Understanding Revenue in a Monopoly
What is Average Revenue?
Average revenue (AR) refers to the revenue earned per unit of output sold by a firm. It is calculated by dividing total revenue (TR) by the quantity of goods sold (Q). Mathematically, it is expressed as:
AR = TR / Q
In a monopoly, the average revenue is essentially the price at which the good is sold, since total revenue is the product of price and quantity:
TR = Price (P) × Quantity (Q)
Therefore, the average revenue in a monopoly is equal to the price of the product:
AR = P
Since monopolists face a downward-sloping demand curve, the price they charge depends on the quantity they decide to produce and sell.
What is Marginal Revenue?
Marginal revenue (MR), on the other hand, measures the additional revenue generated from selling one more unit of output. It is derived by taking the change in total revenue when quantity increases by one unit:
MR = ΔTR / ΔQ
In a monopoly, marginal revenue is not equal to the price of the product because to sell additional units, the monopolist must lower the price not only for the extra unit but also for all previous units sold. This price reduction affects total revenue, making the marginal revenue decrease faster than the price.
The Relationship Between Average Revenue and Marginal Revenue in Monopoly
Graphical Representation
In a typical monopoly diagram, the demand curve (D) represents the average revenue curve (AR), since AR equals price at each quantity. The marginal revenue curve (MR) lies below the demand curve because of the effect of price reduction on total revenue when output expands.
The key features of the graph are:
- The demand curve (AR): downward sloping, indicating that to sell more units, the monopolist must lower the price.
- The marginal revenue curve (MR): also downward sloping but steeper than the demand curve.
- The marginal revenue curve intersects the quantity axis at half the maximum quantity where the demand curve intersects the marginal revenue curve.
Mathematical Relationship
For a linear demand curve, the relationship between AR and MR can be expressed as:
MR = AR - (Q × ΔAR / ΔQ)
But more specifically, for a linear demand curve with slope b, the equations are:
- Demand (AR): P = a - bQ
- Total Revenue: TR = P × Q = (a - bQ)Q = aQ - bQ²
- Marginal Revenue: MR = d(TR) / dQ = a - 2bQ
From these equations, it is evident that:
- AR = P = a - bQ
- MR = a - 2bQ
This shows that the marginal revenue curve has the same intercept as the demand curve but has twice the slope, making it steeper and always below the demand curve.
Implications of the Relationship in Monopoly Pricing and Output Decisions
Why Is Marginal Revenue Less Than Average Revenue?
Since the MR curve lies below the AR (demand) curve, the marginal revenue for each additional unit sold is less than the price at which the unit is sold. This is due to the necessity of reducing the price to sell more units, which affects the revenue from all previous units.
Key points include:
- When AR decreases with increased output, MR declines even faster.
- At the point where MR = 0, the total revenue reaches its maximum.
- Producing beyond this point will decrease total revenue.
How Does This Affect Monopolist's Decision-Making?
A monopolist maximizes profit by producing the quantity where marginal cost (MC) equals marginal revenue (MR):
MC = MR
Given the relationship between AR and MR, the monopolist's optimal output level is determined by the intersection of the MC and MR curves. The corresponding price is then found on the demand (AR) curve.
The critical points to note are:
- Profit maximization occurs where MR = MC, not where AR = MC.
- The monopolist charges a price above the marginal revenue, which is above the marginal cost at the profit-maximizing output.
Differences Between Monopoly and Perfect Competition
In perfect competition:
- Price (AR) equals marginal revenue (MR).
- Firms are price takers, with no ability to influence market price.
- The demand curve is perfectly elastic, and AR = MR = P.
In contrast, in a monopoly:
- Price (AR) exceeds MR.
- The firm has market power and can influence the price.
- Marginal revenue is less than the price, and MR declines faster than AR as output increases.
Real-World Examples and Applications
Understanding the concepts of average and marginal revenue in a monopoly has practical implications across various industries:
- Utility Companies: Often natural monopolies, they set prices based on revenue considerations to maximize profits.
- Technology Firms: Some tech giants operate as monopolies or near-monopolies, adjusting output and pricing strategies based on revenue calculations.
- Pharmaceuticals: Patent protections grant monopoly power, and firms analyze marginal revenue to determine optimal production levels.
Knowing how marginal revenue behaves relative to average revenue aids businesses in strategic pricing and output decisions to maximize profits while considering consumer welfare and market regulation.
Summary and Key Takeaways
- In a monopoly, average revenue (AR) is equal to the price at which goods are sold.
- Marginal revenue (MR) is the additional revenue from selling one more unit and is always less than AR beyond the initial units.
- The MR curve lies below the AR (demand) curve and has twice the slope in the case of linear demand.
- The monopolist maximizes profit where MR = MC, which generally results in higher prices and lower outputs compared to perfect competition.
- The relationship between AR and MR explains why monopolies have market power and how they decide on optimal output levels.
By mastering these concepts, economists and business strategists can better analyze monopoly dynamics, predict pricing strategies, and assess the impact on market efficiency and consumer welfare.
Frequently Asked Questions
What is the difference between average revenue and marginal revenue in a monopoly?
In a monopoly, average revenue is the total revenue divided by the quantity sold, which equals the price of the product. Marginal revenue is the additional revenue gained from selling one more unit of output. While average revenue remains constant along the demand curve, marginal revenue decreases as output increases due to the downward-sloping demand curve.
Why is marginal revenue less than average revenue in a monopoly?
Because monopolists face a downward-sloping demand curve, to sell additional units, they must lower the price, which reduces revenue from previous units. This causes marginal revenue to be less than average revenue, especially as output increases.
How is average revenue calculated in a monopoly?
Average revenue is calculated by dividing total revenue by the quantity sold, which also equals the price per unit, since total revenue = price × quantity.
How does marginal revenue behave as output increases in a monopoly?
Marginal revenue decreases as output increases because each additional unit must be sold at a lower price, leading to diminishing marginal revenue, eventually becoming negative if the price drops sufficiently.
What is the significance of the marginal revenue curve in a monopoly?
The marginal revenue curve helps monopolists determine the profit-maximizing level of output by showing how additional sales affect total revenue, which in turn influences their production decisions.
At what point does marginal revenue equal zero in a monopoly?
Marginal revenue equals zero at the point where the demand curve reaches its maximum total revenue, which occurs at the midpoint of the demand curve.
How are average revenue and marginal revenue related on a graph in a monopoly?
On a graph, the average revenue curve coincides with the demand curve, while the marginal revenue curve lies below the demand curve and slopes downward, reflecting the decreasing additional revenue from each extra unit sold.
Why does a monopolist's marginal revenue curve slope downward faster than the demand curve?
Because to sell additional units, the monopolist must lower the price for all units sold, causing marginal revenue to decline faster than the price (average revenue), which remains on the demand curve.
How does understanding average and marginal revenue help a monopoly maximize profits?
By analyzing where marginal revenue equals marginal cost, a monopoly can identify the optimal output level for maximum profit, since profit is maximized when the additional revenue from selling one more unit equals the additional cost.
Can average revenue ever be less than marginal revenue in a monopoly?
No, in a monopoly, average revenue is equal to the price, which is always higher than marginal revenue at the profit-maximizing output point, except in the case where marginal revenue is zero at maximum total revenue.
