Perfect Competition Equilibrium: Short Run and Long Run

1 year ago

Atiqur Rahman

25 minutes

Long Run vs Short Run

The distinction between the long run and short run is not with respect to certain time periods but with respect to the flexibility in the usage of the resources at the disposal of the producers. In the short run, some factors are fixed, and some are variable. However, in the long run, all the factors are variable.

Therefore, in the context of economics, the long run is the period long enough for the firm to be able to vary all its factors of production, and not just few. All the factors of production, including the plant size, are variable in the long run.

Thus, in a perfectly competitive industry, the firms can change their plant size in the long run according to the demand and price conditions prevailing in the market.

Equilibrium in the Short Run

Total and Marginal Approach

In the short run, some factors are fixed, and some are variable. The presence of fixed factors distinguishes the short run from the long run. In the short run, the output per period can only be changed by changing the use of variable inputs, keeping the fixed factors constant.

The profit maximization condition for a firm is to produce at the output level where the difference between TR and TC is maximum. In other words, MR should be equal to MC and steeper than MC at the point of intersection. The profit maximization principle has been discussed in the last module. Let’s revisit the point with the help of an example in the table.

1	2	3	4	5	6	7	8	9
Price	Output	TR	TC	MR	MC	AC	Unit Profit	Total Profit
20	1	20	68	20	–	68	-48	-48
20	2	40	74	20	6	37	-17	-34
20	3	60	78	20	4	26	-6	-18
20	4	80	83	20	5	20.75	-0.75	-3
20	5	100	89	20	6	17.8	2.2	11
20	6	120	97	20	8	16.16	3.84	23
20	7	140	110	20	13	15.71	4.28	30
20	8	160	130	20	20	16.25	3.75	30
20	9	180	162	20	32	18	2	18
20	10	200	210	20	48	21	-1	-10

The first two columns show the demand curve faced by the competitive firm. The price is constant at 20 for every output level. Thus, the demand curve is a horizontal line facing the quantity axis.

TR (Price × Quantity) is calculated in the third column. The total cost is given in the fourth column. MR, MC and AC (Average cost) are given in columns 5, 6 and 7, respectively. The unit profit is calculated in column 8 as the excess of price over AC. The unit profit multiplied by the output level provides the total profit in column 9.

According to the total approach, profit is maximized where the difference between TR and TC is maximum. It happens at the 7th and 8th output levels. However, according to the marginal approach, profit is maximized at the 8^th output level where MR = MC and MC is increasing after it (MC is steeper than MR).

As the price remains constant in perfect competition, the average revenue (AR) is also constant. Thus, in perfect competition:

MR = Price = AR

Since MR equals the price for the perfectly competitive producer, the short-run equilibrium occurs at the output level for which the MC is equal to the price. The short-run profit-maximizing condition for a competitive firm is, thus,

MC = Price

This condition implies that no firm has the incentive to deviate from charging a price equal to marginal cost which is the same for every firm in the industry. If a firm charges a price more than its marginal cost, then it will lose all its consumers to its competitors as the products are homogeneous. The firm will regain the market share only when it charges the price the same as the marginal cost.

On the other hand, lowering a price below the marginal cost will result in the firm producing a lesser quantity. This will lower the firm’s profits. It might cross your mind that if all the firms simultaneously start charging a higher price, then all can have profits. But this scenario will not be sustainable because the total demand will be less than the supply and the firm will be left with unsold stock.

Thus, every firm will have the incentive to lower the price and grab the entire market share. Therefore, the equilibrium situation, where the firms would want to stay put, will occur only at the level where MC = P.

Profits in the Short Run

The profit of a firm is defined as the excess of TR over TC

π(Q) = TR(Q) – TC(Q)

π(Q) = P.Q – AC.Q

π(Q) = Q(P – AC)

Thus, the excess of price over AC multiplied by the quantity gives the profit. There are following three cases:

Case I: (P – AC) > 0

In this case, the price is more than the average cost and thus, the profits are positive.

In the above figure, the equilibrium is at E1 where MR is equal to MC and the price charged is P1. However, the average cost at Q^* is P2 which is less than the price charged. The dashed area is the economic profit of the firm. It is the excess of price over AC multiplied by the quantity.

Case II: (P – AC) = 0

If the price charged is the same as the average cost of the firm, then the profits are zero for the firm. It is a no-profit, no-loss situation.

In the above figure, the price is the same as AC at the point of equilibrium. Thus, there are no positive economic profits for the firm.

Case III: (P – AC) < 0

If the price charged is less than the average cost, then the firm receives negative economic profits or losses.

In the above figure, the equilibrium is at E2 where MC is equal to MR and the price charged is P2. However, at the equilibrium level of output Q* AC is more than the price and therefore, the firm is making losses, as shown by the shaded area.

Supply Decision of a Competitive Firm

The supply curve is defined as the locus of the minimum price at which the firm is willing to sell different quantity levels. To understand the shape of the supply curve for a competitive firm, the following two things should be considered.

The least price at which the firm is willing to supply various quantities of the good.
The minimum price which the firm is willing to accept. The firm will shut down business below this point.

The response of the output level to the change in the price level graphs the supply curve of the firm. In the figure below, the price line is shifted, and the change in equilibrium is noted.

The initial equilibrium of a perfectly competitive firm in the above figure is at E1 where MR1 is equal to the MC of the firm. The price is set at P1. As the price increases in the industry from P1 to P2, the MR curve shifts for an individual firm from MR1 to MR2 and the equilibrium shifts to E2.

Similarly, as the price increases to P3, the equilibrium for a firm shifts to E3. With the increase in the price level, the supply by an individual firm is increasing. Increased production becomes profitable at higher price levels.

By looking closely at the figure, it can be seen that the firm is supplying according to the MC curve. As the price is rising, the firm is supplying along the MC curve. So, the MC curve is, in fact, the supply curve of a competitive firm in the short run, as it identifies the most profitable output level at each possible price.

It is important to identify the minimum price at which the firm will be willing to supply at all. The MC curve above that level will be the supply curve for a perfectly competitive firm. To find the minimum price, consider the following example for a perfectly competitive firm,

Let AR = Rs.150, AC = Rs.180, AVC = Rs.100 and AFC = Rs.80

Here AR<AC, and thus, the firm is making losses. But the firm will keep on operating as it is covering a part of fixed costs. AR covers the whole of AVC and a part of AFC (Rs.50 out of Rs.80)

If the firm shuts down business in this situation, then none of the fixed costs will be covered, and the loss will be Rs.80 as opposed to a loss of Rs.30 in operating. If a firm covers the variable costs in the short run, then it should produce. Therefore, as long as the AR > AVC (or TR > TVC) is at the equilibrium output, a smaller loss will be incurred if the production takes place.

Thus, if the price is below AVC, the firm will shut down. The minimum of the AVC curve is the shutdown point, i.e., the firm will close down if the price is below the minimum of AVC as no fixed cost will be covered then. As a consequence, the portion of the MC curve which is above the minimum of the AVC curve is the supply curve of the competitive firm. It is shown in the figure below.

In the above figure, E1 is the initial equilibrium for a competitive firm with price and quantity as P1 and Q1, respectively. As the price falls to P2, the MR curve shifts to MR2 and the new equilibrium is E2. At E1, the firm was making economic profits, while at E2 the firm is earning enough to pay all its factors.

If the price falls further to P3, then the quantity supplied falls again along the MC curve to Q3. At E3, the firm is making losses as the AR < AC, but is covering the AVC as the AR curve is still above the AVC curve. Therefore, the firm will remain in operation.

However, when the price falls to P4, the AR touches the minimum of the AVC curve, which means that the price is sufficient only to cover the variable costs, and none of the fixed costs is covered. Thus, P4 is the shutdown point for the firm as below P4, and the firm will be making more losses than to shut down. When P = AVC, no part of AFC is covered, and losses are minimized.

Therefore, the bold red part of the MC curve is the supply curve of a perfectly competitive firm and below the price level P4, i.e. the minimum of AVC curve, the firm is unwilling to supply any quantity at all.

Short Run Demand Curve of a Competitive Industry

Industry can be defined as all the firms taken together. A competitive industry faces a normal downward-sloping demand curve, unlike a firm which faces a horizontal demand curve. It implies that all the firms have taken together or the industry faces the fear of losing sales if they increase the price. The short-run demand curve for a competitive industry is shown in Figure 1(a) above.

Short-Run Supply Curve of a Competitive Industry

The short-run supply curve of a competitive industry is the horizontal summation of the supply curves of the firms. Let’s take the case of three firms for the sake of illustration. In the figure below, the supply curve of the industry is obtained by horizontally summing the MC curves of the individual firms.

The above figure shows the supply curves of the individual firms (AMC1, BMC2, and CMC3). The third firm has a lower average cost curve; therefore, its supply curve starts at a lower price level. At a price below P1, the third firm’s supply curve is the industry supply curve, as no other firm is willing to supply below that price level.

Above P1, the quantity supplied by all the firms taken together is the industry’s supply curve. For example, at price P2, the first firm supplies 0Q1 quantity, and the second and third firms supply 0Q2 and 0Q3 quantity, respectively. Thus the industry supplies 0Q^* = 0Q1 + 0Q2 + 0Q3.

The industry supply curve is positively sloped, implying that a higher price induces the industry to supply more because of a higher profit incentive. Each firm’s MC curve slopes upwards because it reflects the law of diminishing marginal returns to variable inputs.

Therefore, the short-run supply curve of the industry too is determined by the law of diminishing marginal returns. The kink in the industry supply curve in Figure 5.3.10 disappears when the number of firms is increased. Thus, the industry supply curve of a competitive market becomes a smooth upward-sloping curve.

The above derivation of the industry supply curve has been done on the assumption that it is a constant-cost industry, i.e. as the output expands, the cost of variable inputs remains constant.

If, however, the cost of factors change, then the MC curve will shift for each firm, and the industry supply curve derived above will not be valid. If the input prices are allowed to vary, then the industry supply curve will be steeper for an increasing-cost industry and flatter for a decreasing-cost industry. This possibility is studied in the long-run analysis.

Short-Run Equilibrium in a Competitive Industry

Putting together the demand and the supply curves of the industry, we get the equilibrium as shown in figure below.

The supply curve of the competitive industry intersects with the demand curve D1 at E1, and the price in the initial equilibrium is P1. All the firms face the price as given, and the MR curve for an individual curve is shown by MR1 in Figure 7(b). The total quantity supplied by the industry is Q1, and the individual firm’s supply is q1. If the industry expands output to Q2, consequent to an increase in demand, then the equilibrium price jumps to P2.

This shifts the MR curve up and thus, the equilibrium quantity of firm 1 also increases to 0q2. In the above figure, the input prices are assumed to be unchanged due to expansion of output (MC curve is same after shift in MR).

Equilibrium in the Long Run

Long Run Equilibrium: Entry and Exit

The long-run equilibrium for a perfectly competitive industry demands three conditions to be met.

1). The individual perfectly competitive firms should be operating at a point where the long-run marginal cost (LMC) is equated to the price level. It implies that they are producing the output level, which maximizes their profits.

LMC = Price for all the firms

2). There should not be any incentives for the firms to enter or exit the industry, i.e. they are in a stay-put situation. This condition can be obtained if the firms operating in the industry are making zero economic profits. This will not attract new firms, and the existing firms will have no incentive to leave the industry.

Price = Long Run Average Cost for all the firms

3). The industry demand is equal to the industry supply.

Total Demand = Total Supply for the industry

The long-run equilibrium for the perfectly competitive firm and the industry as a whole can be understood from the figure below.

In the figure above, DD and SS are the long run demand and supply curves for the perfectly competitive industry respectively. The industry equilibrium is at E with P^* and Q^* as the equilibrium price and output level. Every firm in the industry is a price taker and therefore, faces P^* as the price. The equilibrium for the firm is obtained at ‘e’ where MR = LMC = Price.

Moreover, at the firm’s equilibrium, average cost is just covered and thus, the firm makes zero economic profits. Positive economic profits would have encouraged the new firms to enter and the losses would have led to existing firms exiting the industry. At this point, there is no incentive to enter or exit the industry. All the three conditions for the long run equilibrium in the perfectly competitive industry and firm are met in the above figure.

The second condition of long run equilibrium distinguishes it from the short run analysis. In the short run, the firms can have positive or negative economic profits. However, in the long run firms have zero economic profits.

Optimal Plant Size in the Long Run

All the factors of production are variable in the long run and thus, the firm adjusts its plant size in the long run for maximizing profits. The optimal plant size adjustment in the long run is shown below in figure.

In the long run, the firm faces the horizontal demand curve just like short run. It is shown as MR in the above figure. The short run equilibrium is at A where short run marginal cost (SMC) intersects MR curve. The firm is making economic losses in the short run as the price is below the average cost.

In the long run, the firm can exit the industry or can vary the plant size. If the firm operates at the plant size represented by SAC2 and SMC2, then the firm is making economic profits. And similarly, at SAC4 and SMC4 the firm is making economic profits as the price charged is more than the average cost of production.

In this case, the new firms will enter the industry, shifting down the market supply curve and thus lowering the market price faced by an individual firm. Thus, the long run equilibrium will be at E where LAC is at its minimum. The adjustment to the optimal plant size in the long run and the equilibrium are explained using figure below.

In figure (a), the perfectly competitive industry is initially at equilibrium at E, where DD intersects initial supply curve S1S1. The short run equilibrium for an individual firm is at QSR and the firm is making positive economic profits at this output level equal to P1ABC.

Moreover, in the long run with MR1 as the marginal revenue curve, the firm would produce at QLR with P1A’B’C’ level of economic profits. But this situation is not the equilibrium situation as it does not meet the first two conditions of the long run equilibrium. The firms have an incentive to enter the industry.

In figure (a), the total supply curve shifts down to S2S2 and the equilibrium changes to E2 for the industry as a whole. At this price level the first two conditions for long run equilibrium are met by the individual firm and each firm produces Q^* level of output. LMC is equal to MR and the economic profits are zero.

Long Run Supply Curve of a Competitive Industry

The long run industry supply curve gives a relationship between the quantity supplied and the prices in the long run as the industry expands. The short run industry supply curve was obtained simply by a summation of a given number of firm’s supply curves.

However, in the long run as firms enter and exit the market with change in market prices, the individual firms’ supplies cannot be added to obtain the industry supply. The prices of inputs do change in the long run with the increase/decrease in the industry output.

In case of economies of scale, the cost of production will fall with the increase in the volume of output. On the other hand, in case of diseconomies of scale, the input prices will increase with the scale of output.

Three cases are studied to derive the industry supply curve: Constant cost industry, Decreasing cost industry and Increasing cost industry. However it is assumed that all the firms in the industry continue to use the same available technology with no inventions or innovations. Also it is assumed that the market conditions for factors of production do not change with the expansion or contraction of the output of the industry.

1. Constant Cost Industry

A constant cost industry implies that as the new firms enter the market, encouraged by an increase in demand, the long run average cost curve of individual firms is not affected. Thus the input prices are assumed to be constant in the constant cost industry.

The long run supply curve of a constant cost competitive industry is a horizontal line at a price equal to the long run minimum average cost. In a constant cost industry additional inputs required to produce higher levels of output can be purchased without any increase in the prices of the inputs.

Consider the above figure 2.4 (a). The industry is initially at equilibrium at E where demand curve DD intersects the supply curve SS. The price P is the equilibrium price and the firm is in the equilibrium at e producing q^* level of output.

As the demand increases to D’D’, the industry equilibrium changes to E’’ and price increases to P’’. The firm equilibrium is at e’’, where price is more than the average cost and thus, the firm is making positive economic profits.

The profitable situation creates incentives for new firms to enter and therefore, the supply curve in figure 2.4(a) shifts to S’S’. Since the industry is a constant cost industry input prices are unaffected by the increase in output. The LAC curve of existing firms does not shift and the new entrants can operate with an identical LAC curve. Entry of firms and expansion in output would continue until the original price OP is obtained.

Long run equilibrium is therefore established when the number of firms expands to an extent that the new short run supply curve S’S’ intersects the demand curve D’D’ at point E’. Prices are back to OP and firms are again at long run equilibrium earning zero profits with no incentives to expand output or encouragement to new entrants.

The long run industry supply curve SL is obtained by joining points like E and E’. It is a horizontal line. The long run industry supply price will be constant if industry output can be expanded or contracted by expanding and contracting the number of firms without affecting the minimum average cost of production.

2. Decreasing Cost Industry

In the decreasing cost industry, the input prices fall with the expansion of output. These are industries where the long run average cost curve of individual firms shifts downwards with expansion in industry output maybe because of external economies of scale such as growth in supplementary facilities and services such as transport etc.

The economies of scale enjoyed by these firms are external because they arise due to industry output expanding and not due to the output of a single firm expanding.

The long run supply curve of a decreasing cost competitive industry is a downward sloping line. As the price increases the industry is willing to supply a lesser quantity of output. In a decreasing cost industry, additional inputs required to produce higher levels of output can be purchased with a fall in the prices of the inputs.

Consider the above figure 2.5 (a). The industry is initially at equilibrium at E where demand curve DD intersects the supply curve SS. The price P is the equilibrium price and the firm is in the equilibrium at e producing q^* level of output.

The profitable situation creates incentives for new firms to enter and therefore, the supply curve in figure 2.5(a) shifts to S’S’. Since the industry is a decreasing cost industry input prices fall with expansion of output and the LAC curve shifts down to LAC’ and the LMC shifts to LMC’.

Entry of firms and expansion in output would continue until the price reaches the minimum of LAC’. Long run equilibrium is therefore established when the number of firms expands to an extent that the new short run supply curve S’S’ intersects thedemand curve D’D’ at point E’. Price is set at P’ and firms are again at long run equilibrium earning zero profits with no incentives to expand output or encouragement to new entrants.

The long run industry supply curve SL is obtained by joining points like E and E’. It is a downward sloping line. The industry produces more output at lower prices brought about by economies of scale enjoyed by the firms.

3. Increasing Cost Industry

In increasing cost industry, an increase in demand triggers higher production costs and an upward shift of the long run average cost curve as new firms entering the industry bid up the price of the key inputs.

The long run supply curve of an increasing cost industry is upward sloping. In an increasing cost industry additional inputs required to produce higher levels of output can be purchased only with an increase in the prices of the inputs.

In an increasing cost industry, additional inputs required to produce higher levels of output can be purchased with a rise in the prices of the inputs. Consider the above figure 2.6 (a). The industry is initially at equilibrium at E where demand curve DD intersects the supply curve SS. The price P is the equilibrium price and the firm is in the equilibrium at e producing q^* level of output.

Since the industry is an increasing cost industry, input prices rise with expansion of output and the LAC curve shifts up to LAC’ and the LMC shifts to LMC’. The firm is making economic loss at the new equilibrium level e’’. Exit of firms would continue until the price reaches the minimum of LAC’.

Long run equilibrium is therefore established when the number of firms expands to an extent that the new short run supply curve S’S’ intersects the demand curve D’D’ at point E’. Price is set at P’ and firms are again at long run equilibrium earning zero profits with no incentives to expand output or encouragement to new entrants.

The long run industry supply curve SL is obtained by joining points like E and E’. It is an upward sloping line. Production of more output requires an increase in inputs and some of these inputs are available in larger quantities only at higher prices.

This is obviously in contrast to the case of constant cost industries discussed above where any amounts of inputs can be hired without affecting their prices.

Perfect Competition Equilibrium: Short Run and Long Run

Long Run vs Short Run