Introduction:
In a Monopoly, a single firm dominates the entire market for a product with no close substitutes and significant barriers to entry. The monopolist is a price maker, meaning it has the power to influence the market price of its product. The determination of price and output under monopoly follows a specific process aimed at profit maximization. The price and output under monopoly determine by time factor.
The price – output determination under monopoly market:
Assumptions:
- The aim of Monopoly firm is to gain maximizing profit
- It is totally free from government control
- It changes a single and similar high price to all customer
Price output determination under short period:
Short period is a time period in which there are two types of factor of production, the first one is the fixed factor and other one is the variable factors. In the short period, only by changing the variable factor of production one can change production. Fixed factor of production cannot be changed. In other words supply can be changed only to some extent in the short period and the volume of production can be changed slightly but capacity of the plant cannot be changed. The firm can increase the supply only with the help of existing machines and plants etc. and plants equipment cannot be installed.
The aim of monopolist is also to make maximum profit or incur minimum loss. If he is compelled to do so. Monopolist, a single seller of his product can fix his price equal to above or less than the short period average cost of product. Than he earns normal profit, supernormal profit or incurs losses even in the short period.
This depends upon the nature and extent of the demand for product. In order to make maximum profit or incur minimum loss, a monopolists compares his marginal revenue and marginal cost. If marginal revenue exceeds the marginal cost of a product the Monopoly can increases profit by increasing his production on the other hand if marginal cost exceeds marginal revenue at a particular level of output the monopolist can minimize his losses by reducing the production. So the monopolist is said to be in equilibrium when his marginal cost cuts the marginal revenue curve from below. In other words the correct point of price output determination for a monopolist is that where marginal revenue is equal to the marginal cost.
In the short period, a Monopoly can earn supernormal profit, normal profit or incur losses. In case of losses price must be covering at least average variable cost otherwise the firm will stop production. The maximum loss can be equal to fixed cost.
The three cases of monopoly equilibrium can be shown through the figures drawn below
- in figure a: AR>AC, hence super normal profit
- in figure b:AR=AC, hence normal profit
- in figure c: AR< AC, hence losses
Figure (A)

Figure (B)

Figure (C)

This is how a Monopoly firm can earn super normal profit, normal profit or incurred losses.
Price output determination in the long run:
The Monopoly firm in the long run will continue its operation till it reaches the equilibrium point where long run marginal revenue equals long run marginal cost the price changed at this level of output is known as equilibrium price.

In the diagram the Monopoly firm reaches the position of equilibrium at E. A this point MR equal MC and MC curve cuts MR curve below. the monopolist will stop his output before AC reaches its minimum point he does not bother to reaches the minimum point on AC.
In the long run there is adequate time to make all kind of adjustment in both fixed as well as variable factor inputs. Supply can be adjusted to demand condition the total amount of long run profit will depend on the cost condition under which the monopolist has to operate production and demand curve has to face in the long run.
Under Monopoly, the AR or demand curve slope downwards from left to right this is because the monopolist can increase his sales and maximize is profit only when he reduces the price MR is less than AR and hence the MR curve lies below the AR curve. this is in accordance with the usual relationship between AR and MR.
The law of returns influences the cost curve of the Monopoly firm. the price has to change for his product mainly depends on the nature of his cost curve.
He restricts his output in order to maximum his profit. OQ is the output the price changed by the firm is QR (PQ) that is equal to AR. this price is higher than average cost QM per unit. The excess profit per unit of output is PM and the total profit of the firm is PM* MN=NRPM. The shaded area under Monopoly, no doubt MR = MC but MR is less than AR. hence monopoly price = AR only. price is greater than AC, MC and MR.
also read: what is production? explain its types.