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# Monopoly and Marginal Revenue

Monopolies are, literally, the "single seller" in a particularindustry. While perfectly monopolized markets are as rare as perfectly competitive markets, there are elements of monopoly power in many markets, and understanging those elements is easiest if we consider the actions which would be taken by a perfect monopoly.

There are two categories of monopoly:

• A natural monopoly, with its market dominance resting on high fixed costs (making entrance difficult for other firms) and on low marginal costs of production and -- as a result -- declining average costs. Declining average costs imply that large scale producers can produce more cheaply and hence undersell new entrants.

• Legal monopolies , where market dominance does not rest on a cost advantage but on a legal prohibition of other firms entering. If a state-owned telecommunications service or postal service prohibits other firms from entering, we have a legal monopoly. If patents prevent other firms from entering an industry, we have a legal monopoly granted to the firm owning the patent.

Both categories will make decisions in the same manner; it is however simpler to begin with the natural monopoly and to assume that the lower marginal costs of the natural monopoly may be modelled as constant rather than rising marginal costs.

The basic economic logic used by the monopolist is the same as that used by the competitive firm --

• INCREASE output if marginal benefits are ABOVE marginal costs.
• DECREASE output if marginal benefits are BELOW marginal costs.
• STAY AT THE CURRENT LEVEL of output if marginal benefits are EQUAL to marginal costs.

Understanding the application of this logic by a monopolist requires, however, careful attention to both the COST side and the BENEFIT side.

### COSTS of a NATURAL MONOPOLIST

the cost graph of a natural monopolist is constructed on the assumption of constant marginal costs.
Let us assume that:
MC = k

where k is a constant marginal cost.

We know that Variable cost = sum of the marginal costs,
but if marginal cost is constant at k, we can compute this more easily as

VC = kQ , where Q is the Quantity of output.

Since total cost = fixed cost + variable cost, and

since average cost = Total Cost/Quantity,

we have for the natural monopoly:

AC = ( FC + kQ)/Q = FC/Q + k

As Q becomes larger, the first term will tend to zero; another way of saying this is that average cost will fall as output increases, and as output becomes very large, AC will approach MC.

Graphically, the average cost curve for a natural monopoly looks like this:

### MARGINAL REVENUE

While marginal revenue is the same as price for a competitive firm, it is less than price for a monopolist.

A competitive wheat farmer will take the price of wheat as given by the market at (say) \$5 a bushel. Sellinganother bushel of wheat brings the farmer a marginal revenue of another \$5.

The monopolist does not take the price of his product as given. Indeed, he knows that in order to sell more he will have to REDUCE the price of his product. In our introductory model of monopoly, we assume that the monopolist cannot price discriminate ; that is, that he must sell all output at the same price.

In calculating marginal revenue, the monopolist will have to consider consumer demand. Monopolists may be the only one selling the product, but they cannot force consumers to buy more than they wish.

Let us assume thAt demand is given by the equation

P = 3000 - 2 Q

Note that it is convenient to write the demand equation with price on the left hand side of the equation. To find REVENUE we need only multiply the demand equation through by Q.

REVENUE = PQ = 3000 Q - 2 Q*Q

This equation may be used to calculate marginal revenue. Simply consider the revenue at quantities of (say) 500 and 501 and calculate the CHANGE IN REVENUE.

At Q = 500, P = 3000 - 2(500) = 2000 and hence revenue = PQ = 1,000,000. At Q = 501, P = 3000 - 2(501) = 1998 and hence revenue = PQ = 1,000,998.

Marginal revenue at Q = 500 is \$ 998.

Note that Marginal revenue is less than price ; marginal revenue is \$998 and price was \$2000.

Note for those who haVe taken calculus:
marginal revenue, like all marginal concepts, deals with changes.
In calculus, you learn that to find the change in a function, you differentiate the function; if we differentiate the revenue function above with the aid of the power rule we find that

MR = 3000 - 4 Q

Note for those who have not taken calculus:
The MARGINAL REVENUE function may be derived from a straight line demand equation by:

1. Arranging the demand equation with price on the left hand side.
That is, given the equation Qd = 1500 - .5 P,
rearrange it to read P = 3000 - 2Q

2. Doubling the coefficient on the quantity term.

With the previous demand equation, marginal revenue is:

MR = 3000 - 4 Q

A full justification of this trick requires calculus, but note that it works:

at Q = 500, MR = 3000 - 4 (500) = \$1000,

close to the \$998 calculated above.

(If we had used 500.5, halfway between our two values, we would be exactly on target)

GRAPHICALLY, the marginal revenue curve will be sloping downward and falling exactly twice as steeply as the demand curve.

### Monopoly Output and Pricing Decisions

OUTPUT

Choose the output level at which MC = MR.

If we assume that MC = 500 and DEMAND is given by Q = 1500 - .5 P
we find as above that MR = 3000 - 4 Q.

Monopoly output will be found by setting

MR = MC
3000 - 4 Q = 500
4 Q = 3000 - 500
Q = 2500/4 = 625

PRICE

Monopoly price will be found by looking at the demand curve and charging as much as the market will bear for the level of output chosen.

Since DEMAND is

P = 3000 - 2 Q

at Q = 375, the price charged by the monopoly will be

P = 3000 - 2 (625) = 3000 - 1250 = \$ 1750.

Price is much higher than the marginal cost of \$ 500.

Profits

Operating profit = REVENUE - VARIABLE COST

In the case above, REVENUE = PQ = (\$1750) (625) = \$ 1,093,750

VARIABLE COST = MC x Q = \$500 x 625 = \$ 312,500

OPERATING PROFIT = PQ - VC = 1,093,750 - 312,500 = \$781,250

Without a figure given for fixed costs, we cannot tell if the monopoly is making an overall profit or not.

You can however vary the output decision and see if the monopoly has in fact found the profit-maximizing output level.