Short Run and Long Run Equilibrium under Perfect Competition (with diagram)

Short Run and Long Run Equilibrium under Perfect Competition (with diagram)!

Under perfect competition, price determination takes place at the level of industry while firm behaves as a price taker. It produces a quantity depending upon its cost structure. The industry under perfect competition is defined as all the firms taken together. Price determination will take place at this level only.

Equilibrium under Perfect Competition:

As such, equilibrium under perfect competition has to be discussed at two levels: at the level of a firm and at the level of an industry.

Further, equilibrium has to be discussed both in short run and long run.

There are two methods of finding equilibrium of a firm – TR-TC method and MR-MC method. Price determination in industry takes place through price mechanism, i.e., through interaction of demand and supply forces.

The complete scenario can be depicted as follows:

Conditions of Equilibrium:

In case of TR-TC method, profit (Ɖ) will maximize at a level of output where the following two conditions are satisfied,

(i) The gap between TR and TC should be maximum, and

(ii) TR > TC at the point of equilibrium.

In case of MR-MC method, profit maximization will take place where,

(i) MR = MC, and

(ii) MC is rising at the point of equilibrium.

The first condition is known as first order condition, which is a necessary condition for equilibrium, while the second one is called as second order condition or sufficient condition.

The conditions of equilibrium under MR-MC method can be understood as follows:

i. The first order condition implies that revenue received from the sale of an additional unit of a product should be equal to cost (inclusive of normal profit) incurred on its production.

ii. The second order condition implies that at the equilibrium level of output, the MC curve should have a positive slope or it must be rising at the point of intersection. This is possible when the MC curve cuts the MR curve from below. In this situation, the firm will operate under increasing cost or diminishing return condition.

Short Run Equilibrium of a Firm — TR-TC Method:

Equilibrium of a firm following the TR-TC method in short run is attempted in Figure 10.3.

In the Figure-10.3, the TR curve, is represented by a straight line originating from the point of origin while the TC curve is an inverse-S-shaped.

Based on it, following discussion can be carried out:

i. TC exceeds TR in the figure up to point R which means that the firm is incurring losses up to the output level OQ₂. At point R, the losses are completely wiped out and the firm reaches a breakeven point where TR = TC, a situation of normal profit.

ii. A further increase in output beyond OQ₂, leads firm to earn super normal profits as TR > TC. When output reaches OQ₄ at point R₁, the firm is at another breakeven (TR = TC). Thus, the firm earns super normal profit in the output range OQ₂ and OQ₄ or between points R and R₁.

iii. Beyond OQ₄ or point R₁, the TC again exceeds the TR and the firm enters in a state of loss again.

iv. Given such behaviour, a profit maximizing situation will be in the output range OQ₂ to OQ₄ or between point R and R₁.

Profit will be at its maximum where the slope of TC curve equals to slope of TR curve, as stated above under the conditions of equilib­rium. As we know, two parallel lines have same slope. Thus, the point at which tangent at TC is parallel to TR will be the profit maximizing position.

v. We have not drawn a tangent on TR curve as it will be same as the TR curve itself for being a straight line. If it is drawn, it will overlap the TR curve. Hence, the TR curve is also taken as a tangent on it.

vi. To find out such a profit maximizing output level, we draw tangent at each point on TC between R and R₁. The tangent at point S₁ is found to be parallel to TR curve. At point S₁, vertical distance between TR and TC curves is at maximum. Hence, it is the point of equilibrium, satisfying both the conditions. The firm will produce OQ₃ level of output and earn a maximum profit SS₁.

vii. Tangent on TC curve is parallel to TR curve at output level OQ₁ as well, but TR < TC. Thus, it is a loss maximization position. One can see that as output increases from this level, per unit loss will decline and the breakeven will be reached at point R. Thus, the firm will not return back to output level OQ₁.

viii. Break-even – Incidentally, one can also observe that the figure pro­vides two break-even points, one at the output level OQ₂ and other at OQ₄.

Based on them, we may define break-even as a level of output or sales at which total revenue of a firm equalizes to total cost inclusive of normal profit. It represents a situation of no-loss-no-profit for the firm in a layman’s language.

The two break-evens are distinguishable on the basis of the fact that first one comes after a situation of loss and the second one comes after a situation of super normal profits. Obviously, the firm will not stop at first break-even because it will not maximize the total profit. Similarly, the firm will not cross the second break-even point as beyond this TC will exceed TR.

Loss Minimizing Equilibrium:

If the TC curve remains above the TR curve at all its points, no profit maximizing equilibrium level of output can be found at any level of output. In such situation, firm has to decide whether to continue or stop produc­tion.

This will depend upon the fact that the firm is able to generate revenue equal to or more than the fixed cost or not. If the firm is unable to do so, it should stop production altogether. However, if the firm could do so, it should continue to produce, despite losses, at some loss minimizing level of output in short run.

Short Run Equilibrium of a Firm – MR-MC Method:

The MR-MC method is more often used to find out equilibrium of a firm since it is simpler and accurate. It does not require, as in the case of TR-TC method, drawing tangent and locating the output level where the tangent is exactly parallel to the TR curve. In this method, we have to just locate the point at which MC intersects MR and the slope of MC is positive.

Equilibrium of a firm through the MR-MC method has been attempted in Figure-10.4 in which MR and Short Run Marginal Cost (SMC) curves are drawn.

The MR (= AR = P) curve is a straight line parallel to quantity axis while the MC curve is a U-shaped one which can intersect the MR curve at more than one point.

Based on the figure, following discussion may be carried out:

i. There are two points, R and R₁, at which first order condition, i.e. MR = MC, is satisfied.

ii. At point R, the slope of SMC is less than that of MR since the SMC is downward sloping. This shows that second order condition is not satisfied at point R. Thus, equilibrium at this point or at the output level OQ₁ will be unstable.

iii. To show that the equilibrium is unstable, let us consider that output increases beyond OQ₁. As such, MC will further decline while MR will remain same and, hence, profit will rise. Thus, the firm will not return back to OQ₁ level of output. This shows that the equilibrium at point R will be unstable.

iv. At point R₁, slope of SMC is more than the slope of MR or, SMC is positively sloped. This satisfies the second order condition. Hence, the equilibrium at R₁ will be stable at which the firm will produce OQ₂ level of output.

v. If, for any reason, output increases beyond OQ₂, the SMC becomes more than MR resulting into a loss to the firm. Hence, the firm will stick to point R₁ or OQ₂ output level. If the output level remains below OQ₂, the firm will earn super normal profit and, hence, increase the output up to OQ₂. This shows that equilibrium once reached at point R₁ will be a stable one. Any deviation from it will lead market forces to work in a fashion so as to return to OQ₂ level of output.

The above discussion deals only with equilibrium of a firm but does not show the profit earned or the loss incurred by the firm. For this, we need to take into account the AC curves.

In short run, a firm may earn super normal profit or normal profit or incur losses.

Each of the three situations has been attempted in the following paragraphs:

i. Super Normal Profit:

A firm will earn super normal profit in short run if its SAC is less than the AR at the point of equilibrium. Such a firm has been depicted in Figure 10.5.

It shows firm’s equilibrium at point R where its output is OQ₁. At this point, both the equilibrium conditions are satisfied, i.e. MR = MC and, the MC curve is positively sloped at the point of intersection. The average cost of the firm, as represented by the SAC curve, is OT (= SQ₁) at this output level. Based on it, profit can be estimated as —

Total revenue – Total cost

Given that total revenue is OPRQ₁ and total cost is OTSQ₁,

Profit = PTSR = OPRQ₁ – OTSQ₁

This is the profit which the firm earns over and above the normal profit and, hence, termed as super normal profit. It has been shown by the shaded area in the figure.

ii. Normal Profit:

Figure 10.6 depicts case of a firm which has been earning only a normal profit.

The figure shows equilibrium at point R where the output is OQ₁. At this level of output, AC is RQ₁, as shown by its SAC curve. It is equal to the per unit revenue which is also RQ₁. It means that firm is making only normal profit which is a part of average cost. In this case —

Total revenue = Total cost = OPRQ₁

iii. Firm Incurring Losses:

A firm can incur loss in short run. Such a firm is represented in Figure 10.7.

In the given situation, firm’s equilibrium is at point R where the output level is OQ₁. The average cost of the firm is represented by SAC curve and the average variable cost by SAVC curve. Obviously, the gap between SAC and SAVC will represent the average fixed cost (SAFC).

The figure shows that at output level OQ₁, average cost (SQ₁) is more that its average revenue (RQ₁). Thus, the firm has incurred a per unit loss of SR (= SQ₁ – RQ₁).

Total loss = Total cost – Total revenue

Given that total cost = OTSQ₁ and total revenue = OPRQ₁ in the figure,

Total loss = TSRP = OTSQ₁ – OPRQ₁

In this situation, one may ask what a firm should do to minimize its losses. Should it continue production and bear the losses or should it stop production and wait for higher price level to come for a re-entry in the market? Answer to such questions will depend upon the fact that, is the firm able to recover at least the variable cost from its revenue or not?

i. If the firm is able to recover the variable cost, or a little more, it should continue production and bear the loss which will be equal to or less than its fixed cost. In such a scenario, the firm will minimize losses by way of continuing production.

The firm will continue to do so in short run even if AR = SAVC. It is because of the fact that its loss will be equal to the fixed cost whether it stops production or continue to produce. In such situation, the firm may be advised to continue the production and remain in the market.

ii. However, if the AR < SAVC, firm should stop production and minimize the loss which will be equal to its fixed cost. If the firm continues production, in this situation, per unit loss will be —

AFC + (SAVC – AR) > AFC Since, SAVC > AR

Thus, it will minimize losses (= AFC) by stopping the production altogether.

Based on above, we can discuss two situations in which a firm will minimize losses (i) by continuing production and (ii) by stopping it altogether.

Minimizing Losses by Continuing Production:

Figure 10.7 presents a case where a firm will minimize losses if it continues production. The firm is in a state of equilibrium at point R at which output level is OQ₁. In this situation, his average cost (SQ₁) is more than the average revenue (RQ₁) and, hence, the per unit loss of SR (= SQ₁ – RQ₁) is reported by the firm.

At this level, however, the SAVC is UQ₁ which is less than its AR (= RQ₁). It means that firm is not only able to cover the entire variable cost but also generating a part of fixed cost. Thus, the firm’s per unit loss (SR) will be less than AFC (= SU).

In such situation, firm will be better off if it continues production at OQ₁ output level. Its total loss will be –

= OQ₁ * SR

Or, = PR * SR = PRST < AFC (= VUST)

Thus, the firm should continue production to minimize losses.

Minimizing Losses by Stopping Production:

Unlike the above case, we will now consider a firm which will minimize losses by way of stopping production. In this situation, its losses would be equal to the fixed cost. But, if it continues production, its losses will be more than the fixed cost. Hence, the firm will be better off if it stops production. This is called as shut down situation.

In Figure 10.8, the firm finds its equilibrium at point R which suggests an output level OQ₁. At this level, average cost is SQ₁ which is more than the AR (= RQ₁) generating per unit loss of SR (= SQ₁ – RQ₁) and total loss of TSRP.

One can see that per unit loss (SR) is more than the AFC (= SU) at this level of output. It means that the AR is unable to cover even the variable cost. The firm should, therefore, stops production to minimize losses equal to the AFC.

Short Run Equilibrium of Industry:

Industry in perfect competition is defined as a group of firms supplying homogenous product in market. Price determination takes place at the level of industry and every firm will follow the price so determined. That is why industry in the perfect competition is known as price maker.

The price determination by industry will follow the interaction of demand and supply forces. For this purpose, demand is considered as exogenously given depending upon the buyers’ behaviour. On the other hand, industry supply will be derived from the supplies made by all the firms in the industry. For this purpose, we first derive the supply curve of each firm belonging to the industry.

Supply Curve of a Firm:

A firm’s supply curve is that portion of its SMC curve which lies above the SAVC curve. In Figure-10.9, we have drawn SMC and SAVC curves of a firm. The SAVC curve intersects the SMC curve at point R. Hence the SMC curve above point R, i.e. RS portion of SMC curve, will be the supply curve of the firm.

Now the question arises, why the SMC curve above the SAVC curve will only form its supply curve and why not the entire SMC curve? It is because of the fact that equilibrium is found where SMC = MR (= P). If the price is less than SAVC, firm will stop production and, hence, its supply will be zero. Thus, a firm’s market supply will be represented only by the SMC curve above the SAVC curve.

Short run supply curve of a firm is that part of its MC curve which lies above the SAVC curve.

Derivation of Supply Curve of Industry:

A short run supply curve of an industry will show the output that the industry will supply for every possible price in the short run. It can be constructed by making a horizontal summation of the supply curves of all the firms belonging to the industry. In simple words, supplies made by each firm at a price are summed up to find industry’s supply at that price level. This procedure is repeated for every possible price and a market supply curve is constructed.

Considering that there are three firms in the industry, we will first derive supply curve of each of them with the help of their respective MC and AVC curves. Supply curves belonging to them are shown as MC₁, MC₂ and MC₃ in the Figure-10.10. Subsequently, a horizontal summation of these three supply curves is made and shown as dotted line in the same figure.

At a price below P₁, no firm will produce any output since the price is less than the minimum average variable cost of the lowest-cost firm. Hence, the industry supply will be zero.

Between price P₁ and P₂, only firm-Ill will produce. For the other two firms, the price is still low for taking up any production. Hence, industry supply curve (SS₁S₂S₃) will be same as the firm-III’s marginal cost curve (MC₃) in this price range.

As the price increases, all the three firms will take up production as per their respective MC curves. Thus —

Industry supply = supply of Firm A + supply of Firm B + supply of Firm C

At price P₂, for example, industry supply will be,

15 units = 2 units + 5 units + 8 units

(Firm-I) (Firm-II) (Firm-in)

Similarly, at price P₃, industry supply will be, 21 units = 4 units + 7 units + 10 units

The industry’s supply so derived is plotted as SS₁S₂S₃ curve in the figure. It has a kink at price P₂, which is the lowest price at which all three firms produce. Such a kink will become increasingly unimportant when number of firms grow. That is why we usually draw an industry supply as a smooth upward-sloping curve presuming numerous firms in the industry.

Supply Curve of Industry and Time Horizon:

The shape of industry supply curve or its slope will depend upon the time period available for adjustment when there is a shift in demand. For this purpose, let us consider three time horizons: a very short period, a short period, and a long period.

Completely Inelastic Supply – A Very Short Period:

If the period under review is very short, no adjustment in market supply will be possible. It is represented by a straight line parallel to Y-axis (Figure- 10.11). In such situation, price will solely depend upon the demand. Higher the demand more will be price.

The figure shows that as demand curve shifts from DD₁ to D₄D₅, price increases from OP₁ to OP₂ for a supply SS₁ and if demand curve shifts downwards from DD₁ to D₂D₃, price will fall from OP₁ to OP₀ again for the same supply.

Price Determination and Supply in Short Period:

Industry supply in a short run is somewhat elastic as compared to the same in a very short period. The firm can adjust output to an extent only depending upon the availability of the fixed factors. A short run industry supply curve under perfect competition shows the amount of output which all the firms will supply collectively at different price levels. Figure 10.12 presents the case of an industry consisting of two firms.

In its panel A, S^*S^* represents the supply curve for a very short period and S₁S₂ for a short period. Demand is depicted as D₁D₂ curve. The equilibrium market price is OP₁ in short period (as also in very short period) where the demand and supply intersects. The price so determined (OP₁) is followed by both the firms to find out their respective equilibrium.

i. They will find equilibrium at a point where their respective SMC curve intersects the price line OP₁ (= MR) and the SMC curve is positively sloped. This has been shown in Panel B for firm A and Panel-C for firm B.

ii. Both firms find equilibrium at price OP₁ and supplies respectively Oq₁ and Oq₂ quantity. The industry supply will be OQ^* = Oq₁ + Oq₂.

iii. Their respective SAC curve further indicates a super normal profit for firm A and a loss for firm B. Still, the firm B is able to meet its variable cost and a part of fixed cost and, hence, will continue to operate for minimizing losses. The super normal profit for firm A is P₁e₁RS while loss for firm B is P₁e₂TV.

This shows that in short run firms will find their respective equilibrium following the price determined by industry and can earn super normal profit or incur loss or even a normal profit.

An upward shift in demand curve from D₁D₂ to D₃D₄ will push the short period price up to OP₂. Industry will enhance its supply to OQ^**. Firms will find new equilibrium positions at a higher price. Firm A will supply Oq₃ (> Oq₁) and firm B Oq₄ (> Oq₂). Firm A’s super normal profit will enlarge while firm B will wipe out its entire loss at the higher price.

Long Run Equilibrium of Industry and Firm:

In the long run, all the firms will earn only a normal profit following an adjustment process which can be described as follows:

i. If the firms are earning super normal profit in short run, they will produce more by expanding plant size and new firms will enter in long run. As a result, industry supply will increase pushing down the price. This will wipe out the super normal profits and ultimately all the firms will earn only normal profit at long run equilibrium.

ii. If the firms are incurring losses in short run, some of them will stop production and quit industry permanently in long run. This will reduce industry supply and push the price up. As such, firms will be able to generate normal profit in long run.

iii. Further, each firm will adjust its plant size so as to produce at a minimum average cost. That is, in the long run, each firm will produce equilibrium output at the minimum point of its AC curve.

iv. Once long run equilibrium is reached, there will be no incentive for firms to exit or new firms to enter. Each firm will make only normal profit.

v. The long run adjustment process will affect the demand of inputs and, hence their prices. If input demand increases, supply remaining the same, their respective price will rise leading a firm’s MC curve to shift to its left. It implies that firm will produce same output at a higher marginal cost.

Long Run Supply Curve and Firm’s Equilibrium:

A long run industry supply curve under perfect competition shows the amount of output which all the firms will supply collectively at different price levels subject to the condition that each firm makes a normal profit. It will be an outcome of the adjustment process in the short run which will be influenced by the laws of production.

i. If the industry is operating under increasing cost conditions (or under diminishing returns to scale), the long run industry supply curve will be positively sloped.

ii. The supply curve will be downward sloping, or negatively sloped, if the industry is under decreasing cost conditions (or under increasing returns to scale).

iii. It will be parallel to quantity axis (X-axis) if operating under constant cost conditions (or under constant returns to scale).

Increasing Cost Condition:

The increasing cost conditions imply that more output can be supplied at a higher price only as the industry is exposed to diseconomies of scale. It will push the input demand and input price. This can be represented by a positive sloped long run industry supply curve, a derivation of which has been attempted in Figure 10.13.

i. The figure shows that initial short run equilibrium is at point e₁ where short run supply curve (S₁S₂) intersects demand curve (D₁D₂). At this point, equilibrium price is OP₁ and industry supply is OQ₁. This is also initial long run equilibrium and, hence, will be represented by a point on the long run supply curve.

ii. An upward shift in demand curve (D₃D₄) will push the short run price up to OP₃ at which the industry supply will be OQ₂. At this higher price, each firm will supply more which will push the supply curve rightward to S₃S₄. The shift in supply curve is by a smaller margin because of rising input prices.

iii. New long run equilibrium (e₂) will be at higher price OP₂ (> OP₁) due to increasing cost conditions. Industry will supply OQ₃.

iv. The long run supply curve (S*S*) will be formed by joining e₁ and e₂. It is an upward looking, or positively sloped, curve.

Constant Cost Condition:

The constant cost conditions mean that the industry is a scale neutral. A change in output will not affect the input prices and hence there will be no impact on average and marginal cost curves. As such, a higher supply is possible at a same price in long run. In such a situation, long run supply curve will be parallel to quantity axis. Derivation of such a supply curve under constant cost conditions is attempted in Figure 10.14.

i. Initial equilibrium, interaction of demand (D₁D₂) and supply (S₁S₂) curves, is at point e₁ where the industry supply is OQ₁ at OP₁ price. It is the equilibrium applicable to both the short run and long run, to start with.

ii. An increase in demand is shown as an upward shift in demand curve (D₃D₄) which pushes the short run price to OP₂ at which industry supply is OQ₂.

iii. It will encourage each firm to take advantage of higher market price and supply more for maximizing profit. As such, the supply curve will shift rightward to S₃S₄ and a new equilibrium is reached at e₂.

iv. At this point of equilibrium, price is re-established at OP₁ level at which the industry supply has increased to OQ₃. We get a long run supply curve (e₁e₂) by joining e₁ and e₂, which is a straight line parallel to quantity axis.

Diminishing Cost Conditions:

The diminishing cost conditions will be witnessed when, for instance, if the industry or firm enjoys a strong scale economies or a new more efficient technology is introduced or supply of inputs increase for whatsoever the reasons. But all these are not a common or regular occurrence. Hence, the diminishing cost conditions are accorded a lower priority in analysis.

When diminishing cost conditions prevail, cost of production will fall along with an increase in production. As such, a higher supply will be accompa­nied by a lower price. This can be represented by a downward sloping industry supply curve, as derived in Figure 10.15.

i. In the figure, initial short run equilibrium is at point e₁ where the short run supply curve (S₁S₂) intersects the demand curve (D₁D₂). At this point, equilibrium price is OP₁ and industry supply is OQ₁. This is also long run equilibrium, to begin with. Hence, e₁ will be a point on the long run supply curve.

ii. An upward shift in demand curve (D₃D₄) will push the short run price to OP₂ at which the industry will supply OQ₂. It will give rise to a super normal profit and, hence, facilitate new firms to enter and existing firms to expand plant size. This will push the supply curve rightward to S₃S₄.

iii. It may be noted that the rightward shift in the supply curve is by a significantly large margin. It is because of the fact that industry is operating under diminishing cost condition which implies a fall in cost as output increases more and more.

iv. New long run equilibrium is reached at e₃ where equilibrium price is OP₃ and industry supply is OQ₃. One can see that the while the OP₂ (the short run price) was more than OP₁, the post adjustment long run equilibrium price (OP₃) is less than the initial one (OP₁). It is due to the diminishing cost conditions.

v. We get a long run supply curve by joining e₁ and e₂, which is downward looking or negatively sloped.

vi. It can be stated, therefore, that the long run industry supply curve under diminishing cost condition will have a negative slope.