Question

With a downward-sloping demand curve, why is average revenue equal to price? Why is marginal revenue less than price?

Short answer

In the downward-sloping demand curve, average revenue equals price because it is the price of each unit sold. However, the marginal revenue is less than the price because to sell an additional unit, the price must be lowered, which also reduces the price for all units, not just the extra one. Hence the loss on earlier units causes marginal revenue to be less than price.

Step-by-step solution

Understanding Average Revenue and Price

Average revenue refers to the average amount of money that a firm receives per unit of output sold. This is calculated by dividing the total revenue by the quantity of the product sold. In any market structure, the average revenue is always equal to the price of the product. Mathematically, \(Price = AR = \frac{TR}{Q}\) where TR is the Total Revenue and Q is the quantity of goods sold.

Recognizing Downward Sloping Demand Curve

A downward-sloping demand curve is a characteristic of monopolistic and oligopolistic market structures. It implies that in order to sell more units of output, the firm must lower the price of its product. This is because the additional units are sold at a lower price than the previous ones, reducing the total revenue gained per unit.

Understanding Marginal Revenue and Price

Marginal Revenue is the additional revenue that the firm gains from selling one more unit of its product. In a market with a downward-sloping demand curve, the marginal revenue is always less than the price. This is because the firm needs to lower the price to sell the extra unit, which leads to a loss of revenue on the previous units that could have sold at a higher price. Mathematically, \(MR < Price\), since as quantity sold increases, the price decreases.

Key concepts

Understanding Average Revenue

Average revenue is a key concept to grasp when studying economics and demand curves. In simple terms, average revenue is the income a firm receives from selling each unit of product. This can be calculated by dividing total revenue (TR) by the number of units sold (Q). Therefore, the formula is \( \text{AR} = \frac{\text{TR}}{\text{Q}} \).
It turns out, this average revenue always equals the price of the product. This is true no matter what market structure is in place, whether it's perfect competition or monopolistic.
So, why is average revenue equal to the price? Because when the firm sells more units, each unit is sold at the price set by the market, making the average revenue per unit equivalent to this price.

The Marginal Revenue Mystery

Marginal revenue might sound complicated, but it's quite straightforward once broken down. Simply put, it's the additional revenue earned from selling one more unit of a product. For a clearer picture, picture the demand curve as a downward slope. This indicates that as more units are sold, prices must decrease to attract more buyers.
In a market consisting of a downward-sloping demand curve, marginal revenue (MR) is less than the price. Why? Because the firm must decrease the price of all previous units to sell that extra unit. This reduction results in some of the revenue being "lost" from the earlier units compared to what they could have fetched at the higher price. Importantly, this makes MR less than the price, captured mathematically as \( \text{MR} < \text{Price} \).
Understanding this equation helps in realizing how companies decide on pricing strategies for maximizing profits.

Exploring Downward-Sloping Demand

The concept of a downward-sloping demand curve is foundational to studying economics, particularly within monopolistic and oligopolistic markets. This curve visually expresses the idea that demand for a product typically increases when the price drops.
Why is the demand curve downward-sloping? Here are a few reasons:

• Substitution Effect: As prices lower, consumers may switch from higher-priced alternatives to the cheaper option.
• Income Effect: Lower prices increase consumers' purchasing power, making them more likely to buy additional quantities.

For firms operating under such curves, adjustments in pricing are crucial. Lowering prices can attract more buyers but comes at the cost of reduced revenues from existing sales, creating a delicate balance that firms must manage.