There are two categories of monopoly:
The basic economic logic used by the monopolist is the same as that used by the competitive firm --
Understanding the application of this logic by a monopolist requires, however, careful attention to both the COST side and the BENEFIT side.
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:
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:
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
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.
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:
With the previous demand equation, marginal revenue is:
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.
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
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
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.