantity sold, while marginal revenue is the change in total revenue resulting from a change in output.
- The AR curve is always downward sloping, while the MR curve lies below the AR curve and is also downward sloping.
- The MR curve intersects the x-axis at a point where MR is zero, indicating the revenue-maximizing level of output.
- The AR and MR curves coincide when AR is constant, such as in a perfectly competitive market.

Conclusion:
Understanding the relationship between average and marginal revenue curves is essential for firms to make informed decisions about pricing and production levels. By analyzing these curves, firms can determine the optimal level of output that maximizes their revenue and ultimately leads to profit maximization.