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Equilibrium of Firm under Perfect Competition!
A perfectly competitive market is one in which the number of buyers and sellers is very large, all engaged in buying and selling a homogeneous product without any artificial restrictions and possessing perfect knowledge of market at a time. In the words of Joan Robinson, “Perfect competition prevails when the demand for the output of each producer is perfectly elastic. This entails, first that the number of sellers is large so that the output of any one seller is a negligible small proportion of the total output of the commodity, and second, that buyers are alike in respect of their choice of rival sellers, so that the market is perfect.”
The following are the conditions for the existence of perfect competition:
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1. Large Number of Buyers and Sellers:
The first condition is that the number of buyers and sellers must be so large that none of them individually is in a position to influence the price and output of the industry as a whole. The demand of an individual buyer relative to the total demand is so small that he cannot influence the price of the product by his individual action. Similarly, the supply of an individual seller is so small a fraction of the total output that he cannot influence the price of the product by his action alone.
In other words, the individual seller is unable to influence the price of the product by increasing or decreasing its supply. Rather, he adjusts his supply to the price of the product. A seller is “output adjuster.” Thus, no buyer or seller can alter the price by his individual action. He has to accept the price for the product as fixed for the whole industry. He is a “price taker.”
2. Homogeneous Product:
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Each firm produces and sells a homogeneous product so that no buyer has any preference for the product of any individual seller over others. This is only possible if units of the same product produced by different sellers are perfect substitutes. In other words, the cross elasticity of the products of sellers is infinite. No seller has an independent price policy. Commodities like salt, wheat, cotton and coal are homogeneous in nature. He cannot raise the price of his product. If he does so, his customers would leave him and buy the product from other sellers at the ruling lower price.
The above two conditions between themselves make the average revenue curve of the individual seller or firm perfectly elastic. It means that a firm can sell more or less at the ruling market price but cannot influence the price as the product is homogeneous and the number of sellers very large.
3. Absence of Artificial Restrictions:
The third condition is that there is complete openness in buying and selling of goods. Sellers are free to sell their goods to any buyers and the buyers are free to buy from any sellers. In other words, there is no discrimination on the part or buyers of sellers. Moreover, prices are liable to change freely in response to demand-supply conditions. There are no efforts on the part of the producers, the government and other agencies to control the supply, demand or price of the products. The movement of prices is unfettered.
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4. Freedom of Entry of Exit of Firms:
The next condition is that the firms should be free to enter or leave the industry. It implies that whenever the industry is earning excess profits, some new firms attracted by these gains enter the industry. In case of loss being sustained by the industry, some firms leave it. This condition holds true in the long-run when all firms must earn normal profits.
5. Perfect Mobility of Goods and Factors:
Another requirement of perfect competition is the perfect mobility of goods and factors between industries. Goods are free to move to those places where they can fetch the highest price. Factors can also move from a low-paid to a high-paid industry.
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6. Perfect Knowledge of Market Conditions:
This condition implies a close contact between buyers and sellers. Buyers and sellers possess complete knowledge about the prices at which goods are being bought and sold, and of the prices at which others are prepared to buy and sell. They have also perfect knowledge to the place where the transactions are being carried on. Such perfect knowledge of market conditions forces the sellers to sell their product at the prevailing market price and the buyers to buy at that price.
7. Absence of Transport Costs:
The last condition is that there are no transport costs in carrying a product from one place to another. This condition is essential for the existence of perfect competition which requires that a commodity must have the same price everywhere at any time. If transport costs are added to the price of the product, even a homogeneous commodity will have different prices depending upon transport costs from the place of supply.
Equilibrium of the Firm and Industry:
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Conditions of Equilibrium of the Firm:
A firm is in equilibrium when it has no tendency to change its level of output and it needs neither expansion nor contraction. It is earning minimum profits in equilibrium by equating its marginal cost with marginal revenue. The profits maximization condition of the firm can be expressed algebraically as π = R – C where π are profits, R the total revenue, and C the total costs of the firm. When profits are a maximum, the first derivative of π to the quantity of output Q is zero. Therefore –
Where dR/dQ is marginal revenue and dC/dQ is marginal cost. Hence, profits are maximized. But for fulfilling the condition of maximum profits, another essential condition is that the marginal cost must be less than the marginal revenue before it equals the latter –
And after the point of equality, the marginal cost must exceed the marginal revenue. Diagrammatically, it means that the MC curve must cut the MR curve from below and after the point of equilibrium it must be above the latter. This holds true under perfect competition, monopoly and imperfect condition.
Under conditions of perfect competition, the MR curve of a firm coincides with its AR curve. The MR curve is horizontal to the X-axis. Therefore, the firm is in equilibrium when MC = MR = AR (price).
In Fig. 4.1(a), the MC curve cuts the MR curve first at point A. It satisfies the condition of MC = MR, but is not a point of maximum profits because after point A, MC curve is below the MR curve. It does not pay the firm to produce the minimum output when it can earn larger profits producing beyond OM.
It will, however, stop further production when it reaches the OM level of output where the firm satisfies both conditions of equilibrium. If it has any plans to produce more than OM1, it will be incurring losses, for the marginal cost exceeds the marginal revenue beyond the equilibrium point B.
Same conclusions hold good in case of a straight line MC curve as shown Fig. 4.1(b) in. Any infinitesimal increase or decrease in quantity will not add to profits. “It means that we are at an output at which the total profit curve (not shown) is level going neither uphill nor downhill. But while the top of a hill (the maximum profit output) is such a level spot, plateaus and valleys (minimum profit outputs) also have the same characteristics—they are level. That is, they are points of zero marginal profit, where marginal cost equals marginal revenue.”
Conditions of Equilibrium of the Industry:
An industry is in equilibrium firstly, when there is no tendency for the firms either to leave or enter the industry, and secondly, when each firm is also in equilibrium. The first condition implies that the average cost curves coincide with the average revenue curve of all the firms in the industry.
They are earning only, normal profits, which are supposed to be included in the average cost curves of the firms. The second condition implies the equality of MC and MR. These two conditions for industry’s equilibrium hold true under all market conditions, viz., perfect competition, monopoly and imperfect competition.
However, under a perfectly competitive industry these two conditions must be satisfied at the point equilibrium, i.e.,
MC = MR = AC = AR
Since AR = MR, MC = AC = AR, such a situation represents full equilibrium of the industry. Under monopoly or imperfect competition, this double condition will not be fulfilled at the point of equilibrium since AR is above MR throughout its length.
Short-Run Equilibrium of Firm and Industry:
The short-run is a period of time in which the firm can vary its output by changing the variable factors of production in order to earn maximum profits or to incur minimum losses. The number of firms in the industry can enter it.
The short-run equilibrium of the firm can be explained with the help of the marginal analysis as well as with total cost-revenue analysis. We first take the marginal analysis under identical cost conditions and different cost conditions.
1. Identical Cost Conditions:
The analysis of the equilibrium of the firm and the industry under identical cost conditions is based on the assumptions that all factors are homogeneous and are freely available at constant factor prices so that all firms have identical cost curves. A firm is in equilibrium at a point where (i) MC equals MR and AR, and (ii) the MC curve cuts the MR curve from below.
A firm earns normal profits when the MR curve is tangent to the AC curve at its minimum point. Figure 4.2 shows the equilibrium position of the firm under identical cost conditions. At OP price, the firm is earning normal profits. The firm is incurring a loss at OP1 price.
If the price is higher than the minimum average total costs, each firm will be earning supernormal profits. Suppose the price rises to OP2 where the MC curve cuts the new marginal revenue curve MR2 (= AR2) from below at point A which now becomes the equilibrium point. In this situation each firm produces OQ2 output and earns supernormal profits equal to the area of the rectangle P2 ABC.
If the price falls below OP, the firm will make a loss because the average total costs of production will be higher than the price. In the short-run it will pay the firm to produce and sell OQ1 output OP1 price so long as it covers its average variable cost.
S is, thus, the shut-down point at which the firm is incurring the maximum loss equal to the rectangle P1 SKT. If the price falls below OP1, the firm will close down because it will fail to cover even the minimum average variable cost. OP1 is, thus, the shut-down price.
We can conclude from the above discussion that in the short-run, each firm makes either supernormal profits, or normal or losses depending upon the price of the product.
So far as the entire industry is concerned, it will be in full equilibrium by sheer accident when MC = MR = AR = AC, i.e., all the firms earn only normal profits. “An industry is in equilibrium in the short-run when the output of the industry holds steady, there being no force acting to expand output or contract it. If all firms are in equilibrium, then so is the industry.”
2. Different Cost Conditions:
If entrepreneurs differ in efficiency the cost curves of the firms vary from each other. Firms with more efficient entrepreneurs will be able to produce at lower costs than the others. Thus, different firms selling the same product at one price will be producing different quantities at different costs. We may divide the firms under three categories whose cost positions are shown in Fig. 4.3.
Firms of category (1) with the most efficient entrepreneurs are in equilibrium at £, where they produce OQ, output and earn PTSE, supernormal profits.
Category (2) firms are in short-run equilibrium at E2 where MC = MR – AC – AR (price). Thus, they earn normal profits at OQ2 level of output. Firms in category (3) posses still efficient entrepreneurs who are able to able to cover EQ1 average variable cost and a part of the average fixed costs which is more than the price OP, it still incurs a loss of APE3B.
The firms will continue to produce goods as long as the price covers at least average variable cost. If the price is unable to cover even the average variable cost at any level of output, they must shut down.
The conclusion is that under different cost conditions firms can be of all categories, earning supernormal or normal profits or incurring losses. In such a situation, the industry cannot be in full equilibrium.
The short-run equilibrium of the firm can also be shown with the help of total cost and total revenue curves. The firm is able to maximize its profits at that level of output where the difference between total revenue and total cost is the maximum. This is shown in Fig. 4.4 where TR is the total revenue curve and TC total cost curve.
The total revenue curve is an upward sloping straight line curve is an upward sloping straight line curve starting from O. This is because the firm sells small or large quantities of its product at a constant price under perfect competition. If the firm produces nothing, total revenue will be zero. Hence, the TR curve is linear and slopes upward.
The firm will maximize its profits at that level of output where the gap between the TR curve and the TC curve is the maximum. Geometrically, it is that level at which the slope of a tangent drawn to the total revenue curve. In Fig. 4.4 the amount of profit is measured by TP at OQ outputs smaller or larger than OQ between A and B points the firm’s profits shrink. If the firm produces OQ1 output, its losses are the maximum because the TC curve is above the TR curve. At Q1 its profits are zero.
Since the marginal revenue equals the slope of the total revenue curve and the marginal cost equals the slope of the tangent to the total cost curve, it follows that the slopes of the total cost-revenue curves are equal at P and T, the marginal cost equals the marginal revenue. It should be clear that the point of maximum profits lies in the region of rising marginal cost (when TC is below TR) and of maximum loss in the falling marginal-cost region (where TC is above TR).
The output level of maximum profit can also be known with the help of the total profit curve. The total profit curve shows the difference between total revenue and total cost curves at different levels of output. In Fig. 4.4, PC is the total profit curve. Its highest point E shows the maximum profit EQ at OQ level of output. EQ = TP, the difference between TR and TC curves.
Upto OQ1 output level, the PC curve is below the X-axis which shows negative profits or the loss to the firm. At Q1 profits are zero because the PC curve touches the X-axis at this point. Profits increase successively with output between Q1 and Q and are the maximum at OQ level of output. They are EQ. If the firm produces beyond this output level, its profits will continue to decline and will be zero at OQ2.
The explanation of the equilibrium of the firm by using total cost-revenue curves does not throw more light than is provided by the marginal cost-revenue analysis. It is useful only in the case of certain marginal decisions where the total cost curve is also linear over a certain range of output.
But it makes the equilibrium of the firm a cumbersome and difficult analysis particularly when one has to compare the change in cost and revenue resulting from a change in the volume of output. Further, maximum profits cannot be known at once. For this, a number of tangents are required to be drawn which is real difficulty.
Long-Run Equilibrium of the Firm and Industry:
In the long run, it is possible to make more adjustments than in the short-run. The firm can adjust its plant capacity and scale of operations to the changed circumstances. Therefore, all costs are variable. Firms must earn only normal profits. In case the price is above the long-run average cost, new firms will enter the industry and if it is below the long-run average cost some of the firms will leave the industry so that no firm earns more than normal profits.
As in the short run, we study the long-run competitive equilibrium of the firm under identical and different cost conditions.
Identical Cost Conditions:
It is assumed that all entrepreneurs are of equal efficiency. All factors are homogeneous and are available at constant and uniform prices, so that the cost curves of the firms are identical. Each firm will be in equilibrium at level of output where LMC equals MR and cuts the latter from below and at the same time. AR equals LAC, i.e., LMC equals MR and cuts the latter from below and at the same time AR equals LAC, i.e., LMC = MR = LAC.
In Fig. 4.5, the firm is in equilibrium at point L where the LAC curve is at its minimum. At Op price, it produces OQ units of the commodity and earns normal profit. If price happens to be OP1 it would find it profitable to expand its scale beyond the minimum point of the LAC curve until the LMC curve equals the marginal revenue curve at OQ1 output, new firms will enter the industry. Supply will increase, shifting the industry supply curve S1 towards S and price will be forced down to OP where OQ output will again be produced at the equilibrium point L.
If price OP2, the firm will reduce its output to OQ2. It would be incurring CD losses per unit. Some firms, unable to sustain these losses, will leave the industry. Supply will be reduced and the industry supply curve S2 will shift to the left as S curve a result price will raise to OP where equilibrium will be reestablished at the minimum point L of LAC. In the long-run, all firms will earn normal profits and will be of the optimum size and shall be called optimum firms.
Thus, under perfect competition in the long-run all firms will be in equilibrium. They will be no earning or any profits and will have no tendency to either enter or leave the industry. The industry will also be in full equilibrium by satisfying the double condition of LMC = MR = AR = LAC. In the words of Stonier and Hague, “In perfect competition, with all factors homogeneous, each firm and the industry as a whole will in full equilibrium be where marginal revenue = marginal cost = average cost = average revenue (price).”
In case the entrepreneurs are of different efficiency, the cost curves of the firms will also differ. A firm with a superior entrepreneur than the others will be able to produce the same output at lower costs. Such a firm will be earning supernormal profits even in the long-run as compared to the other firms which may be earning only normal profits. The firm which earns supernormal profits is the intra-marginal firm as distinct from the marginal firm which just earns normal profits. These two cases are shown in Fig. 4.6.
Firm (A) having a more efficient entrepreneur earns PABE supernormal profits at OQ1 output whereas firm (B) earns only normal profits at OQ2 output level.
If entrepreneurs with greater efficiency than firm (A) enter the industry the supernormal profits of the firm (A) will disappear, for supply will increase thus bringing down the price where AR is tangent to the minimum point of the LAC curve. In such a situation firm (A) will become the marginal firm where as the firm (B) will leave the industry.
Thus, in the long-run where cost curves are not identical some firms may be earning supernormal profits. The industry will be in full equilibrium only by accident. A firm which is earning supernormal profits even in the long-run is known as intra-marginal firm. A firm which is earning normal profits in the long-run is called ‘marginal firm’.
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