Introduction to Economic Analysis Chapter 17 Imperfect Competition

Chapter 17 Imperfect Competition there are only a handful of in most industries from which consumers assumptions of perfect competition are unreasonable . But with two or more firms , monopoly isn a good model either . Imperfect competition refers to the case of firms that individually have some ability or market power but are constrained by rivals . Our analysis starts with one model of imperfect competition formulated over 170 years ago . Oligopoly LEARNING OBJECTIVES . How do industries with only a few firms behave ?

How is their performance measured ?

The oligopoly model is the most popular model of imperfect competition . It is a model in which the number of firms matters , and it represents one way of thinking about what happens when the world is neither perfectly competitive nor a monopoly . In the model , there are , who simultaneously set quantities . We denote a typical firm as i and number the firms from i to i Firm i chooses a quantity to sell , and this quantity costs Ci ( qi ) The sum of the quantities produced is denoted by . The price that emerges from the competition among the firms is ( and this is the same price for each . It is probably best to think of the quantity as really representing a capacity , and competition in prices by the determining a market price given the market capacity . The that a i obtains is ( qi ) URL , org books 416

Each firm chooses qi to maximize profit . The conditions give ( i ( qi ) This equation holds with equality provided qi . A simple thing that can be done with the conditions is to rewrite them to obtain the average value of the margin ( i ( qi ) Here is i market share . Multiplying this equation by the market share and summing over all i , 11 yields ( i ( qi ) where the Index ( The has the property that if the are identical , so that Si for all i , then the is also For this reason , antitrust economists will sometimes use as a proxy for the number of firms , and describe an industry with , meaning an of . We can draw several inferences from these equations . First , larger , those with larger market shares , have a larger deviation from competitive behavior ( price equal to marginal cost ) Small are approximately competitive ( price nearly equals marginal cost ) while large firms reduce output to keep the price higher , and the amount of the reduction , in cost terms , is proportional to market share . Second , the the deviation from perfect competition on average that is , it gives the average proportion by which price equal to marginal cost is violated . Third , the equation the inverse elasticity result proved for monopoly , which showed that the margin was the inverse of the elasticity of demand . The generalization states that the weighted average of the cost margins is the over the elasticity of demand . Because the margin the deviation from competition , the provides a measure of how large a deviation from competition is present in an industry . A large means the industry looks like URL , org books ( 909 417

In contrast , a small looks like perfect competition , holding constant the elasticity of demand . The case of a symmetric ( identical cost functions ) industry is especially enlightening . In this case , the equation for the condition can be rewritten ( or ( Thus , in the symmetric model , competition leads to pricing as if demand was more elastic , and indeed is a substitute for elasticity as a determinant of price . KEY TAKEAWAYS Imperfect competition refers to the case of firms that individually have some ability or market power but are constrained by rivals . The oligopoly model is the most popular model of imperfect competition . In the model , firms choose quantities simultaneously and independently , and industry output determines price through demand . A equilibrium is a Nash equilibrium to the model . In a equilibrium , the margin of each firm is that firm market share divided by the elasticity of demand . Hence the weighted average margin is the sum of market squared market shares divided by the elasticity of demand . The Index ( is the weighted average of the margins . In the model , larger firms deviate more from competitive behavior than do small firms . The measures the industry deviation from perfect competition . The model the inverse elasticity result proved for monopoly . The is one with monopoly . URL books 418

A large value for means the industry looks like In contrast , a small looks like perfect competition , holding constant the elasticity of demand . With identical firms , a industry behaves like a monopoly facing a demand that is times more elastic . Industry Performance LEARNING OBJECTIVE . What happens to firms when there are fixed costs of entry ?

How does the industry perform ?

Let us return to the more general model , which doesn require identical cost functions . We already have one answer to this question the average margin is the divided by the elasticity of demand . Thus , if we have an estimate of the demand elasticity , we know how much the price deviates from the perfect competition benchmark . The general industry actually has two sources of inefficiency . First , price is above marginal cost , so there is the deadweight loss associated with unexploited gains from trade . Second , there is the inefficiency associated with different marginal costs . This is because a rearrangement of production , keeping total output the same , from the firm with high marginal cost to the with low marginal cost , would reduce the cost of production . That is , not only is too little output produced , but what output is produced is inefficiently produced , unless the firms are identical . To assess the productive , we let ' be the lowest marginal cost . The average deviation from the lowest marginal cost , then , is ( i ) i ) URL books 419

( i ) Thus , while a large means a large deviation from price equal to marginal cost and hence a large level of monopoly power ( holding constant the elasticity of demand ) a large also tends to indicate greater productive is , less output produced by producers . Intuitively , a monopoly produces efficiently , even if it has a greater reduction in total output than other industry structures . There are a number of worth mentioning in the assessment of industry performance . First , the analysis has held constant the elasticity of demand , which could easily fail to be correct in an application . Second , costs have not been considered . An industry with large economies of scale , relative to demand , must have very few firms to perform efficiently , and small numbers should not necessarily indicate the market performs poorly even if margins are high . Third , it could be that entry determines the number of firms and that the have no market power , just market power . Thus , entry and costs could lead the to have approximately zero , in spite of price above marginal cost . Using Exercise , suppose there is a fixed cost that must be paid before a can enter a market . The number of firms 11 should be such that are able to cover their fixed costs , but add one more cost and they can . This gives us a condition determining the number of ( Thus , each firm net profits are ( Note that the monopoly profits are ( Thus , with free entry , net are less than ( and industry net profits are less than ( URL , org books ( 909 420

Table Industry Profits as a Fraction of Monopoly shows the performance of the , industry when costs are taken into account and when they aren . With two firms , gross industry are of the monopoly profits , not substantially different from monopoly . But when costs to ensure that only two enter are considered , the industry profits are at most 39 of the monopoly . This large because fixed costs could be relatively low , so that the third firm is just deterred from entering . That still leaves the two firms with significant , even though the third can profitably enter . As the number of increases , gross industry fall slowly toward zero . The net industry profits , on the other hand , fall dramatically and rapidly to zero . With 10 firms , the gross are still about a third of the monopoly level , but the net profits are only at most of the monopoly level . Table as a Fraction of Mono ol Number of Firms Gross Industry Profits ( Net Industry Profits ( 10 15 20 The model gives a useful model of imperfect competition , a model that readily permits assessing the deviation from perfect competition . The URL , org books 421

model embodies two kinds of inefficiency ( a ) the exercise of monopoly power and ( technical in production . In settings involving entry and fixed costs , care must be taken in applying the model . KEY TAKEAWAYS The industry has two sources of inefficiency too little output is produced , and what output is produced is inefficiently produced ( unless the firms are identical ) The analysis has held constant the elasticity of demand , which could easily fail to be correct , and fixed costs have not been considered . Consideration of fixed costs reduces the apparent inefficiency of industry . EXERCISES the inverse demand curve is ( and that there are firms , each with constant marginal cost , selling in the market . a . Show that the equilibrium quantity and price are ( Show that each firm gross profits are ( Suppose the inverse demand curve is ( and that there are firms , each with marginal cost selling in the market . a . Find the equilibrium price and quantity . Determine the gross profits for each firm . What formula from the model is used in antitrust analysis ?

How is it used ?

Consider identical firms in equilibrium . a . Show that the elasticity of market demand satisfies a . URL books 422 . Is this consistent in the case when ( monopoly ) The market for Satellite Radio consists of only two firms . Suppose the market demand is given by 250 , where is the price and is the total quantity , so 02 . Each firm has total costs given by ( Qi a . What is the market price predicted by the duopoly model ?

If the industry produces a total quantity , what allocation of quantity ( with ) between the two companies minimizes total cost ?

Your answer should express total cost as a function . If the firms merge with the cost found in , what is the market price ?

Differentiation LEARNING OBJECTIVE . What are the types of differentiated products and how do firms selling differentiated products behave ?

Breakfast cereals range from indigestible , unprocessed whole grains to boxes that are filled almost entirely with sugar , with only the odd molecule or two of grain thrown in . Such cereals are hardly good substitutes for each other . Yet similar cereals are viewed by consumers as good substitutes , and the standard model of this kind of situation is the model . was the to use a line segment to represent both the product that is sold and the preferences of the consumers who are buying the products . In the model , customers preferences are located by points on the same line segment . The same line is used to represent URL books 423

products . For example , movie customers are differentiated by age , and we can represent moviegoers by their ages . Movies , too , are designed to be enjoyed by particular ages . Thus , a preteen movie is unlikely to appeal very much to a or to a , while a Disney movie appeals to a , but less to a . That is , movies have a target age , and customers have ages , and these are on the same line . Figure Bre ( Cere ( High Fiber Adult Cereals Kid Cereals Sugar Content Breakfast cereal is a classic application of the line , and this application is illustrated in Figure Model for Breakfast Cereals . Breakfast cereals are primarily distinguished by their sugar content , which ranges on the line from low on the left to high on the right . Similarly , the preferences of consumers also fall on the same line . Each consumer has a most desired point , and he or she prefers cereals closer to that point than cereals at more distant points . There are two main types of differentiation , each of which can be modeled using the line . These types are quality and variety . Quality refers to a situation where consumers agree on which product is better the disagreement among consumers concerns whether higher quality is worth the cost . In automobiles , faster acceleration , better braking , higher gas mileage , more cargo space , more legroom , and greater durability are all good things . In computers , faster processing , brighter screens , higher resolution screens , lower heat , greater durability , more megabytes of RAM , and more gigabytes of hard drive space are all good things . In contrast , varieties are the elements about which there is not widespread agreement . Colors and shapes are usually varietal rather than quality . URL , org books 424

Some people like appliances , others choose white , with blue a distant third . Food are varieties , and while the quality of ingredients is a quality differentiator , the type of food is usually a varietal differentiator . Differences in music would primarily be varietal . Quality is often called differentiation , while variety is horizontal differentiation . The standard model fits two ice cream vendors on a beach . The vendors sell an identical product , and they can choose to locate wherever they wish . For the time being , suppose the price they charge for ice cream is at . Potential customers are also spread randomly along the beach . We let the beach span an interval from to . People desiring ice cream will walk to the closest vendor because the price is the same . Thus , if one vendor locates at and the other at , and , those located between and ( go to the left vendor , while the rest go to the right vendor . This is illustrated in Figure Sharing the Market . Figure Sharing the I ( Note that the vendor at sells more by moving toward , and vice versa . Such logic forces vendors to both locate in the middle . The one on the left sells to everyone left of , while the one on the right sells to the rest . Neither can capture more of the market , so equilibrium locations have been found . To complete the description of an equilibrium , URL , org books 425

we need to let the two share a point and still have one on the right side and one on the left side of that point . This solution is commonly used as an explanation of why political parties often seem very similar to each have met in the middle in the process of chasing the most voters . Political parties can directly buy votes , so the price is the only thing parties can do is locate their platform close to voters preferred platform , on a scale of left to But the same logic that a party can grab the middle , without losing the ends , by moving closer to the other party will tend to force the parties to share the same platform . The model with constant prices is unrealistic for the study of the behavior of firms . Moreover , the model on the beach is complicated to solve and has the undesirable property that it matters whether the number of firms is odd or even . As a result , we will consider a model on a circle and let the choose their prices . KEY TAKEAWAYS In the model , there is a line , and the preferences of each consumer are represented by a point on this line . The same line is used to represent products . There are two main types of differentiation quality and variety . Quality refers to a situation where consumers agree on which product is better . Varieties are the about which there is not widespread agreement . Quality is often called vertical differentiation , while variety is horizontal differentiation . The standard model involves two vendors selling an identical product and choosing to locate on a line . Both charge the same price . People along the line buy from the closest vendor . URL books 425

The Nash equilibrium for the standard model involves both sellers locating in the middle . This is inefficient because it does minimize transport costs . The standard model is commonly used as a model to represent the positions of political candidates . Suppose there are four ice cream vendors on the beach , and customers are distributed uniformly . Show that it is a Nash equilibrium for two to locate at and two to locate at . The Circle Model LEARNING OBJECTIVE . Is there a simple , convenient model of differentiated product competition , and how does it perform ?

In the circle model , a model is set on a circle . There are evenly spaced around the circle whose circumference is . Thus , the distance between any firm and each of its closest neighbors is Consumers care about two things how distant the they buy from is and how much they pay for the good . Consumers minimize the sum of the price paid and times the distance between the consumer location ( also on the circle ) and the firm . Each consumer preference is uniformly distributed around the circle . The locations of firms are illustrated in Figure A Segment of the Circle Model . Figure A Circle URL books 427

length length We conjecture a Nash equilibrium in which all firms charge the price To identify , we look for what must be to make any one firm choose to charge , given that the others all charge So suppose the firm in the middle of Figure A Segment of the Circle Model charges an alternate price , but every other firm charges A consumer who is units away from the firm pays the price from buying at the firm , or ( from buying from the rival . The consumer feels indifferent toward the nearby firms if these are equal , that is , where is the location of the consumer who is indifferent . Thus , consumers who are closer than to the firm charging buy from that , and consumers who are further away than buy from the alternative firm . Demand for the firm charging is twice ( because the sells to both sides ) so profits are price minus marginal cost times two that is , The condition for profit maximization ( We could solve the condition for But remember that the question is , when does represent a Nash equilibrium price ?

The price is an equilibrium price if the firm wants to choose Thus , we can conclude that is a Nash equilibrium price when . This value of ensures that a facing rivals who charge also chooses to charge Thus , in the model , price exceeds marginal cost by an URL , org books 428

amount equal to the value of the average distance between the firms because the average distance is nand the value to a consumer for traveling that distance is The profit level of each firm is , so industry are . How many will enter the market ?

Suppose the fixed cost is We are going to take a slightly unusual approach and assume that the number of can adjust in a continuous fashion , in which case the number of firms is determined by the zero condition , or . is the socially efficient number of firms ?

The socially number of firms minimizes the total costs , which are the sum of the transportation costs and the fixed costs . With 11 , the average distance a consumer travels ( Thus , the socially efficient number of firms minimizes the transport costs plus the entry costs . This occurs at . The socially efficient number of firms is half the number of firms that enter with free entry . Too many firms enter in the circle model . This extra entry arises because efficient entry is determined by the cost of entry and the average distance of consumers , while prices are determined by the marginal distance of consumers , or the distance of the marginal consumer . That is , competing firms prices are determined by the most distant customer , and that leads to prices that are too high relative to the efficient level free entry then drives net to zero only when it is excess entry . The model is sometimes used to justify an assertion that will advertise too much , or engage in too much research and development ( as a means of differentiating themselves and creating profits . URL , org books 429

KEY TAKEAWAYS A symmetric Nash equilibrium to the circle model involves a price that is marginal cost plus the transport cost divided by the number of firms The profit level of each firm is , so industry profits are . The socially efficient number of firms is half the number that would enter with free entry . The circle model is sometimes used to justify an assertion that firms will advertise too much , or engage in too much , relative to the socially efficient amount . URL books