Introduction to Economic Analysis Chapter 10 Producer Theory Dynamics

Chapter 10 Producer Theory Dynamics How do shocks affect competitive markets ?

Reactions of Competitive Firms LEARNING OBJECTIVE . How does a competitive firm respond to price changes ?

In this section , we consider a competitive ( or entrepreneur ) that can affect the price of output or the prices of inputs . How does such a competitive respond to price changes ?

When the price of the output is , the firm earns ( where ( is the total cost of producing , given that the firm currently has capital Assuming that the firm produces at all , it maximizes by choosing the satisfying ' IK ) which is the quantity where price equals marginal cost . However , this is a good strategy only if producing a positive quantity is desirable , so that ( IK ) which maybe rewritten as ( IK ) The side of this inequality is the average variable cost of production , and thus the inequality implies that a firm will produce , provided price exceeds the average variable cost . Thus , the firm produces the quantity , where price equals marginal cost , provided price is as large as minimum average variable cost . If price falls below minimum average variable cost , the firm shuts down . The behavior of the competitive firm is illustrated in Figure supply . The thick line represents the choice of the firm as a function of the price , which is on the vertical axis . Thus , if the price is below the minimum average variable cost ( the shuts down . When price is above the minimum average variable cost , the marginal cost gives the quantity supplied URL , org books 217

by the firm . Thus , the choice of the is composed of two distinct segments the marginal cost , where the produces the output such that price equals marginal cost and shutdown , where the firm makes a higher , or loses less money , by producing zero . Figure supply also illustrates the average total cost , which doesn affect the behavior of the but does affect the behavior because , when price is below average total cost , the firm is not making a profit . Instead , it would prefer to exit over the long term . That is , when the price is between the minimum average variable cost and the minimum average total cost , it is better to produce than to shut down but the return on capital was below the cost of capital . With a price in this intermediate area , a firm would produce but would not replace the capital , and thus would shut down in the long term if the price were expected to persist . As a consequence , minimum average total cost is the shutdown point for the competitive . Shutdown may refer to reducing capital rather than literally setting capital to zero . Similarly , in the long term , the firm produces the quantity where the price equals the marginal cost . Figure supply URL books ( 999 218

ATC AV Figure supply illustrates one other fact The minimum of average cost occurs at the point where marginal cost equals average cost . To see this , let ( be total cost , so that average cost is ( Then the minimum of average cost occurs at the point satisfying ( But this can be rearranged to imply ' where marginal cost equals average cost at the minimum of average cost . The marginal cost has a complicated relationship to marginal cost . The problem in characterizing the relationship between run and marginal costs is that some costs are marginal in the long run that are fixed in the short run , tending to make marginal costs larger than marginal costs . However , in the long run , the assets can be configured , While some assets are fixed in the short run , and this optimal tends to make costs lower . Instead , it is more useful to compare the average total costs and average total costs . The advantage is that capital costs are included in average total costs . The result is a picture like Figure Average and marginal costs . URL books ( 909 219

In Figure Average and marginal costs , the short run is there is a average cost , average variable cost , and run marginal cost . The average total cost has been added , in such a way that the minimum average total cost occurs at the same point as the minimum average cost , which equals the marginal cost . This is the lowest average cost , and has the nice property that run average cost equals average total cost equals marginal cost . However , for a different output by the firm , there would necessarily be a different plant size , and the equality is broken . Such a point is illustrated in Figure Increased plant size . In Figure Increased plant size , the quantity produced is larger than the quantity that minimizes average total cost . Consequently , as is visible in the figure , the quantity where average cost equals average cost does not minimize average cost . What this means is that a factory designed to minimize the cost of producing a particular quantity won necessarily minimize average cost . Essentially , because the average total cost is increasing , larger plant sizes are getting increasingly more expensive , and it is cheaper to use a somewhat too small plant and more labor than the plant size with the minimum average total cost . However , this situation wouldn likely persist because , as we shall see , competition tends to force price to the minimum average total cost . At this point , then , we have the equality between average total cost , average total cost , and marginal cost . Figure In ( URL books ( 220

I KEY TAKEAWAYS The firm produces the quantity where price equals marginal cost , provided price is as large as minimum average variable cost . If price falls below minimum average variable cost , the firm shuts down . When price falls below average cost , the firm loses money . If price is above average variable cost , the firm loses less money than it would by shutting down once price falls below average variable cost , shutting down entails smaller losses than continuing to operate . The minimum of average cost occurs at the point where marginal cost equals average cost . If price is below average cost , the firm exits in the long run . Every point on average total cost must be equal to a point on some average total cost . The quantity where average cost equals average cost need not minimize average cost if average cost constant . EXERCISE . Suppose a company has total cost given by , where capital is fixed in the short run . What is average total cost and what is URL books 221

marginal cost ?

Plot these curves . For a given quantity qo , what level of capital minimizes total cost ?

What is the minimum average total cost of qo ?

Economies of Scale and Scope LEARNING OBJECTIVES . When firms get bigger , when do average costs rise or fall ?

How does size relate to profit ?

An economy of larger scale lowers when an increase in output reduces average costs . We met economies of scale and its opposite , of scale , in the previous section , with an example where run average total cost initially fell and then rose , as quantity was increased . What makes for an economy of scale ?

Larger volumes of productions permit the manufacture of more specialized equipment . If I am producing a million identical automotive taillights , I can spend on an automated plastic stamping machine and only affect my costs by cents each . In contrast , ifI am producing units , the stamping machine increases my costs by a dollar each and is much less economical . Indeed , it is somewhat more of a puzzle to determine what produces a of scale . An important source of is managerial in a large , complex enterprise is a challenge , and larger organizations tend to devote a larger percentage of their revenues to management of the operation . A bookstore can be run by a couple of individuals who rarely , if ever , engage in management activities , where a giant chain of bookstores needs finance , human resource , risk management , and other overhead type expenses just in order to function . Informal operation of small enterprises is replaced by formal procedural rules in large organizations . URL , org books 222

This idea of managerial of scale is in the aphorism A platypus is a duck designed by a In his 1975 book The Mythical , IBM software manager Fred Books describes a particularly severe of scale . Adding software engineers to a project increases the number of conversations necessary between pairs of individuals . If there are engineers , there are ( pairs , so that communication costs rise at the square of the project size . This is pithily summarized in Brooks Law Adding manpower to a late software project makes it Another related source of of scale involves system slack . In essence , it is easier to hide incompetence and laziness in a large organization than in a small one . There are a lot of familiar examples of this insight , starting with the Peter Principle , which states that people rise in organizations to the point of their own incompetence , meaning that eventually people cease to do the jobs that they do well . The notion that slack grows as an organization grows implies a of scale . Generally , for many types of products , economies of scale from production technology tend to reduce average cost , up to a point where the operation becomes difficult to manage . Here the tend to prevent the firm from economically getting larger . Under this view , improvements in information technologies over the past 20 years have permitted firms to get larger and larger . While this seems logical , in fact firms aren getting that much larger than they used to be and the share of output produced by the top firms has been relatively steady that is , the growth in the largest firms just mirrors world output growth . Related to an economy of scale is an economy of scope . An economy of scope is a reduction in cost associated with producing several distinct goods . For example , Boeing , which produces both commercial and military jets , can amortize some of its research and development ( costs over both types of URL books 223

aircraft , thereby reducing the average costs of each . Scope economies work like scale economies , except that they account for advantages of producing multiple products , where scale economies involve an advantage of multiple units of the same product . Economies of scale can operate at the level of the individual but can also operate at an industry level . Suppose there is an economy of scale in the production of an input . For example , there is an economy of scale in the production of disk drives for personal computers . This means that an increase in the production of will tend to lower the price of disk drives , reducing the cost of , which is a scale economy . In this case , it doesn matter to the scale economy whether one or many are responsible for the increased production . This is known as an external economy of scale , or economy of scale , because the scale economy operates at the level of the industry rather than in the individual firm . Thus , the average cost of individual may be , while the average cost of the industry slopes downward . Even in the presence of an external economy of scale , there may be of scale at the level of the . In such a situation , the size of any individual firm is limited by the of scale , but nonetheless the average cost of production is decreasing in the total output of the industry , through the entry of additional . Generally there is an external of scale if a larger industry drives up input prices for example , increasing land costs . Increasing the production of soybeans significantly requires using land that isn so well suited for them , tending to increase the average cost of production . Such a is an external rather than operating at the individual farmer level . Second , there is an external economy if an increase in output permits the creation of more specialized techniques and a greater effort in is made to lower costs . Thus , if an increase in output increases the development of specialized URL books 224

machine tools and other production inputs , an external economy will be present . An economy of scale arises when total average cost falls as the number of units produced rises . How does this relate to production functions ?

We let ( be the output when the inputs , are used . A of the inputs involves increasing the inputs by a fixed percentage , multiplying all of them by the constant A ( the Greek letter lambda ) where A . What does this do to output ?

If output goes up by more than A , we have an economy of scale ( also known returns to scale ) Scaling up production increases output proportionately more . If output goes up by less than A , we have a of scale , or decreasing returns to scale . And , if output rises by exactly A , we returns to scale . How does this relate to average cost ?

Formally , we have an economy of scale iff ( Af ( ifA . This corresponds to decreasing average cost . Let be the price of input one , the price of input two , and so on . Then the average cost of producing ( What happens to average cost as we scale up production byA ?

Call this ( A ) A ) Ax ! Ax , Thus , average cost falls if there is an economy of scale and rises if there is a of scale . Another insight about the returns to scale concerns the value of the marginal product of inputs . Note that if there are constant returns to scale , then . Ax , URL books ( 399 225

The value is the marginal product of input , and similarly is the marginal product of the second input , and so on . Consequently , if the production function exhibits constant returns to scale , it is possible to divide up output in such a way that each input receives the value of the marginal product . That is , we can give to the suppliers of input one , to the suppliers of input two , and so on and this exactly uses up all of the output . This is known as paying the marginal product , because each supplier is paid the marginal product associated with the input . If there is a of scale , then paying the marginal product is feasible but there is generally something left over , too . If there are increasing returns to scale ( an economy of scale ) then it is not possible to pay all the inputs their marginal product that is , KEY TAKEAWAYS An economy of scale arises when an increase in output reduces average costs . Specialization may produce economies of scale . An important source of is managerial in a large , complex enterprise is a challenge , and larger organizations tend to devote a larger percentage of their revenues to management of the operation . An economy of scope is a reduction in cost associated with producing several related goods . Economies of scale can operate at the level of the individual firm but can also operate at an industry level . At the industry level , scale economies are known as an external economies of scale or an industry economies of scale . The average cost of individual firms may be flat , while the run average cost of the industry slopes downward . URL books 225

Generally there is an external of scale if a larger industry drives up input prices . There is an external economy if an increase in output permits the creation of more specialized techniques and a greater effort in is made to lower costs . A production function has increasing returns to scale if an increase in all inputs by a constant factor increases output by more than A production function has decreasing returns to scale if an increase in all inputs by a constant factor increases output by less than The production function exhibits increasing returns to scale if and only if the cost function has an economy of scale . When there is an economy of scale , the sum of the values of the marginal product exceeds the total output . Consequently , it is not possible to pay all inputs their marginal product . When there is a of scale , the sum of the values of the marginal product is less than the total output . Consequently , it is possible to pay all inputs their marginal product and have something left over for the entrepreneur . EXERCISES . Given the production function ( show that there is constant returns to scale if , increasing returns to scale if , and decreasing returns to scale if . Suppose a company has total cost given by , where capital be adjusted in the long run . Does this company have an economy of scale , of scale , or constant returns to scale in the long run ?

A production homogeneous if ( Consider a firm with a production function that is homogeneous of degree Suppose further that the firm URL books 227 pays the value of marginal product for all of its inputs . Show that the portion of revenue left over is Dynamics With Constant Costs LEARNING OBJECTIVE . How do changes in demand or cost affect the and prices and quantities traded ?

Having understood how a competitive firm responds to price and input cost changes , we consider how a competitive market responds to demand or cost changes . Figure The basic picture of a equilibrium is presented in Figure run equilibrium . There are three curves , all of which are already familiar . First , there is demand , considered in the first chapter . Here , demand is taken to be the demand . Second , there is the supply , which two shutdown point at minimum average variable URL books 228

cost , and quantity such that price equals marginal cost above that level . The supply , however , is the market supply level , which means that it sums up the individual effects . Finally , there is the average total cost at the industry level , thus any external or economy of scale . As drawn in Figure equilibrium , there is no scale effect . The average total cost is also the industry supply . As drawn , the industry is in equilibrium , with price equal to , which is the average total cost , and also equates supply and demand . That is , at the price of , and industry output of , no firm wishes to shut down , no firm can make positive from entering , there is no excess output , and no consumer is rationed . Thus , no market participant has an incentive to change his or her behavior , so the market is in both and equilibrium . In equilibrium , demand equals run supply , and demand equals supply , so the market is also in equilibrium , where demand equals supply . Now consider an increase in demand . Demand might increase because of population growth , or because a new use for an existing product is developed , or because of income growth , or because the product becomes more useful . For example , the widespread adoption of the Atkins diet increased demand for products like beef jerky and eggs . Suppose that the change is expected to be permanent . This is important because the decision of a firm to enter is based more on expectations of future demand than on present demand . Figure A shift in demand reproduces the equilibrium figure , but with the curves out to indicate a starting position and a darker , new demand curve , URL books 229

Figure ' The initial effect of the increased demand is that the price is bid up , because there is excess demand at the old price , Po . This is by a change in both price and quantity to and , to the intersection of the supply ( and the new demand curve . This is a equilibrium , and persists temporarily because , in the short run , the cost of additional supply is higher . At the new , equilibrium , price exceeds the supply ( cost . This higher price attracts new investment in the industry . It takes some time for this new investment to increase the quantity supplied , but over time the new investment leads to increased output , and a fall in the price , as illustrated in Figure Return to equilibrium . As new investment is attracted into the industry , the supply shifts to the right because , with the new investment , more is produced at any given price level . This is illustrated with the darker supply , The increase in price causes the price to fall back to its initial level and the quantity to increase still further to . Figure Return to URL , org books ( 909 230

02 It is tempting to think that the effect of a decrease in demand just the steps of an increase in demand , but that isn correct . In both cases , the effect is the intersection of the new demand with the old supply . Only then does the supply adjust to equilibrate the demand with the supply that is , the initial effect is a equilibrium , followed by adjustment of the supply to bring the system into equilibrium . Moreover , a small decrease in demand can have a qualitatively different effect in the short run than a large decrease in demand , depending on whether the decrease is large enough to induce immediate exit of . This is illustrated in Figure A decrease in demand . In Figure A decrease in demand , we start at the equilibrium where and Do and all intersect . If demand falls to , the price falls to the intersection of the new demand and the old supply , along . At that point , exit of firms reduces the supply and the price rises , following along the new demand . Figure ( I ' IS ( in demand URL books 231

5351 If , however , the decrease in demand is large enough to push the industry to minimum average variable cost , there is immediate exit . In Figure A big decrease in demand , the fall in demand from Do to , is sufficient to push the price to minimum average variable cost , which is the shutdown point of suppliers . Enough suppliers have to shut down to keep the price at this level , which induces a shift of the supply , to , Then there is additional shutdown , shifting in the supply still further , but driving up the price ( along the demand curve ) until the equilibrium is reached . Figure ) lowland URL books 232

. Consider an increase in the price of an input into production . For example , an increase in the price of crude oil increases the cost of manufacturing gasoline . This tends to decrease ( shift up ) both the supply and the supply by the amount of the cost increase . The effect is illustrated in Figure A decrease in supply . The increased costs reduce both the supply ( prices have to be higher in order to produce the same quantity ) and the supply . The supply shifts upward to and the run supply to . The effect is to move to the intersection of the supply and demand , which is at the price and the quantity . This price is below the average cost , which is the supply , so over time some firms don replace their capital and there is in the industry . This causes the supply to be reduced ( move left ) to . Figure A ( in supply URL books 233

, The case of a change in supply is more challenging because both the supply and the supply are shifted . But the at a equilibrium , then look for the intersection of current demand and supply , then look for the intersection of current demand and the same whether demand or supply have shifted . KEY TAKEAWAYS A equilibrium occurs at a price and quantity when the demand equals the supply , and the number of firms is such that the supply equals the demand . At equilibrium prices , no firm wishes to shut down , no firm can make positive profits from entering , there is no excess output , and no consumer is rationed . An increase in demand to a system in equilibrium first causes a increase in output and a price increase . Then , because entry is profitable , firms enter . Entry shifts out supply until the system achieves equilibrium , decreasing prices back to their original level and increasing output . URL books 234

A decrease in demand creates a equilibrium where existing supply equals demand , with a fall in price and output . If the price fall is large enough ( to average variable cost ) some firms shut down . Then as firms exit , supply contracts , prices rise , and quantity contracts further . The case of a change in supply is more challenging because both the run supply and the supply are shifted . General Dynamics LEARNING OBJECTIVE . If costs are constant , how do changes in demand or costs affect and prices and quantities traded ?

The previous section made two simplifying assumptions that won hold in all applications of the theory . First , it assumed constant returns to scale , so that supply is horizontal . A perfectly elastic supply means that price always eventually returns to the same point . Second , the theory didn distinguish from demand . But with many products , consumers will adjust more over the than immediately . As energy prices rise , consumers buy more cars and appliances , reducing demand . But this effect takes time to be seen , as we don immediately scrap our cars in response to a change in the price of gasoline . The effect is to drive less in response to an increase in the price , while the effect is to choose the appropriate car for the price of gasoline . To illustrate the general analysis , we start with a equilibrium . Figure Equilibrium with external scale economy a economy of scale , because the supply slopes downward , so that larger volumes URL books 235

imply lower cost . The system is in equilibrium because the supply and demand intersection occurs at the same price and quantity as the supply and demand intersection . Both supply and run demand are less elastic than their counterparts , greater substitution possibilities in the long run . Figure ' I ) Figure ) in URL books 235

Now consider a decrease in demand , decreasing both and demand . This is illustrated Decrease in demand . To reduce the proliferation of curves , we colored the old demand curves very faintly and marked the initial equilibrium with a zero inside a small rectangle . The intersection of supply and demand is marked with the number . Both supply and demand are more elastic than their counterparts , which has an interesting effect . The demand tends to shift down over time , because the price associated with the equilibrium is above the demand price for the equilibrium quantity . However , the price associated with the equilibrium is below the supply price at that quantity . The effect is that buyers see the price as too high , and are reducing their demand , while sellers see the price as too low , and so are reducing their supply . Both supply and demand fall , until a equilibrium is achieved . Figure ( in URL books ( 909 237

In this case , the equilibrium involves higher prices , at the point labeled , because of the economy of scale in supply . This economy of scale means that the reduction in demand causes prices to rise over the long run . The supply and demand eventually adjust to bring the system into equilibrium , as Figure after a decrease in demand illustrates . The new equilibrium has demand and supply curves associated with it , and the system is in equilibrium because the demand and supply , which determine the current state of the system , intersect at the same point as the demand and supply , which determine where the system is heading . There are four basic permutations of the dynamic increase or decrease and a supply increase or decrease . Generally , it is possible for supply to slope is the case of an economy of for demand to slope up . This gives 16 variations of the basic analysis . In all 16 cases , the procedure is the same . Start with a equilibrium and shift both the and levels of either demand or supply . The first stage is the intersection of the curves . The system will then go to the intersection of the curves . URL books 238

An interesting example of competitive dynamics concepts is the computer memory market , which was discussed previously . Most of the costs of manufacturing computer memory are fixed costs . The modern DRAM plant costs several billion dollars the cost of other , energy , labor , silicon modest in comparison . Consequently , the supply is vertical until prices are very , very low at any realistic price , it is optimal to run these plants 100 of the time . The nature of the technology has allowed manufacturers to cut the costs of memory by about 30 per year over the past 40 years , demonstrating that there is a strong economy of scale in production . These two supply and strong economies of are illustrated in Figure DRAM market . The system is started at the point labeled with the number , with a relatively high price , and technology that has made costs lower than this price . Responding to the of DRAM , supply shifts out ( new plants are built and permit increasing output from existing plants ) The increased output causes prices to fall relatively dramatically because demand is inelastic , and the system moves to the point labeled . The fall in causes DRAM investment to slow , which allows demand to catch up , boosting prices to the point labeled . One should probably think of Figure DRAM market as being in a logarithmic scale . Figure URL books ( 909 239

The point labeled with the number looks qualitatively similar to the point labeled with the number . The prices have followed a pattern , and the reason is due to the relatively slow adjustment of demand compared to supply , as well as the inelasticity of demand , which creates great price swings as supply shifts out . Supply can be increased quickly and is increased in lumps because a ( making the chips smaller so that more fit on a given silicon wafer ) tends to increase industry production by a large factor . This process can be repeated starting at the point labeled . The system is marching inexorably toward a equilibrium in which electronic memory is very , very cheap even by current standards and is used in applications that haven yet been considered but the process of getting there is a wild ride , indeed . The pattern is illustrated in Figure DRAM revenue cycle , which shows DRAM industry revenues in billions of dollars from 1992 to 2003 , and projections of 2004 and 2005 . Figure I ( URL books 240

50 40 30 20 10 1992 1994 1996 1998 2000 2002 2004 KEY TAKEAWAY In general , both demand and supply may have and curves . In this case , when something changes , initially the system moves to the intersections of the current supply and demand for a equilibrium , then to the intersection of the supply and demand . The second change involves shifting supply and demand curves . EXERCISES . Land close to the center of a city is in fixed supply , but it can be used more intensively by using taller buildings . When the population of a city increases , illustrate the and effects on the housing markets using a graph . Emus can be raised on a wide variety of ranch land , so that there are constant returns to scale in the production of emus in the long run . In the short run , however , the population of emus is limited by the number of breeding pairs of emus , and the supply is essentially vertical . Illustrate the and effects of an increase in demand for emus . In the late , there was a speculative bubble in emus , with prices reaching per breeding pair , in contrast to or so today . There are economies of scale in the manufacture of computers URL books and their components . There was a shift in demand away from desktop 241

computers and toward notebook computers around the year 2001 . What are the and effects ?

Illustrate your answer with two diagrams , one for the notebook market and one for the desktop market . Account for the fact that the two products are substitutes , so that if the price of notebook computers rises , some consumers shift to desktops . To answer this question , start with a time and a market in equilibrium . Shift demand for notebooks out and demand for desktops in . What happens in the short run ?

What happens in the long run to the prices of each ?

What does that price effect do to demand ?

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