True or False a Monopolist Continues to Make Profit in the Long Run Due to Barriers to Entry

Here is an elaborated discussion on the short-run and long-run equilibrium of a monopolist.

Short-Run Equilibrium of a Monopolist:

We continue to assume that the monopolist maximises profits. Profit is same way for both competitive firms and monopolists: profit is the difference between total revenue and total cost or;

II = TR – TC

In order to maximise profit, the monopolist must find the output that maximises the difference between revenue and total cost. In order to continue to expand output as long as the increase in revenue from doing so exceeds he increase in cost.

But marginal revenue is the increase in total revenue when the firms sells one more unit, whereas marginal cost in the increase in total cost incurred by producing one more unit.

Profit is maximised by producing where marginal revenue equals marginal cost, that is, where:

MR = MC

In Fig. 22.3 marginal revenue and marginal cost are equal at an output of Q₁. To see that profit is indeed maximised at Q₁, let us consider movements away from Q₁. Each time output increases by one unit, total revenue increases by marginal revenue; this is given by the height of the marginal revenue curve at that quantity.

Suppose that output increases from Q₁ to Q₁ + 1. The resulting change in total revenue equals the height of the marginal revenue curve at Q₁ + 1, which is shown by C. Similarly, the height of the marginal cost curve shows the increase in total cost each time output increases by one unit.

The increase in total cost due to an increase in output from Q₁ to Q₁ + 1 is given by the height of the marginal cost curve at Q₁ + 1, which is shown by B. As output expands beyond Q₁, total cost is clearly rising more rapidly than total revenue, resulting in lower profits. In fact, the difference between B and C represents the decrease in profits caused by increasing output from Q₁ to Q₁ + 1.

We may now examine the effect of a decrease in output from Q₁ to Q₁ – 1. The resulting reduction in total revenue equals the height of the marginal revenue curve at Q₁ – 1, which is shown by D. This represents the revenue that is lost by producing the smaller output.

Similarly, the reduction in total cost is given by the height of the marginal cost curve at Q₁ – 1, which is shown by F. This height represents the costs that are saved by producing less output. On balance, we can see that the revenue lost exceeds the costs saved when output is reduced from the point where marginal cost equals mar­ginal revenue. As a result profit falls and, in fact, the difference between D and E measures the fall in profit due to output reduction.

Thus, we have found that any movement away from Q₁ results in lower profit. This means that profit is maximised at output Q₁.

In Fig. 22.4, we have shown the monopolist's average and marginal cost curves along with his demand and marginal revenue curves. Marginal revenue equals marginal cost at an output of Q₁. The price that consumers are willing to pay to con­sume Q₁ can be seen from the demand curve. In this case, a price of P₁ corresponds to the output of Q₁.

The monopolist thus charges a price that exceeds the cost of producing one more unit of output (MC). To find the firm's profit, we need to know its average total cost curve at Q₁ (ATC₁). Con­sequently, profit can be calculated as;

II = P₁Q₁ – ATC₁Q₁ = (P₁ – ATC₁) Q₁ which is shown as the shaded rectangle.

Fig. 22.5 gives a more complete picture. In part (a) profit is maximised when total revenue exceeds total cost by the largest amount possible. Maximum profit occurs at output Q₁, where the slopes of TR and TC (MR and MC) are equal. In part (b) the per-unit revenue and cost curves illustrate the same situation as shown in part (a).

Sub-Optimal Outcome under Monopoly :

Monopoly profits are not necessarily positive:

There is no reason for supporting that all monopolists earn excess profits. The fact that there is only one firm in the industry is not a guarantee that the monopolist will always make a positive profit, not to speak of an excessive one. If the production costs are high relative to the demand for the product, profits will tend to be low.

In part (a) of Fig. 22.6, we see the position of a monopolist that will continue producing in the short run, even though it is making losses. Profit maximisation requires producing the output where marginal cost equals marginal revenue, which is Q₁ units. For the monopolist to sell Q₁ units, the firm must charge a price of P₁.

The per unit cost is given by the height of the ATC curve at Q₁ units of output, which is ATC₁ and greater than P₁. The monopolist, however, will find that its best business strategy is to produce Q₁ and sell at P₁, because P₁ exceeds AVC₁.

When price exceeds average variable cost, total revenue covers all of the variable costs and part of the fixed costs. If the monopolist decided to produce no output, its loss would be equal to the fixed cost. Thus, losses are minimised by producing that output where marginal revenue and marginal cost are equal if price exceeds average variable cost.

In part (b) of Fig. 22.6, we see the position of a monopolist that should not produce any positive quantity. The maximum profit that it can make while producing occurs at Q₂ units of output, where marginal revenue equals marginal cost.

However, in this case, the price that corresponds to Q₂ is P₂ and that is less than the average variable cost of producing Q₂ (AVC₂). If the firm were to product Q₂, it would lose all of the fixed costs plus the difference between total revenue and total variable costs.

Thus, the extra loss that would be suffered by producing where marginal cost equals marginal revenue is (AVC₂ – P₂) Q₂, which is shown in part (b) as the shaded area. But the manager can confine the firm's loss to the fixed costs simply by producing no output. Even though the firm is a monopolist, the manager will not produce any output, because losses are minimised by not producing any output.

The consideration of the three cases that we have just examined leads to the following rule for profit maximisation:

A monopolist will produce that output where marginal revenue equals marginal cost and charge the price corresponding to that output on the demand curve, provided that price exceeds average variable cost. If price is less than average variable cost, then optimal output is zero.

Formal derivation of the equilibrium condition of the monopolist:

Given the demand function:

Q = g (P)

which may be solved for P

P =f₁ (Q)

and given the cost function

C=f₂ (Q)

the monopolist aims at the maximisation of his profit

∏ = R – C

(a) The first-order condition for maximum profit ∏

Example :

Given the demand curve of the monopolist:

Q = 50 – 0.5P

which may be solved for P

p = 100 – 2Q

and the cost function of the monopolist

C = 50 + 40Q

find out its profit-maximising output level.

Solution:

∏ = R – C

(i) We first find the MR

R = QP = Q (100 – 2Q)

R = 100Q – 2q²

MR = dR/dQ = 100 – 4Q

(ii) We next find the MC

C = 50 + 40Q

MC = dC/dQ = 40

(iii) We equate MP and MC

MP = MC

100 + 40Q = 40

Q = 15

(iv) The monopolism's price is found by substituting Q = 15 into the demand-price equation

P = 100 – 2Q = 70

(v) The profit is

∏ = R – C = 1050 – 650 = 400

This profit is the maximum possible, since the second-order condition is satisfied:

(a) From = dC/dQ = 40

we have d²C/dQ² = 0

(b) From dR/dQ = 100 – 40

we have d²R/dQ² = -4.

Clearly -4 < 0.

Long-Run Equilibrium of a Monopolist:

In an industry characterised as a monopoly, there is only a single firm Thus, when he firm is in long-run equilibrium, the industry is also in long-run equilibrium. In the competitive model, free entry drove the profits of at least some firms to zero. But in the monopoly model, entry is foreclosed and, therefore, profits may be positive even in long-run equilibrium.

In the long run, output and fixed inputs are adjusted until profit is maximised. The solution is very similar to the short-run solution: profit is maximised at the output at which marginal revenue equals the appropriate marginal cost. In the long run, the relevant marginal cost is the long-run marginal cost.

In Fig. 22.7, profit is maximised by producing where long-run marginal cost (LMC) curves cuts MR curve. This occurs at Q₀ units of output. The firm will produce and sell Q₀ units of output at the profit- maximising price of P₀. The long-run average cost of producing Q₀ is C₀. Consequently, long- run profits are (P₀ – C₀) Q₀.

When the firm decides on an output of Q₀, it must make commitments on some inputs that may become fixed for a certain period of time. These fixed inputs generate the short-run average cost curve (SAC₀), which is tangent to the long- run average cost curve Q₀ units of output. The short-run marginal cost curve associated with SAC₀ (that is, SMC₀) intersects LMC curve at Q₀ and passes through the minimum point of the SAC₀ curve.

Thus, we can see that the conditions for long-run profit maximisation in a monopoly are:

MR = LMC = SMC

SAC = LAC

P ≥ LAC

The essence of long-run equilibrium is that the monopolist is producing where long-run marginal cost equals marginal revenue, and it has no incentive to alter the size of the plant.

Sub-Optimal and Optimal Adjustment in the Long Run :

In the long run the monopolist gets sufficient time to adjust the size of his plant or to use his existing plant at any level so as to maximise his profit. Since entry is totally blocked (i.e., no new firm can join the industry) it is not necessary for the monopolist to reach an optimal scale (that is, adjust his plant in such a way as to reach the lowest point of the LAC curve).

There is also no guarantee that the monopolist will use his existing plant at optimum capacity. However, the monopolist will not operate in the long run by incurring losses, i.e., TR < LTC and P < ATC. He will probably continue to make excess profits even in the long run, as long as entry is blocked.

However, the size of his plant and the degree of capacity utilisation of any existing plant (of fixed size) depend entirely on the size of the market for his product. He may reach the optimal scale (minimum point of LAC) or remain at sub-optimal scale (declining portion of his LAC) or go beyond the optimal scale (indicated by minimum LAC) depending on the size of the market (or the intensity of demand for his product).

In Fig. 22.9 we see that the size of the market is not wide enough to permit the monopolist to expand to the minimum point of LAC (point b). This means that his plant is of sub-optimal size (in the sense that he cannot fully derive economies of scale).

Moreover, the existing plant is under-utilised the reason is that to the left of the lowest point of the LAC curve (b) the SAC curve is tangent to the LAC curve at its falling part and also because the SMC must equal LMC (as a point E). Since b is the minimum point of LAC curve optimum use of the existing plant occurs at point a and there is excess capacity at point E'.

A different type of situation is shown in Fig. 22.9. Here the size of the market is so large that the monopolist, in order to maximise his output, must build a plant larger that the optimal and overutilise it. The reason is that to the right of the minimum point of the LAC curve both the SAC curve and LAC curve are tangent at a point where their slope is positive (each curve is sloping upward from left to right) as also because the SMC curve must be equal to the LAC curve.

Thus the profit-maximising plant makes the monopolist a high-cost producer.

There are two reasons for this:

(i) It is larger than the optimal size and

(ii) It is more than fully utilised.

This is usually the case with public utility concerns which have economy-wide operations.

Finally Fig. 22.10 shows the case of a monopolist whose market size is optimal and whose capacity utilisation is full. The figure is self-explanatory.

It is not possible to predict which of the above three situations will emerge in any particular case. Much depends on the size of the market (given the technology of the monopolist). There is no guarantee that in the long run the monopolist will reach the optimal scale, as is the case of a firm operating in a purely competitive market.

Competitive market forces do not operate in monopoly so as to ensure that the monopolist operates at optimum plant size (and utilise it at its full capacity) in the long run.

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Source: https://www.microeconomicsnotes.com/monopoly/short-run-and-long-run-equilibrium-of-a-monopolist-microeconomics/14222

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