Equilibrium Price and Output Determination in Monopoly

Short-Run Equilibrium

In a short run, the monopolist has no sufficient time to expand its plant size (or capacity). In other words, market supply cannot be adjusted according to the change in the market demand. A monopolist has two obligations; a) to determine the level of output and b) to determine the price.

A monopolist determines the level of output at the point where the two conditions for profit maximization are fulfilled: a) MC = MR and b) the slope of MC > the slope of MR. Being a sole seller, the monopolist determines the price of his product on the basis of the law of demand. Thus, the demand curve (AR) of a firm slopes downwards. In perfect competition the firm is a price-taker, so only decision is a determination of output. The monopolist has to make two decisions: setting the price and his output. However, considering the downward-sloping demand curve, the two decisions are dependent on each other. The core of monopoly power is the capability to change the price of a product.

Generally, being a sole seller, monopolist enjoys excess profit (AR > AC) at short run equilibrium. However, there is no certainty that a monopoly firm will always earn an excess or supernormal profit. Monopolist profit will be maximum and will obtain equilibrium at the level of output where marginal revenue is equal to marginal cost. The monopolist will never place his level of output where the elasticity of demand or average revenue curve is less than unity. Whether a monopoly firm earns an excess profit or normal profit or incurs loss depends on i) its cost and revenue conditions ii) threat from potential competition or presence of remote substitutes and iii) government policy in respect of monopoly. In other words, the level of profit depends upon the efficiency of the firm and market demand. A monopolist firm has to realize three possibilities when it produces any level of output at a point where two conditions are satisfied. They are:

1. If AR > AC, firm obtains excess profit.
2. If AR = AC, firm obtains normal profit.
3. If AR < AC, firm bears the loss.

Excess Profit (AR > AC)
According to the figure, the firm is in equilibrium at point E because the firm satisfies two firm equilibrium conditions (i.e. MC = MR and MC cuts MR from below, at E point).

Thus,
Level of output (Q) = OQ
Per unit price (P) = OP = aQ
Per unit cost (C) = OC = bQ
Total Revenue (TR) = PQ = OP × OQ = Area of OPaQ
Total Cost (TC) = CQ = OC × OQ = Area of OCbQ
Since, Profit (π) = TR – TC = Area of OPaQ – Area of OCbQ = Area of Pabc

Normal Profit (AR = AC)
According to the figure, the firm is in equilibrium at point E where two conditions are satisfied, i.e. MC = MR and MC cuts MR from below.
Thus,
Level of output (Q) = OQ
Per unit price (P) = OP = aQ
Per unit cost (C) = OC = bQ
Total Revenue (TR) = PQ = OP × OQ = Area of OPaQ
Total Cost (TC) = Area of OPaQ
Here, Area of TR = Area of TC. Thus, the firm obtains normal profit.

Losses (AR < AC)
In the figure, the firm is in equilibrium at point E, where MC = MR and MC cuts MR from below. Thus,
Level of output (Q) = OQ
Per unit price (P) = OP = aQ
Per unit cost (C) = OC = bQ
Total Revenue (TR) = PQ = OP × OQ = Area of OPaQ
Total Cost (TC) = CQ = OC × OQ = Area of OCbQ
Here, Area of TC > Area of TR. Thus, firm incurs losses shown by the area Pabc. Loss bearing firm exists in a market when it recovers variable costs at prevailing price (i.e. P = AVC). Hence, point ‘a’ is a shut-down point.

Long Run Equilibrium

In long run, the monopolist has sufficient time to expand its plant size or to use its existing plant at any level, which will maximize profit. In other words, due to the availability of sufficient time, market supply can be adjusted according to change in market demand. There is a possibility for the firm earning an excess profit in the long run because entry of new firms is blocked. However, the size of his plant and the degree of utilization of any given plant size depend entirely on the market demand cost condition and market size. Long-run average cost curve and its corresponding long-run marginal cost curves present the alternative plants including various plant sizes from which the firm is to choose for operation in the long run. If the market demand for the product is enough to meet the output produced at optimal capacity by the monopolist, he obtains rational excess profit.

But if the market demand is less or if the market size is small, he operates his plant only on a sub-optimal scale and obtains less excess profit. Similarly, if the market demand is more or its size of the market is large, he operates his plant at more than optimal capacity and obtains more excess profit. In addition, the firm will function at a point on the long- run average cost curve at which the short-run average cost is tangent to it. However, the monopolist operates its plant at sub-optimal scale due to market imperfection. In this way, monopolist earns an excess profit in the long run if he satisfies the following conditions:
i) MC = MR 

ii) MC cuts MR from below

In the given figure, the firm is in equilibrium at point E where,

 i) MC = MR 

ii) MC cuts MR from below.

Here, the area of TR (area of OPaQ) > area of TC (area of OcbQ). Thus, the monopolist maximizes his profit by producing the OQ level of output and maximum profit area is the area of Pabc. The monopolist operates his plant at a sub-optimal capacity. It is shown by point b where the falling part of AC cuts the Qa vertical line. Thus, the bK position of the plant is unused capacity.

Reference

Koutosoyianis, A (1979), Modern Microeconomics, London Macmillan