Chapter 17
Price and Output: Perfect Competition
Chapter Summary
1.An industry is perfectly competitive if it is composed of a large number of firms selling a homogeneous product and firms can easily enter or leave the industry.
2.A firm maximizes total profits in the short run at the point where total revenue exceeds total cost by the largest amount.
3.Marginal revenue is the change in total revenue per unit change in the quantity sold. The perfectly competitive firm can sell any quantity at the prevailing price, so its marginal revenue equals price. Such a firm maximizes profits at the point where marginal revenue (or price) intersects the rising portion of the marginal cost curve.
4.A firm breaks even if price equals average cost. It minimizes total losses if price is greater than average variable cost but less than average cost: and it minimizes losses by shutting down if price is less than average variable cost.
5.The perfectly competitive firm's short-run supply curve is given by the rising portion of its marginal cost curve over and above its average variable cost curve or shutdown point.
6.All firms in a perfectly competitive industry in long-run equilibrium produce where price equals the lowest long run average cost.
7.The demand for factors of production increases as industry output expands. Factor prices may remain constant, rise, or fall. This determines if the firm is in a constant-cost, increasing-cost, or decreasing-cost industry.
Important Terms
Break-even point. The output level at which the finn's total revenue equals its total costs, and its total profits are zero.
Constant-cost industry. An industry whose long-run supply curve is horizontal because factor prices remain constant as industry output expands.
Decreasing-cost industry. An industry whose long-run supply curve is negatively sloped because factor prices fall as industry output expands.
External diseconomy. An upward shift in a firm's cost curves as industry output expands. External economy. The downward shift in a firm's cost curves as industry output expands.
Increasing-cost industry. An industry whose long-run supply curve is positively sloped because factor prices rise as industry output expands.
Marginal revenue (MR). The change in total revenue for a unit change in the quantity sold. With perfect competition, price (P) is constant, and MR = P.
276
CHAP. 17]PRICE AND OUTPUT: PERFECT COMPETITION277
Perfect competition. An industry composed of a large number of firms selling a homogeneous product and in which firms can easily enter or leave the industry.
Perfectly competitive firm's short-run supply curve. The rising portion of the firm's marginal cost curve above its average variable cost curve or shutdown point.
Shutdown point. The output level at which price equals average variable cost.
Outline of Chapter 17: Price and Output: Perfect Competition
17.1 Perfect Competition Defined
17.2 Profit Maximization in the Short Run: Total Approach
17.3 Profit Maximization in the Short Run: Marginal Approach
17.4 Short-Run Profit or Loss
17.5 Firm's Short-Run Supply Curve
17.6 Long-Run Equilibrium of the Competitive Firm
17.7 Constant-, Increasing-, and Decreasing-Cost Industries
17.1 PERFECT COMPETITION DEFINED
An industry is said to be perfectly competitive if (1) it is composed,of a large number of independent sellers of a commodity, each too small to affect the commodity price; (2) all firms in the industry sell homogeneous (identical) products; and (3) there is perfect mobility of resources, and firms can enter or leave the industry in the long run without much difficulty. As a result, the perfectly competitive firm is a "price taker" and can sell any amount of the commodity at the prevailing market price.
EXAMPLE 17.1. Perhaps the closest we have ever come to perfect competition is in the market for such agricultural commodities as wheat, corn, and cotton. There, we may have a large number of producers each too small to affect commodity price. The output of each farmer (say wheat of a given grade) is identical, and it is rather easy to enter or leave this industry. The perfectly competitive model is used to analyze markets, such as these. that approximate perfect competition. It is also used to evaluate the efficiency of the other forms of market organization (see Chapters 18 and 19).
17.2 PROFIT MAXIMIZATION IN THE SHORT RUN: TOTAL APPROACH
A firm maximizes total profits in the short run when the (positive) difference between total revenue (TR) and total costs (TC) is greatest. TR equals price times quantity. TC were examined in Section 16.3.
v-....sf+ EXAMPLE 17.2. In Table 17-1, quantity (column 1) times price (column 2) equals TR (column 3). TR minus TC any (column 4) equals total profits (column 5). Total profits are maximized (at $16.90) when the firm sells 6.5 units of Mathes(' output (if we assume that fractional units, such as parts of a bushel of wheat, can be produced and sold).
,‘„:;+EXAMPLE 17.3. The profit-maximizing level of output for this firm can be seen graphically in Fig. 17-1 (obtained by plotting the values of columns 3 and 4 of Table 17-1). TR is a positively sloped straight line through the origin
Mathcad because P is constant at $8. At outputs smaller than 3 and larger than 8. TC exceeds TR and the firm incurs losses. At the outputs of 3 and 8 (points A and B), TR = TC and the firm breaks even. Between A and B, TR exceeds TC and the firm makes a profit. Total profits are maximized at 6.5 units of output when TR exceeds TC by the greatest amount ($16.90).
278PRICE AND OUTPUT: PERFECT COMPETITION[CHAP. 17
Table 17-1
(I) / (2) / (3) / (4) / (5)Q / P ($) / TR ($) / TC ($) / Total Profits ($)
0 / 8 / 0 / 8 / — 8
1 / 8 / 8 / 20 / —12
2 / 8 / 16 / 23 / — 7
3 / 8 / 24 / 24 / 0
4 / 8 / 32 / 25.40 / + 6.60
5 / 8 / 40 / 28 / +12
6 / 8 / 48 / 32 / +16
*6.5 / 8 / 52 / 35.10 / +16.90*
7 / 8 / 56 / 40 / +16
8 / 8 / 64 / 64 / 0
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17.3 PROFIT MAXIMIZATION IN THE SHORT RUN: MARGINAL APPROACH
In general, it is more useful to analyze the short-run behavior of the firm by using the marginal-revenue—marginal-cost approach. Marginal revenue (MR) is the change in TR per unit change in the quantity sold. Since the perfectly competitive firm can sell any quantity of the commodity at the prevailing price, its MR = P, and the demand curve it faces is horizontal at that price. The perfectly competitive firm maximizes its short-run total profits at the output at which MR or P equals MC (and MC is rising).
maEXAMPLE 17.4. In Table 17-2, MR (column 4) is the change in TR and is recorded between the various quantities sold. MC (column 7) is the change in TVC and in TC and is also entered between the various levels of output. AVC (column 8) equals TVC/Q. AC (column 9) equals TC/Q. Profit per unit (column 10) equals P — AC. Total profits
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(column I I) equal profits per unit times the quantities sold (and are the same as in column 5 of Table 17-1, except for rounding). Note that total profits are maximized at $16.90 when the firm produces and sells 6.5 units of output (as in the total approach of Table 17-1). At that level of output, MR or P = MC and MC is rising.
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EXAMPLE 17.5. The profit-maximizing (or best) level of output of this firm can also be viewed in Fig. 17-2. The MC
MI and AC values are from Table 17-2. The demand curve facing the firm is horizontal at P = $8 = MR. As long as MR
'ad exceeds MC, it pays for the firm to expand output. The firm would be adding more to its TR than to its TC and so its total profits would rise. It does not pay for the firm to produce past point C since MC exceeds MR. The firm would add more to its TC than to its TR and so its total profits would fall. Thus, the firm maximizes its total profits at the output level of 6.5 units (given by point C where P or MR equals MC and MC is rising). The profit per unit at this level of output is CF, or $2.60 (see Table 17-2), and total profit is given by the area of rectangle CFGH, which equals $16.90.
CHAP. 171PRICE AND OUTPUT: PERFECT COMPETITION279
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17.4 SHORT•RUN PROFIT OR LOSS
If, at the point where MR = P = rising MC, P exceeds AC, the firm is maximizing its total profits. If P = AC, the firm is breaking even. If P is larger than AVC but smaller than AC, the firm minimizes total losses. If P is smaller than AVC, the firm minimizes its total losses by shutting down. Thus, P = AVC is the shutdown point for the firm.
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280PRICE AND OUTPUT: PERFECT COMPETITION[CHAR 17
/4-EXAMPLE 17.6. In Fig. 17-3. the AVC curve (from column 8 of Table 17-2) and three alternative demand and MR curves that the firm might face are shown with the MC and AC curves of Fig. 17-2. With d3, the firm produces
math"' at C, and Q = 6.5; profit per unit equals $2.60, and total profits = $16.90 (as in Example 17.5). With d,, the firm produces at J and breaks even (since P = AC). With d;, P = AVC (point 7') and the firm incurs a loss per unit equal to its AFC and a total loss equal to its TFC, whether it produces or not. Thus, T is the shutdown point. Below P = $4, the firm minimizes its total losses (equal to its TFC) by shutting down. Between the prices of $4 and $5.33, P exceeds AVC so that the firm is also covering part of its AFC. In this case, the firm minimizes its total losses by staying in business.
17.5 FIRM'S SHORT-RUN SUPPLY CURVE
Since the perfectly competitive firm always produces where MR = P = rising MC (as long as P exceeds AVC), the firm's short-run supply curve is given by the rising portion of its MC curve over and above its AVC, or shutdown point.
EXAMPLE 17.7. In Fig. 17-3, the short-run supply curve of the firm is the rising portion of its MC curve above T (shutdown point). If factor prices remain constant, the short-run supply curve of the competitive industry is obtained by adding the individual firms' supply curves (see Problem 17.11). The (equilibrium) price at which all firms in this competitive industry sell their output is determined by the intersection of this industry supply curve and the market demand curve (see Problem 17.12).
17.6 LONG-RUN EQUILIBRIUM OF THE COMPETITIVE FIRM
If the firms in a perfectly competitive industry are making short-run profits, more firms will enter the industry in the long run. This increases the market supply of the commodity and reduces the market price until all profits are competed away and all firms just break even. The exact opposite occurs if we start with firms with short-run losses. As a result, all firms in a perfectly competitive industry with long-run equilibrium produce where P = lowest LAC. Resources are utilized in the most efficient way to produce the goods and services most wanted by society, and consumers pay the lowest possible price.
maMahCad / EXAMPLE 17.8. Figure 17-4 shows that each firm in a perfectly competitive industry at long-run equilibrium produces at point E. where P = SAC = SMC = lowest LAC. The forces that inevitably lead to point E are explained in Problem 17.13. Some shortcomings of perfect competition are discussed in Problem 17.15.
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Fig. 17-4
17.7 CONSTANT-, INCREASING-, AND DECREASING-COST INDUSTRIES
When industry output expands as more firms enter the industry and more factors of production are demanded in the long run, factor prices might remain constant, rise, or fall. This leads to a constant-, increasing-, or decreasing-cost industry, respectively. The long-run supply curve of a constant-cost industry is horizontal. It rises in an increasing-cost industry and falls in a decreasing-cost industry (see Problems 17.16 and 17.17). Of the three, increasing-cost industries are the most common.
CHAP. 17)PRICE AND OUTPUT: PERFECT COMPETITION281
Solved Problems
PERFECT COMPETITION DEFINED
17.1. Explain each of the three component parts of the definition of perfect competition given in Section 17.1.
(1)There are a large number of independent sellers of the commodity, each too small in relation to the market to be able to affect the price of the commodity by its own actions. This means that a change in the output of a single firm will not perceptibly affect the market price of the commodity.
(2)The products of the firms in the market are homogeneous, identical, or perfectly standardized. As a result, the buyer cannot distinguish between the product of one firm and that of another and so is indifferent as to the particular firm from which he or she buys. This refers not only to the physical characteristics of the commodity but also to the "environment" (such as the location and pleasantness of the seller, etc.) in which the purchase is made.
(3)There is perfect mobility of resources. That is. workers and other inputs can easily move geographically and from one job to another and can respond very quickly to monetary incentives. In the long run, firms (entrepreneurs) can enter or leave the industry without much difficulty. That is, the products are not patented or copyrighted, vast amounts of capital are not necessary to enter the industry, and already-established firms do not have any lasting cost advantages based on experience over new entrants.
17.2. (a) Does perfect competition, as defined above, exist in the real world? (b) Why do we study the perfectly competitive model?
(a)Perfect competition. as defined above, has never existed. Perhaps the closest we may have come to satisfying the three assumptions is in the market for certain agricultural commodities such as wheat and corn.
(b)The fact that perfect competition has never existed in the real world does not reduce the usefulness of the perfectly competitive model. The pertectly competitive model does give us some very useful (if at times rough) explanations and predictions of many real-world economic phenomena when assumptions are only approximately (rather than exactly) satisfied. In addition, this model helps us evaluate and compare the efficiency with which resources are used under different forms of market organization.
173. A car manufacturer may regard his business as highly competitive because he is keenly aware of his rivalry with the few other car manufacturers in the market. Each car manufacturer undertakes vigorous advertising campaigns seeking to convince potential buyers of the superior quality and better style of his automobiles and reacts very quickly to claims of superiority by his rivals. Is this the meaning of perfect competition from the economist's point of view? Explain.
The above market is diametrically opposed to the economist's view of perfect competition. It describes a market which stresses the rivalry among firms. The economist's view stresses the impersonality of a perfectly competitive market. According to the economist, in a perfectly competitive market there are so many independent sellers of the commodity, each so small in relation to the market, that no seller regards others as competitors or rivals. The products of all firms in the market are homogeneous and so there is no rivalry among firms based on advertising, quality, and style differences.
PROFIT MAXIMIZATION IN THE SHORT RUN: TOTAL APPROACH 17.4. (a) How can the firm increase its output in the short run?
(b)How many units of the commodity can the firm sell in the short run at the prevailing commodity price?
282PRICE AND OUTPUT: PERFECT COMPETITION[CHAP. 17
(c)What is the shape of the total revenue curve of a perfectly competitive firm? Why?
(d)What is the shape of the short-run total cost curve of the firm? Why?
(e)When is the firm in short-run equilibrium?
(a)Within the limitations imposed by its given scale of plant, the firm can vary the amount of the commodity produced in the short run by varying its use of the variable inputs.
(b)The perfectly competitive firm is too small to affect market price and can sell any amount of the commodity at the prevailing market price.
(c)The TR of a perfectly comptetitive firm is shown by a positively sloped straight line through the origin. This is the case whenever commodity price is constant.
(d)The short-run total cost of the firm is equal to its fixed costs at zero output. It rises at a decreasing rate (faces down) as output rises, before the law of diminishing returns begins to operate, and it rises at an increasing rate (faces up) thereafter.
(e)The firm is in short-run equilibrium when it maximizes its total profits or minimizes its total losses. It should be noted that not all firms seek to maximize total profits (or minimize total losses) at all times. However, the assumption of profit maximization is essential if we are to have a general theory of the firm. The short-run equilibrium of the firm can be looked at from a total-revenue—total-cost approach or from a marginal-revenue—marginal-cost approach.
17.5. If short-run TVC and TC of a firm at various outputs are the values n Table 17-3 and P = $4, cf+
SalTable 17-3
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Q / 0 / 10 / 20 / 30 / 40 / 50 / 60 / 65 / 70 / 75 / 80 / 85 / 90TVC / 0 / 35 / 65 / 85 / 95 / 105 / 120 / 131 / 145 / 162 / 185 / 225 / 295
TC / 65 / 100 / 130 / 150 / 160 / 170 / 185 / 196 / 210 / 227 / 250 / 290 / 360
(a)determine the output and dollar amount at which the firm maximizes total profits. At what two levels of output does the firm break even?
(b)Plot the TR and TC schedules on one set of axes and indicate the point of profit maximization.
(a)Table 17-4 shows that this firm maximizes its total profits of $73 at 75 units of output and breaks even at 40 and 90 units of output.
(b)See Fig. 17-5.
Table 17-4
(1) Q / (2)P($) / (3)
TR ($) / (4)
TVC ($) / (5)
TC ($) / (6)
Total Profits ($) / (7)
Position
0 / 4 / 0 / 0 / 65 / —65 / Losses
10 / 4 / 40 / 35 / 100 / —60 / Losses
20 / 4 / 80 / 65 / 130 / —50 / Losses
30 / 4 / 120 / 85 / 150 / —30
40 / 4 / 160 / 95 / 160 / 0 / Losses
Break-even point
50 / 4 / 200 / 105 / 170 / +30 / s
Profits
60 / 4 / 240 / 120 / 185 / +55 / Profits
65 / 4 / 260 / 131 / 196 / +64 / Profits
70 / 4 / 280 / 145 / 210 / +70 / Profits
75 / 4 / 300 / 162 / 227 / +73 / Total profits maximized
80 / 4 / 320 / 185 / 250 / +70 / Profits
85 / 4 / 340 / 225 / 290 / +50 / Profits
90 / 360 / 295 / 360 / 0 / Break-even point
CHAP. 171PRICE AND OUTPUT: PERFECT COMPETITION283