Monopolies are quite common in business. If you offer a product or service that no one else has, then you possess a monopoly. In time, competitors probably will aim to match or improve upon your innovation, and your monopoly position will be removed. But while you are in a position as a market leader, it's important to understand how your monopoly determines your demand curve and why your marginal revenue curve will always be lower than your demand curve. Show
Demand CurveThe law of demand, a fundamental principle of economics, says that as the price of something goes up, the demand for it declines. Conversely, as the price falls, demand goes up, according to Corporate Finance Institute. Plotted on a graph, this forms what's called the demand curve. The vertical axis of the graph is the price charged for an item; the horizontal axis is the quantity sold. The typical demand curve slopes downward from the upper left, where a high price means low demand, to the lower right, where a low price creates high demand. Every good or service has its own demand curve. Monopoly SituationsWhen you've got a monopoly on something, you have no direct competition. You can set any price you want, and the demand curve for your good or service tells you how much you'll sell. If you want to sell more, you have to drop the price – or provide some kind of rebate, coupon, discount or special offer that has the effect of lowering the price. If you raise the price, meanwhile, you'll sell less. In a competitive market, by contrast, no one company can dictate price; you may have to match competitors' prices and compete on service or quality, according to AmosWEB. Applied ExampleSuppose you owned a car wash and had developed some special treatment that kept cars spot-free for a week. You patented the treatment, so you're the only one who can offer it. Through trial and error, you've found out that if you charge $5, you sell 10 treatments a week. If you cut the price to $4.95, you'll sell 11 treatments a week. If you charge $4.90, you'll sell 12 a week. At $4.75, you'll sell 13. And at $4.65, you'll sell 14. Like most demand curves, this one isn't a straight line on a graph, but it still slopes downward from left to right. Marginal RevenueMarginal revenue is the additional revenue you gain with each additional sale. Say you're charging $5 for a spot-free treatment, and you're selling 10 of them a week, for total revenue of $50. If you want to sell 11 treatments next week, you'll have to drop the price to $4.95. That price will apply to all the treatments you sell next week – not just the 11th one. So you'll sell 11 treatments at $4.95 apiece, or $54.45. Gaining one additional sale brought you $4.45 in new revenue, so the marginal revenue for the 11th sale is $4.45. If you want to increase sales the following week from 11 to 12, you must lower the price again, to $4.90. Once again, that lower price applies to all 12 sales – 12 times $4.90 is $58.80, so the marginal revenue for the 12th sale is $4.35. Marginal CurveYou can plot your marginal revenue curve on the same graph as your demand curve. For 11 sales, the demand curve shows a price of $4.95 – but the marginal revenue from that 11th sale is $4.45. For 12 sales, the demand curve shows a price of $4.90 – but the marginal revenue of a 12th sale is $4.35. For a monopoly, the marginal revenue curve is lower on the graph than the demand curve, because the change in price required to get the next sale applies not just to that next sale but to all the sales before it.
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\) We have located the profit-maximizing level of output and price for a monopoly. How does the monopolist know that this is the correct level? How is the profit-maximizing level of output related to the price charged, and the price elasticity of demand? This section will answer these questions. The firm’s own price elasticity of demand captures how consumers of a good respond to a change in price. Therefore, the own price elasticity of demand captures the most important thing that a firm can know about its customers: how consumers will react if the good’s price is changed. The Monopolist’s Tradeoff between Price and QuantityWhat happens to revenues when output is increased by one unit? The answer to this question reveals useful information about the nature of the pricing decision for firms with market power, or a downward sloping demand curve. Consider what happens when output is increased by one unit in Figure \(\PageIndex{1}\).  Increasing output by one unit from \(Q_0\) to \(Q_1\) has two effects on revenues: the monopolist gains area \(B\), but loses area \(A\). The monopolist can set price or quantity, but not both. If the output level is increased, consumers’ willingness to pay decreases, as the good becomes more available (less scarce). If quantity increases, price falls. The benefit of increasing output is equal to \(ΔQ\cdot P_1\), since the firm sells one additional unit \((ΔQ)\) at the price \(P_1\) (area \(B\)). The cost associated with increasing output by one unit is equal to \(ΔP\cdot Q_0\), since the price decreases \((ΔP)\) for all units sold (area \(A\)). The monopoly cannot increase quantity without causing the price to fall for all units sold. If the benefits outweigh the costs, the monopolist should increase output: if \(ΔQ\cdot P_1 > ΔP\cdot Q_0\), increase output. Conversely, if increasing output lowers revenues \((ΔQ\cdot P_1 < ΔP\cdot Q_0)\), then the firm should reduce output level. The Relationship between MR and EdThere is a useful relationship between marginal revenue \((MR)\) and the price elasticity of demand \((E^d)\). It is derived by taking the first derivative of the total revenue \((TR)\) function. The product rule from calculus is used. The product rule states that the derivative of an equation with two functions is equal to the derivative of the first function times the second, plus the derivative of the second function times the first function, as in Equation \ref{3.3}. \[\frac{∂(yz)}{∂x} = \left(\frac{∂y}{∂x}\right)z + \left(\frac{∂z}{∂x}\right)y \label{3.3}\] The product rule is used to find the derivative of the \(TR\) function. Price is a function of quantity for a firm with market power. Recall that \(MR = \frac{∂TR}{∂Q}\), and the equation for the elasticity of demand: \[E^d = \frac{(∂Q/∂P)P}{Q}\nonumber\] This will be used in the derivation below. \[\begin{align*} TR &= P(Q)Q\\[4pt] \frac{∂TR}{∂Q} &= \left(\frac{∂P}{∂Q}\right)Q + \left(\frac{∂Q}{∂Q}\right)P\\[4pt] MR &= \left(\frac{∂P}{∂Q}\right)Q + P\end{align*}\] next, divide and multiply by \(P\): \[\begin{align*}MR &= [\frac{(∂P/∂Q)Q}{P}]P + P\\[4pt] &= [\frac{1}{E_d}]P + P\\[4pt] &= P\left(1 + \frac{1}{E_d}\right)\end{align*}\] This is a useful equation for a monopoly, as it links the price elasticity of demand with the price that maximizes profits. The relationship can be seen in Figure \(\PageIndex{2}\). \[MR = P\left(1 + \frac{1}{E_d}\right) \label{3.4}\] At the vertical intercept, the elasticity of demand is equal to negative infinity (section 1.4.8). When this elasticity is substituted into the \(MR\) equation, the result is \(MR = P\). The \(MR\) curve is equal to the demand curve at the vertical intercept. At the horizontal intercept, the price elasticity of demand is equal to zero (Section 1.4.8, resulting in \(MR\) equal to negative infinity. If the \(MR\) curve were extended to the right, it would approach minus infinity as \(Q\) approached the horizontal intercept. At the midpoint of the demand curve, \(P\) is equal to \(Q\), the price elasticity of demand is equal to \(-1\), and \(MR = 0\). The \(MR\) curve intersects the horizontal axis at the midpoint between the origin and the horizontal intercept. This highlights the usefulness of knowing the elasticity of demand. The monopolist will want to be on the elastic portion of the demand curve, to the left of the midpoint, where marginal revenues are positive. The monopolist will avoid the inelastic portion of the demand curve by decreasing output until \(MR\) is positive. Intuitively, decreasing output makes the good more scarce, thereby increasing consumer willingness to pay for the good. Pricing Rule IThe useful relationship between \(MR\) and \(E_d\) in Equation \ref{3.4} can be used to derive a pricing rule. \[\begin{align*} MR &= P\left(1 + \frac{1}{E_d}\right)\\[4pt] MR &= P + \frac{P}{E_d}\end{align*}\] Assume profit maximization [\(MR = MC\)] \[\begin{align*} MC &= P + \frac{P}{E_d}\\[4pt] –\frac{P}{E_d} &= P – MC\\[4pt] –\frac{1}{E_d} &= \frac{P – MC}{P}\\[4pt] \frac{P – MC}{P} &= –\frac{1}{E_d}\end{align*}\] This pricing rule relates the price markup over the cost of production \((P – MC)\) to the price elasticity of demand. \[\frac{P – MC}{P} = –\frac{1}{E_d} \label{3.5}\] A competitive firm is a price taker, as shown in Figure \(\PageIndex{3}\). The market for a good is depicted on the left hand side of Figure \(\PageIndex{3}\), and the individual competitive firm is found on the right hand side. The market price is found at the market equilibrium (left panel), where market demand equals market supply. For the individual competitive firm, price is fixed and given at the market level (right panel). Therefore, the demand curve facing the competitive firm is perfectly horizontal (elastic), as shown in Figure \(\PageIndex{3}\). The price is fixed and given, no matter what quantity the firm sells. The price elasticity of demand for a competitive firm is equal to negative infinity: \(E_d = -\inf\). When substituted into Equation \ref{3.5}, this yields \((P – MC)P = 0\), since dividing by infinity equals zero. This demonstrates that a competitive firm cannot increase price above the cost of production: \(P = MC\). If a competitive firm increases price, it loses all customers: they have perfect substitutes available from numerous other firms. Monopoly power, also called market power, is the ability to set price. Firms with market power face a downward sloping demand curve. Assume that a monopolist has a demand curve with the price elasticity of demand equal to negative two: \(E_d = -2\). When this is substituted into Equation \ref{3.5}, the result is: \(\dfrac{P – MC}{P} = 0.5\). Multiply both sides of this equation by price \((P)\): \((P – MC) = 0.5P\), or \(0.5P = MC\), which yields: \(P = 2MC\). The markup (the level of price above marginal cost) for this firm is two times the cost of production. The size of the optimal, profit-maximizing markup is dictated by the elasticity of demand. Firms with responsive consumers, or elastic demands, will not want to charge a large markup. Firms with inelastic demands are able to charge a higher markup, as their consumers are less responsive to price changes. In the next section, we will discuss several important features of a monopolist, including the absence of a supply curve, the effect of a tax on monopoly price, and a multiplant monopolist. What is the relationship between the demand curve and marginal revenue curve in a monopoly?A monopolist's marginal revenue curve is always less than its demand curve.
What is the relationship between the marginal benefit curve and the demand curve?1. The demand curve represents marginal benefit. The vertical distance at each quantity shows the mount consumers are willing to pay for that unit. Willingness to pay reflects the benefit derived from each unit.
Is demand curve related to marginal revenue?The demand curve shows the quantity of an item that consumers in a market are willing and able to buy at each price point. The demand curve is important in understanding marginal revenue because it shows how much a producer has to lower his price to sell one more of an item.
What is the relationship between the marginal revenue curve and the demand curve for a single price monopolist?The marginal revenue curve for a single priced monopolist will always be twice as steep as the demand curve. Since the demand curve reflects the price and the marginal revenue curve is below the demand curve, the price is no longer equal to the marginal revenue as it was in pure competition.
Why is the marginal revenue curve under the demand curve?Because marginal revenue is less than price, the marginal revenue curve will lie below the demand curve.
What is the relationship between the demand curve and total revenue?As we move down along the demand curve, the total revenue increases, reaching its maximum at the point b (which is middle-distant from the two ends of the curve) and then declines, reaching zero again at price zero and quantity Qm.
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What is the relationship between the demand curve and the marginal revenue curve?
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