Determination of Market Equilibrium under Perfect Competition

At the point of equilibrium, a perfectly competitive firm earns maximum profits. Profits can be abnormal, supernormal or normal. At the point of equilibrium, the surplus of total revenue over total cost is maximized and correspondingly the marginal cost curve cuts the marginal revenue curve from below.

We would now move to discuss the equilibrium of a perfectly competitive firm with reference to the short-run and long-run.

1. Short-Run Equilibrium of a Competitive Firm:

TR-TC Approach:

At the outset, let us recollect that short-run is a period too short for new firms to enter the industry or exit. The existing firms cannot change the size of their plant in short-run a firm would be maximizing its profit and be in equilibrium when it produces the output that maximizes the difference between total revenue (TR) and total cost (TC).

In view of the feet that the price is constant at all levels of output under perfect competition, the total revenue (TR) curve is a straight line from the origin. This curve is upward sloping, as the monetary receipts increase with an increase in quantity sold. Thus, the slope of TR curve is a positive constant and is equal to MR. In figure 6.5, TC curve is also drawn, which is inverted S-shaped on account of law of variable proportions.

In figure 6.5, for production below level OQ₁ (or above level OQ₂) quantity of output, the firm incurs losses, as here its total cost exceeds total revenue. W and ‘B’ are the break even points of the firm corresponding to OQ₁ and OQ₂ levels of output, where its total revenue equals its total cost. The total revenue (TR) is more than the total cost (TC) between OQ₁ and OQ₂ levels of output, The distance between TR and TC is maximum (CD at the OQ level of output. At this level of output, MR (the slope of the TR curve) equals MC (the slope of the TC curve given by the slope of the tangent line EF to point ‘D’ on TC curve) and the firm maximizes its profit. Hence, the firm is said to be in equilibrium.

MC-MR Approach:

The TR=TC approach has its own limitations. Figure 6.6 demonstrates the equilibrium of a perfectly competitive firm using MR and MC curves. The left part of the figure 6.6 depicts the equilibrium of the industry at point E, where the market demand (DD’) curve and market supply (SS’) curve intersect each other. As the firms are price takers, the equilibrium price OP which is determined by the industry is to be accepted by all the firms.

Thus, the demand curve (i.e. the average revenue curve) of the individual firm is a horizontal straight line parallel to X-axis at a distance equal to price as shown in figure 6.6. Since each additional unit of the product is sold at the prevailing price OP, the marginal revenue curve of the firm coincides with the average revenue curve.

Following the objective of profit maximization, the firm will try to cut its costs and passively adjust its level of output to any given price situation. If the firm wants to get maximum profits (or minimum losses), it should not produce even a single additional unit at a loss for that would reduce the total profits of the firm.

As far as levels of output is below OQ₀, MC curve lies above MR curve. Thus, the addition to cost (i.e. the marginal cost) is more than the addition to revenue (i.e., marginal revenue) implying losses. The losses are equal to the area enclosed by the region PP1C, when OQ₀ level of output is sold in the market. Further, by producing beyond OQ₀ level of output, the firm will be adding to its profits, since, here each extra unit of output brings to the firm a revenue which exceeds its marginal cost (MR curve lies above MC curve).

This means that each extra unit of output contributes more to the total revenue than what it adds to the total cost, so long as the output of the firm remains lower than OQ. In due course, the equilibrium of the firm is established at point ‘B’, where marginal revenue (MR) is equal to marginal cost (MC) and the firm produces OQ level of output. At this level of, the firm gets maximum profits equal to the area enclosed between point ‘C’ and ‘B’ minus the losses equal to the area enclosed by the region PP1C.

If the firm enhances its production of any unit of output beyond OQ level it adds more to total costs than to total revenue ensuing in losses to the firms. Therefore, the profitability of the firm comes down. The firm should contract its output to secure maximum profits.

We can see that the maximum profit of the firm decline with sales beyond OQ level of output, as marginal cost exceeds marginal revenue for output greater than OQ. While there is still scope to raise the level of profits for any level of output below OQ, since marginal cost is less than marginal revenue for output less than OQ.

Therefore, the profit maximizing competitive firm can be in equilibrium only by producing OQ level of output, where the revenue from the last unit (i.e., MR) is equal to the cost of the last unit (i.e. MC).

One has to understand that the equality of MC and MR is necessary condition only but not a sufficient condition for equilibrium. MC=MR equality necessary condition is satisfied even at point ‘C corresponding to OQ level of output. Here, the firm invariably incurs losses equal to the area enclosed by the region PP1C, since total cost (represented by are OP1CQ₀ under the MC curve) exceeds total revenue represented by area OPCQ₀ under the average revenue curve, i.e. price x quantity). Thus point ‘C’ is not the equilibrium of the firm, where MC curve cuts MR curve from above and the former is falling.

There is a prospect to raise the profitability of the firm by expanding output beyond OQ₀ level of output, since in that situation marginal revenue exceeds marginal cost. Further, for output less than OQ₀ marginal cost exceeds marginal revenue, indicating that these units reduce profits. Thus, OQ₀ level of output does not maximize profit, rather it minimizes the profits. Total profits can be increased either by raising or lowering output from OQ₀ level.

The sufficient condition for the equilibrium of the perfectly competitive firm is that the marginal cost curve must be rising (i.e., upward sloping) at the point of intersection with the marginal revenue curve. In other words, MC should exceed MR for levels of output beyond equilibrium, so that there is no incentive or motive to produce additional units of the product. This sufficient condition is satisfied only at point ‘B’ in figure 6.6, while necessary condition for MC-MR equality is satisfied at both the points ‘A’ and ‘B’.

In light of the above discussion, we can conclude that the firm is in equilibrium only at point ‘B’ in figure 6.6. The equilibrium level of output of the firm is OQ.

Now the two conditions to equilibrium can be stated as under:

(a) Necessary Condition- MC = MR

(b) Sufficient condition -Slope of MC > Slope of MR

One has to understand that it is not necessary for a perfect competitive firm in equilibrium to always enjoy positive levels of profit in the short-run. A perfect competitive firm may earn abnormal profits or incur losses or just get normal profits depending upon the cost conditions.

I. Short Run Equilibrium of a Competitive Firm (Maximizing Profits):

Figure 6.7 portrays the case of a perfectly competitive firm earning supernormal profits in the short-run. In this case the average cost curve of the efficient firm lies below its average revenue curve. In this diagram, point ‘E’ is the equilibrium point, where the MC curve cuts the MR curve from below. OQ is the equilibrium output that is sold at the equilibrium price OP. Since this price (OP or EQ) exceeds the average cost (BQ), the firm will earn supernormal or excess profits in this situation. Total profits from the sale of equilibrium output are ‘profit per unit of output x quantity, i.e., (EQ-BQ) x OQ= Area (CPEB).

Super normal profits=Total Revenue – Total Cost = Price x Equilibrium Quantity-Average Cost x Equilibrium Quantity = OP × OQ – BQ x OQ = Area (OQEQ -OCBQ) = Area (CPEB)

II. Short Run Equilibrium of a Competitive Firm (Minimizing Losses):

The firm suffers from losses when the average cost curve of the firm lies above the average revenue (price) curve. This is shown in figure 6.8. Here, the equilibrium point is below the break-even point. In this case, the average cost of the firm corresponding to its equilibrium output OQ is equal to BQ, which is greater than the equilibrium price EQ. The loss per unit of unit incurred by the firm is Q-EQ= EB. The overall losses suffered by the competitive firm under consideration from the sale of equilibrium output are ‘loss per unit of output x equilibrium quantity, i.e. EB x OQ = Area (CPEB.)’.

Total Losses = Total Cost – Total Revenue =Average Cost x Equilibrium Quantity – Price x Equilibrium Quantity = BQ x OQ – OP x OQ = Area (OCBQ – OPEQ) = Area (CPEB)

The competitive firm experience losses in the short-run, when it is unable to cover the full average cost (AC). In such circumstances, the firm tries to minimize the losses. The competitive firm doesn’t mind, rather will be willing to bear the loss, provided price (or total revenue) at least covers the average variable cost (or total variable cost). Here, the competitive firm will continue to produce, since, it is able to cover the entire average variable cost (AVC) and a part of fixed cost (ED per unit of output). Here price is less than AC, but greater than AVC.

If the firm ceases production, it will continue to incur full fixed cost (indicated by the gap between AC and AVC) though variable costs will be avoidable. In that situation, the losses of the firm would be much higher (loss per unit of output x quantity, i.e. BD x OQ= Area (P₁CBD)), since, by continuing to produce, the firm was able to cover a part of the fixed cost. Thus, in the present case, the firm is minimizing losses by choosing to produce and sell.

Till the time these losses are less than the fixed cost, (i.e., when equilibrium price is greater than AVC, but, less than AC), a prudent firm will continue to operate the business rather than to stop production. That means that if the firm is incurring losses in the short run, the maximum losses it can tolerate do not exceed total fixed costs. However, the firm cannot bear losses on the variable costs in the short-run.

When the AVC is greater than the market price (i.e., AVC curve is above AR curve)), the competitive firm should temporarily suspend the operations in the short-run to avoid loss on variable costs i.e., the losses over and above the fixed cost. With no production and consequent zero sales (revenue), the losses equal to fixed cost will still be there, since, fixed cost is unavoidable in the short-run. The firm normally in such a situation, will prefer to incur this loss by closing down and will avoid the losses incurred on variable costs.

Further, if, the AVC is equal to just the market price (i.e., AVC curve touches equilibrium point ‘E’ in diagram 6.8), losses are equal to fixed costs and the competitive firm will be in a position of indecision. Future demand plays an important role in taking the decision to operate or shut. If the firm expects the demand to expand in future, it will continue to operate in the short-run.

III. Short-Run Equilibrium of a Competitive Firm (Earning Normal Profits):

There is another case, the case of firm earning normal profit. In short-run, some firms of average efficiency earning only normal profits just sufficient to induce them to operate in the short-run. These normal profits are included in the costs. Figure 6.9 illustrates such a case for a competitive firm, which is just able to break-even (no profit-no loss situation at point ‘E’.). Here, the AC curve is tangent to the AR curve at the minimum point ‘E’ of the former. This means that the price of the product is equal to its average cost. A competitive firm, which neither makes excess profits in the short-run is called a marginal firm.

The competitive firm in equilibrium always chooses the output for which price (AR=MR) = MC is above the level of average variable cost (AVC). The short-run equilibrium of a competitive firm can be equal to or more than it’s AVC, but, cannot be less than AVC. The minimum price which can induce a firm to produce in the short-run is the one, which just equals AVC. It is also called the shutdown point of the competitive firm the competitive firm closes down the operation, if it is not in a position to cover AVC in the short-run. When price = MC, the price would decrease its profits, if, it either increased or decreased its output. For any point to the left of this equilibrium, price is greater than the marginal cost and it pays to increase output. Similarly, for any point to the right of its equilibrium, price is less than the marginal cost and it pays to reduce output.

2. Long Run Equilibrium of a Competitive Firm:

Long run is a period sufficiently long enough to allow the firms to change the size of the plant, the number of machines or even the techniques of production so as to increase the production capacity in response to a change in demand. If there is an increase in the demand for a product, new firms can enter the industry (raising its size). Even the existing firm can increase the scale of production (raising their sizes) to adjust output completely to changes in demand and price. On the contrary the firm can contract output by reducing their capital equipment through sales or otherwise, in the long-run. Moreover the firms can quit the industry in the long-run. In the long run, all the resources can be varied. The total cost therefore is completely variable. In long run, firms can attain equilibrium, by using long-run cost functions, when they produce profit maximizing output.

When firms earn supernormal profits in the short-run (Price > SAC), new firms will be tempted to enter in the industry and compete with the already established firms by producing the same homogeneous product. This price is called as entry attracting price. The assumption of free entry guarantees that these new firms will also process the same complete information as the old firms). The existing or new firms will add their supply to the already existing supply. The increased product supply will reduce the price of product. Further, the increased supply in the industry results in increase in demand for the scarce factors, which will bid up their prices.

On account of the reduced price and increased cost, the profits will tend to be squeezed down towards zero, until no additional firm find it worth moving in. consequently, the supply curve continues to shift to the right, till S₂ in figure 6.10, so that, its intersection with the demand curve DD determines a price for which price is equal to long-run average cost (LAC). Thus, in the long-run, only normal profits accrues to the firms and the supernormal profits vanish.

Figure 6.10: Long Run Equilibrium of a Competitive Firm

Similarly, when existing firms make losses (i.e. price < SAC), some (inefficient) firms will be induced to leave the industry or reduce their supply. This price is called as exit inducing price. Some firms may even that to attract the efficient factors of production to reduce the cost. Consequent fall in the industrial output will lead to a leftward shift of the supply curve, which will raise the price of the product. Cost may also fall due to decline in demand for certain specialized factors of production. Firms will continue to leave the industry until the intersection of the demand curve with the supply curve determines a price for which losses (or profits) are reduced zero. The remaining firms enjoy only normal profit.

Hence, it can be seen that the free entry and exit characteristics of perfect competition removes extra profit or loss by driving down or up the market price through changes in the supply of the industry. Finally profits or losses vanish and the firms earn only normal profits.

Figure 6.10 depicts how firms adjust to their long run equilibrium position, when there are excess profit in the short-run. In this diagram, a typical competitive firm makes excess profit in the short run. Since the prevailing market price is greater than the average cost of the firm, the firm under consideration is operating with the plant whose cost is denoted by short run average cost curve SAC₁ which is tangent to the falling portion of the long run average cost curve. The excess profits will induce this firm to expand its output and move along its LAC curve to new capacity.

The excess profits will also draw new firms to enter the industry. The increased supply of the concerned product will shift the supply curve right ward. This will lead to a fall in price and upward shift of the cost curves. These changes will continue, until the firm is able to adjust its plant so as to produce at the minimum point of the LAC curve and earn only normal profit.

The new supply curve in the diagram is S₂, while the new equilibrium price is OP₂. Long run equilibrium is established at OQ₂ level of output. Where price P₂ is equal to LAC at the minimum point of the LAC. With the equilibrium condition of the marginal analysis, the long-run equilibrium of the competitive firm requires that long-run marginal cost (LMC) should be equal to the price (P=AR=MR) and to the LAC. Further in the long-run, the firm has adjusted its plant so as to produce at the minimum point of its LAC at the equilibrium. As a result, SMC is equal to LMC and SAC is equal to LAC. Ultimately the equilibrium condition is

P=AR=MR=LMC=SMC=LAC=SAC

I. Short Run Supply Curve of a Competitive Firm:

A firm under perfect competition maintains to operate in the short-run, so long as it is able to cover at least its variable costs. When a firm, finds it impossible to cover its short-run variable costs it will choose to shut down its business by terminating its operations is the short-run. By doing so, the competitive firm minimizes it losses in the short-run. The short-run supply curve of the competitive firm are derived with the aid of short-run equilibrium.

Shut-down point or closing down point is basically the point at which the firm just covers its variable costs of production, with U-shaped cost curves, it is at the minimum point of the average variable cost. The equivalent price is called the shutdown price or reservation price, below which the firm will not sell its product. Further, the corresponding output is called a shutdown output. The concept of shut-down point can be used to derive the supply curve of a competitive firm in the short-run, as explained here.

In the short-run, if the market price is very low and is unable to cover even its variable costs (i.e., total revenue (TR) < total variable cost (TVC), the firm should close down its business and should not supply any output. But, if the price (P) is equal to or more than average variable cost (AVC), the firm should produce and supply an output corresponding to which marginal cost (MC) cuts marginal revenue (MR = P) from below (equilibrium condition). If the market price is OP, the firm will supply an output of OQ₁ and operate at equilibrium point e, where MC is equal to MR.

Similarly, when the price rises to OP₁, the firm will supply an equilibrium output of OQ₁. Further, when the price rises to OP₂ the firm raises the supply to OQ₂. Likewise, the firm supplies OQ₃ output at OP₃ Price.

In figure 6.11, OP is the minimum suitable price in this short-run for the firm under consideration, below which the firm stops production, at this price, only variable costs are covered. The corresponding equilibrium point e is the shut-down point of the firm, where price (P) = minimum of average variable cost (AVC) and TR = TVC. As the market price increase gradually, the firm confronts new demand curves at higher the market price increases gradually, the firm confronts new demand curves at higher and higher level. With positive slope of the MC curve, each higher demand curve (AR=MR) cuts the given MC curve at a point, which lies to the right of previous intersection.

This means that the quantity supplied by the firm along its MC curve increase, as price rises in the short-run. The horizontal coordinate of a point on the rising MC curve measures the quantity of product that the firm will supply at that price. Thus, the MC curve of the firm indicates the quantities of output which the firm will supply at various prices.

It is important to note that the competitive firm’s short-run supply curve is matching with only that portion of the short-run MC curve, which lies above the AVC curve. It is derived by joining the points of intersection of the MC curve with the successive individual demand curves, as the market price of the product keeps rising above its average variable cost. The quantity supplied by the firm is equal to zero at all prices less than those corresponding to the shut-down point. The firm’s supply curve is shown by dark segment in figure 6.11.

II. Long Run Supply Curve of a Competitive Firm:

The method of deriving a long-run supply curve of a competitive firm is analogous to the method used for deriving its short-run supply curve, as shown in figure 6.12 by dark segments. The long-run optimal outputs of a firm corresponding to different price levels is determined by the equality of price (AR = MR) and the long-run marginal cost (LMC). At prices less than the long-run average cost (LAC) no output is produced.

In figure 6.12, OP is the minimum acceptable price in the long-run, since no firm can suffer losses in the long-run. At this price, the competitive firm attains equilibrium at point e and supplies OQ₁ output. At price OP₁, equilibrium is attained at point E₁ with OQ₁ as the output produced. Further, at OP₂ price, the output supplied is OQ₂, while the output supplied is OQ₃ at OP₃ price and so on. All equilibrium points, such as e, e₁, e₂, and e₃ lie on the firm’s LMC curve. These points also depicts the supply of the competitive firm in the long-run at various prices. Therefore, the portion of LMC curve of the competitive firm above its LAC curve is its long-run supply curve. For a perfectly competitive firm, the Long-run supply curve is derived by joining together the points of intersection of the LMC curve with the successive demand curves of the firm, as the market price of the product under consideration keeps rising above its average cost.

During the period of short run, an industry is deemed to be in equilibrium, when the market is cleared at a price, i.e., when industry supply is equal to industry demand. The equilibrium price at which this aggregate demand is equal to aggregate supply is termed as short-run normal price. At equilibrium price, each firm produces and sells a quantity for which price (or MR) is equal to MC, in Fig, 6.13 (a), the industry is in equilibrium at price OP, at which the quantity demanded (OQ) is equal to quantity supplied (OQ).

It is a short-run equilibrium of the industry and the firms may enjoy excess profits (Fig. 6.13 (b)) or suffer losses (Fig. 6.13(c)). The competitive industry- attains its equilibrium in the short-run, when all the firms present therein attain their respective equilibrium positions in the short-run. It is immaterial, whether they enjoy excess profits or suffer losses or get only normal profits depending upon the demand conditions of the industry’s products). Thus, it is not essential that each firm in the short-run earn only normal profits. In the short-run, only existing firms can make adjustments in their outputs, while the numbers of firms remain the same. The size of the industry doesn’t change in short-run equilibrium of the industry.

Short-run industry demand curve under perfect competition can be derived from the horizontal summation of the individual demand curves in the short-run. The short-run demand curve for the industry is downward sloping, as it can sell more at low price and vice-versa. Similarly the short-run supply curve of the industry is derived by the horizontal summation of the short-run supply curves ((i.e. MC curves above the respective AVC curves) of all the firms in the industry, since industry supply is simply the sum of what each firm constituting the industry will supply at all possible prices. In the short-run, the supply curve of the competitive industry is upward sloping, as only the (rising) MC curves above minimum AVC curve are added across all firms to arrive at the industry supply curve. Its elasticity is given by the elasticity of the firm’s short-run MC curves.

III. Long Run Equilibrium of Competitive Industry:

In the state of long-run equilibrium, the industry is characterized with certain features. There is equality of long-run supply and demand for the product of the industry. No firms in (long-run- equilibrium have a tendency to quit and no new firms wishes to enter the industry The long-run equilibrium of the industry would be attained, when the number of firms in the industry is in equilibrium (i.e. no movement into or out of the industry), each making only normal profits. Thus, the individual firms have no incentive to change their output. This is illustrated in figure 6.14, where long-run supply curve (SS) and demand curve (DD) intersect at (equilibrium) point ‘E’.

The equilibrium price OP so determined is unique and all the firms in the industry produce at the same minimum point of the long-run average cost (LAC) curve at OP price. Though the LAC of the firms maybe the same in equilibrium, but, the size and efficiency level of the firms excluding normal profits will be different. Thus, in the long-run equilibrium, all the firms may not have identical cost curves. The more efficient firm employs more productive factors of production and/or more able managers.

They must be paid according to their productivity to avoid their bidding off by the new entrants in the industry, under such conditions, with the more productive resources properly estimated at their opportunity cost, all the firms have the same unit cost in their long-run equilibrium. The long-run equilibrium of teach individual competitive firm will be like the one shown in the right panel of figure 6.14

IV. Long Run Supply Curve of Competitive Industry:

The long-run supply curve portrays the level of output which the firms would be offering for sale at different equilibrium prices in the long-run. During this period all the demand induced changes are taken into consideration. The inflow and exit of firms also take place during the long run period. Only one point of the LMC curve corresponding to the given demand conditions is relevant for getting a point on the long-run supply of the industry. It is the point, where the LMC curves of the competitive firms cut their LAC curves from below. The long-run supply curve connects different long-run equilibrium positions corresponding to different levels of demand in the industry and therefore different equilibrium prices.

The long-run equilibrium price may be greater than, equal to, or less than the original price depending on the cost condition in which the industry operates. The industry operates under increasing, constant and decreasing cost conditions. The long-run supply curve of the industry would be upward sloping, horizontal or downward sloping.