Lecture 9: the Competitive Industry

Lecture 9: The Competitive Industry

Profit Maximization and the Competitive Firm A competitive firm is a “price taker”, who

 Can sell all it produces at the going market price;

 Has no control over the market price

Example: A Kansas wheat farmer

The competitive firm's objective is to set output so as to maximize profits, given by

 = pq -C(q),

The firm must expand output until price is equal to marginal cost. If it is producing where MC < P, it can make more profit by expanding output. If it is producing where MC > P, it can make more profit by contracting output.1

Three Cases of Profit Maximization

Profit Maximization Profit Maximization Profit Maximization where MC = P where ATC>p>AVC where AVC>P

Economic Profits are < 0 but the firm is covering a portion of Economic Profits are < 0 and Economic Profits are > 0. their fixed costs, i.e. should you are not covering your fixed continue operating in the short costs, Shut down -- Now! run.

Suppose that a firm has well-behaved costs, traditional average cost and marginal cost functions.

Data on Cost, Marginal Cost, Average Cost, and Average

1 As we all remember from our elementary calculus, profit maximization requires that

‘ = p -C’(q) = 0, Variable Cost

Q Total Cost Marginal Average Average Cost Cost Variable Cost 0 100 1 115 15 115.0 15.0 2 126 11 63.0 13.0 3 136 10 45.3 12.0 4 148 12 37.0 12.0 5 165 17 33.0 13.0 6 186 21 31.0 14.3 7 217 31 31.0 16.7 8 256 39 32.0 19.5 9 306 50 34.0 22.9 10 360 54 36.0 26.0 11 418 58 38.0 28.9 12 480 62 40.0 31.7  If it cannot get at least $12 for its profit, the firm is better off simply bearing its fixed costs and producing nothing at all.

 If it can get $12-$31, it is best off producing in the short run but attempting to leave the industry.

 It should be willing to stay in the industry only if it can get $31 or more.

Profit Maximizing Production for Different Prices

Price Output Decision

$0- $11.99 Produce Nothing $12 4 units $12.01-$17 5 units $17.01-$21.00 6 units $21-$30.99 7 units If price is $12 to $30.99, the firm will produce only in the S-R $31- $38.99 8 units $39-$49.99 9 units $50-$53.99 10 units $54-$57.99 11 units $58-$61.99 12 units $62 13 units Some Further Analysis

The U-Shaped Average Cost Curve The facts dictate an upward sloping cost curve.  An initial section the ATC curve is downward sloping due to economies of scale, but we don’t see any industry with firms working at infinitesimal size.  If the ATC curve didn't eventually slope upward, a profit maximizing competitive firm producing at the level where MC = P could not make any profits.

How a Change in Price Affects Output

How a Rise in Market Price Changes Optimal Output

Since a competitive firm always produces where P=MC, the MC curve (or at least the

portion above the AC curve) is now the firm's supply curve. When the price is p 2, the

firm will produce q2; when the price is p1, the firm will produce q1, etc. The long –run supply curve is equal to the firm’s marginal cost curve. As long as the price is above pmin, the minimum of the average cost curve.

The short –run supply curve is equal to the firm’s marginal cost curve. As long as the price is above the minimum of the average variable cost curve.

It is a fallacy to say “a firm sets price equal to marginal cost.” The correct way of saying this is to say “a firm sets its level of production where marginal cost equals price.” Be aware of the difference.

A quick summary We have now derived a firm’s cost function C(q) and consequently its supply curves. We know how a competitive firm will act.

The basic rule:

 If I can produce a widget at less (marginal) cost than the market price of widgets, produce it; if I can’t, don’t.

The two qualifications:

 If, by obeying the rule, I cannot cover my fixed costs, shut down.  If, by obeying the rule, I can’t cover my variable and fixed costs, continue producing over the short run at a loss. Industry Conditions There are two cases to be considered.  When all firms have the same cost functions and hence the same marginal cost function, average cost function, and the like.

 When firms do not have the same cost functions.

Firms with Identical Technologies and Cost Functions Suppose initially that there are N firms in the industry. Then the supply curve, holding the number of firms constant, must be N times the supply curve. But if the price is above p min, each firm is making money. And that is a signal for entry.

The Common Average Cost and Supply Curve

All firms are assumed to have a common average cost curve and hence common

marginal cost (supply) curves. As long as the price is above p min, each firm will make

money and others will be induced to enter the business. If the price drops below p min,

firms will leave the business. At a price of pmin, each firm will produce qmin widgets.

At a price of p1, each firm produces q1 widgets; at a price of p2, each firm produces q2 widgets.

(from the table above) Suppose that all firms have the same cost function, then firms will be making a profit if the price is at or above $31. If the price is below that, firms will eventually leave the business. If the price is above that, they will enter. Thus the price will be forced to $31, with each firm making seven units.

Consider firm entry into an industry. As the number of firms rises, the supply curve gets shifted to the right and the price gets driven down to pmin. Over time, firms will exit and the price will get driven up.

Suppose that at a price of pmin the market demand for widgets is Qo. Then N = Qo / qmin firms will produce widgets.

A Numerical Illustration (again from the above table) Suppose the demand curve for the product is Q = 260 - 5p

The price will be $31, The quantity demanded will be 105, and, since each firm is willing to supply seven units of output at that price, there will be 105/7 = 15 firms in the industry.

Changes in Factor Prices Factor prices played a role in determining average cost , C(r,w,q). Two cases of interest:

 Exogenous changes in factor prices and

 Endogenous changes in factor prices

Exogenous changes occur when something outside the industry changes the price of a factor. For example, consider the problems of running a sawmill when gas prices change.

However, the price of timber, an important input to the lumber business, is endogenous to the lumber business.

Example:

Suppose the industry is producing Q1 board feet of lumber, and that, given the price of timber, the average cost curve is Q1, with a minimum of the average cost curve at p1. Each firm wants to produce q1 board feet of lumber. Equilibrium is at the price p1 with N1 firms producing q1 = Q1/N1 board feet of lumber. Now suppose that the industry wants to increase output from Q1 board feet of lumber to Q2 > Q1 board feet of lumber. The sawmill business is intensively competitive and have the same cost functions. If we could ignore the impact of expansion on timber prices, we would expect the industry to expand by "scaling up". That is, more sawmills would start up, with each firm producing q1 board feet of lumber, with the lumber selling at a price of p1. The number of firms would grow from N1 to N2 = Q2/q1.

Alas, we cannot do this. While we could perhaps neglect the impact of the industry expansion on gasoline prices, we cannot neglect its impact on timber prices. The higher price of timber will mean that the average cost curve for the sawmill will shift up to, say, the curve labeled Q2. The new minimum will go up to p2.

If output is to rise from Q1 to Q2 and then to Q3, the new equilibrium price in the lumber industry must be rise from p1 to p2 to p3 and the new long run supply curve is thus upward sloping.

The Supply Curve with Pecuniary Diseconomies

Average Cost Curves at The Long Run Industry Different Scales of Supply and Demand Curves Operations Average cost will rise and fall with the This now gives us the industry supply total level of operation. Each firm faces curve. Each firm is still operating at the a common average cost curve, but as the minimum of its average cost curve, but scale of industry rises from Q1 to Q2 to the price rises with industry output.

Q3, the price of timber will rise and hence average cost will rise. The minimum will go from p1 to p2 to p3 and that means an upward sloping supply curve. The impact on the total profits the lumber owners

Supply and Demand for the Scarce Factor of Production The Demand and Supply of A Shift in the Demand Curve for Timber Lumber

Timber is a scarce resource and there is an When the demand curve for lumber shifts from upward sloping supply curve D to D' there are two effects. Increasing prices of timber give an upward sloping supply curve

Ss and the price of lumber rises. As new sawmills enter, the short run supply curve shifts

to Ss', and the price of lumber falls partway back to the original level. In short, pecuniary external diseconomies can

lead to an upward sloping supply curve SL as illustrated here.

A Numerical Illustration Suppose that it takes one board foot of timber to make one board foot of lumber. Suppose that, right now, the industry is producing 3,000 board feet of lumber. Timber is selling for $1 a board foot. Given the costs of operation, each sawmill will produce 3 board feet of lumber, at an average cost of $4 a board foot. 1,000 sawmills will be required to produce the lumber.

Now suppose the industry wants to increase the supply to 4,000 board feet or 5,000 board feet. As production goes up, the cost of timber will rise to (say) $2 a board foot for 4,000 board feet of timber or $3 a foot for 5,000 board feet of timber. Cost of Operating A Sawmill at $1 a board foot for lumber

Board Feet Cost of Cost of Average Marginal Produced Timber Finishing Total Cost Cost 0 0 3 1 1 4 5 2 2 2 6 4 3 3 3 9 4 4 4 4 14 4.5 6 5 5 20 5 7

As the price rises, each firms average cost curve rises. Since each sawmill has the same production function and cost function as every other sawmill, they all operate at the minimum of their average cost curve. But, if industry production is to rise from 3,000 board feet to 4,000 board feet to 5,000 board feet, the price must rise from $4 to $5 to $6, to reflect the higher price of timber.

Cost of Operating A Sawmill at $2 a board foot for lumber

Board Feet Cost of Cost of Average Marginal Produced Timber Finishing Total Cost Cost 0 0 3 1 2 4 6 3 2 4 6 5 4 3 6 9 5 5 4 8 14 5.5 7 5 10 20 6 8 Cost of Operating A Sawmill at $3 a board foot for lumber

Board Feet Cost of Cost of Average Marginal Produced Timber Finishing Total Cost Cost 0 0 3 1 3 4 7 4 2 6 6 6 5 3 9 9 6 6 4 12 14 6.5 8 5 15 20 7 9

The General Case of Firms with Different Technologies Suppose there are three firms in an industry, A, B, and C, whose average and marginal cost curves differ. Firm A will supply no widgets when the price is below p1. At that price, it will supply q1a, and the supply curve for higher prices is given by its marginal cost curve. To get the supply curve for the industry, we sum the supply curves of each of the individual firms. The Supply Curve with Dissimilar Firms

Firm A Firm B

Average and marginal cost curves for firm Average and marginal cost curves for firm "A" "B"

Firm C Industry

Average and marginal cost curves for firm "C" The industry supply curve is the sum of the three individual supply curves.

A Numerical Example Firm A Firm B Firm C Q C AC MC C AC MC C AC MC 0 16.0 6.0 10.0 1 17.0 17.0 1.0 10.0 10.0 4.0 11.0 11.0 1.0 2 19.0 9.5 2.0 15.0 7.5 5.0 13.0 6.5 2.0 3 22.0 7.3 3.0 21.0 7.0 6.0 16.0 5.3 3.0 4 26.0 6.5 4.0 28.0 7.0 7.0 20.0 5.0 4.0 5 31.0 6.2 5.0 36.0 7.2 8.0 25.0 5.0 5.0 6 37.0 6.2 6.0 45.0 7.5 9.0 31.0 5.2 6.0 7 44.0 6.3 7.0 55.0 7.9 10.0 38.0 5.4 7.0 8 52.0 6.5 8.0 66.0 8.3 11.0 46.0 7.8 8.0

A "*" by the number indicates that the firm is still below average cost, and this constitutes part of the short run supply curve. Output at Different Price Levels

Price Firm A Firm B Firm C Industry (LR) = A + B + C 1 1* 1* 2 2* 2* 3 3* 3* 4 4* 1* 4* 5 5* 2* 5 5 6 6* 3* 6 6 7 7 4 7 18 8 8 5 8 21

Why Firms earn “profits” We have now discussed two cases: one case where all firms have an identical cost function, and another case where there are differences.

To most people it is obvious that firms have different cost functions. But, in a competitive business with complete information, how can one have anything but a temporary cost advantage over the other?

Economic Profits versus Accounting Profits How some competitive firms can earn economic profits? - firm-specific factors of production; “niche” or “forte” resource quality, customer good will,

Conclusions Different firm-specific factors of production can lead to different cost functions, different average costs functions, and different marginal cost functions.

Clearly these differences may be transitory. But transitions take time and money, and for many practical purposes it is useful to assume different production functions.

Government Taxes Consider the case of government taxes on a product made by a competitive industry. Assume an increasing cost industry, one with an upward sloping supply curve. The supply curve is shifted up by $t, but, given the demand curve, part of the price increase will be mitigated by reduced quantity demanded.

For relatively small tax rates, we can define the percent of the tax passed along to the consumer in terms of the price elasticities of demand and supply: Some numerical values

Incidence of Tax

s d Percent  Whatever 100 1 -2.0 33 1 -1.0 50 1 -0.5 67 0 Whatever 0

The Effect of a Tax

We have already seen this case. The key point is that the tax falls partly on the firms in the industry and partly on the consumer.