Economics » Monopoly » How a Profit-Maximizing Monopoly Chooses Output and Price

# Marginal Revenue and Marginal Cost For a Monopolist

## Marginal Revenue and Marginal Cost for a Monopolist

In the real world, a monopolist often does not have enough information to analyze its entire total revenues or total costs curves; after all, the firm does not know exactly what would happen if it were to alter production dramatically. But a monopolist often has fairly reliable information about how changing output by small or moderate amounts will affect its marginal revenues and marginal costs, because it has had experience with such changes over time and because modest changes are easier to extrapolate from current experience. A monopolist can use information on marginal revenue and marginal cost to seek out the profit-maximizing combination of quantity and price.

The first four columns of this table use the numbers on total cost from the HealthPill example in the previous exhibit and calculate marginal cost and average cost. This monopoly faces a typical upward-sloping marginal cost curve, as shown in this figure. The second four columns of this table use the total revenue information from the previous exhibit and calculate marginal revenue.

Notice that marginal revenue is zero at a quantity of 7, and turns negative at quantities higher than 7. It may seem counterintuitive that marginal revenue could ever be zero or negative: after all, does an increase in quantity sold not always mean more revenue? For a perfect competitor, each additional unit sold brought a positive marginal revenue, because marginal revenue was equal to the given market price. But a monopolist can sell a larger quantity and see a decline in total revenue. When a monopolist increases sales by one unit, it gains some marginal revenue from selling that extra unit, but also loses some marginal revenue because every other unit must now be sold at a lower price. As the quantity sold becomes higher, the drop in price affects a greater quantity of sales, eventually causing a situation where more sales cause marginal revenue to be negative.

Marginal Revenue and Marginal Cost for the HealthPill Monopoly

For a monopoly like HealthPill, marginal revenue decreases as additional units are sold. The marginal cost curve is upward-sloping. The profit-maximizing choice for the monopoly will be to produce at the quantity where marginal revenue is equal to marginal cost: that is, MR = MC. If the monopoly produces a lower quantity, then MR > MC at those levels of output, and the firm can make higher profits by expanding output. If the firm produces at a greater quantity, then MC > MR, and the firm can make higher profits by reducing its quantity of output.

Costs and Revenues of HealthPill

Cost InformationRevenue Information
QuantityTotal CostMarginal CostAverage CostQuantityPriceTotal RevenueMarginal Revenue
11,5001,5001,50011,2001,2001,200
21,80030090021,1002,2001,000
32,20040073331,0003,000800
42,80060070049003,600600
53,50070070058004,000400
64,20070070067004,200200
75,6001,40080076004,2000
87,4001,80092585004,000–200

A monopolist can determine its profit-maximizing price and quantity by analyzing the marginal revenue and marginal costs of producing an extra unit. If the marginal revenue exceeds the marginal cost, then the firm should produce the extra unit.

For example, at an output of 3 in this figure, marginal revenue is 800 and marginal cost is 400, so producing this unit will clearly add to overall profits. At an output of 4, marginal revenue is 600 and marginal cost is 600, so producing this unit still means overall profits are unchanged. However, expanding output from 4 to 5 would involve a marginal revenue of 400 and a marginal cost of 700, so that fifth unit would actually reduce profits. Thus, the monopoly can tell from the marginal revenue and marginal cost that of the choices given in the table, the profit-maximizing level of output is 4.

Indeed, the monopoly could seek out the profit-maximizing level of output by increasing quantity by a small amount, calculating marginal revenue and marginal cost, and then either increasing output as long as marginal revenue exceeds marginal cost or reducing output if marginal cost exceeds marginal revenue. This process works without any need to calculate total revenue and total cost. Thus, a profit-maximizing monopoly should follow the rule of producing up to the quantity where marginal revenue is equal to marginal cost—that is, MR = MC.

### Maximizing Profits

If you find it counterintuitive that producing where marginal revenue equals marginal cost will maximize profits, working through the numbers will help.

Step 1. Remember that marginal cost is defined as the change in total cost from producing a small amount of additional output.

$$\text{MC}=\cfrac{\text{change in total cost}}{\text{change in quantity produced}}$$

Step 2. Note that in this table, as output increases from 1 to 2 units, total cost increases from $1500 to$1800. As a result, the marginal cost of the second unit will be:

$$\begin{array}{rcl}\text{MC}& =& \cfrac{\1800–\1500}{1}\\ & =& \300\end{array}$$

Step 3. Remember that, similarly, marginal revenue is the change in total revenue from selling a small amount of additional output.

$$\begin{array}{rcl}\text{MR}& =& \cfrac{\text{change in total revenue}}{\text{change in quantity sold}}\end{array}$$

Step 4. Note that in this table, as output increases from 1 to 2 units, total revenue increases from $1200 to$2200. As a result, the marginal revenue of the second unit will be:

$$\begin{array}{rcl}\text{MR}& =& \cfrac{\2200–\1200}{1}\\ & =& \1000\end{array}$$

Marginal Revenue, Marginal Cost, Marginal and Total Profit

QuantityMarginal RevenueMarginal CostMarginal ProfitTotal Profit
11,2001,500–300–300
21,000300700400
3800400400800
46006000800
5400700–300500
6200700–5000
701,400–1,400–1,400

This table repeats the marginal cost and marginal revenue data from this table, and adds two more columns: Marginal profit is the profitability of each additional unit sold. It is defined as marginal revenue minus marginal cost. Finally, total profit is the sum of marginal profits. As long as marginal profit is positive, producing more output will increase total profits. When marginal profit turns negative, producing more output will decrease total profits. Total profit is maximized where marginal revenue equals marginal cost. In this example, maximum profit occurs at 4 units of output.

A perfectly competitive firm will also find its profit-maximizing level of output where MR = MC. The key difference with a perfectly competitive firm is that in the case of perfect competition, marginal revenue is equal to price (MR = P), while for a monopolist, marginal revenue is not equal to the price, because changes in quantity of output affect the price.