Ch07 Short run cost and output decision
衍生工具和风险管理-ch07
D. M. Chance
An Introduction to Derivatives and Risk Management, 6th ed.
Ch. 7: 10
Money Spreads (continued)
Collars (continued)
See Figure 7.5, p. 244 for AOL July 120/136.23, P1 = $13.625, C2 = $13.625. That is, a call strike of 136.23 generates the same premium as a put with strike of 120. This result can be obtained only by using an option pricing model and plugging in exercise prices until you find the one that makes the call premium the same as the put premium.
D. M. Chance
An Introduction to Derivatives and Risk Management, 6th ed.
Ch. 7: 5
Money Spreads
Bull Spreads
Buy call with strike X1, sell call with strike X2. Let N1 = 1, N2 = -1
D. M. Chance
An Introduction to Derivatives and Risk Management, 6th ed.
Ch. 7: 9
布兰查德：高级宏观经济学ch07
M Y Y , G, T P
( , , )
Macroeconomics, 3/e Olivier Blanchard
© 2003 Prentice Hall Business Publishing
7-3
Equilibrium in the Short Run and in the Medium Run
1. When Y > Yn, P > Pe. 2. When Y < Yn, P < Pe.
3. An increase in Pe shifts the AS curve up, and a decrease in Pe shifts the AS curve down.
© 2003 Prentice Hall Business Publishing Macroeconomics, 3/e Olivier Blanchard
P P (1 ) F (u, z)
e
In words, the price level depends on the expected price level and the unemployment rate. We assume that and z are constant.
© 2003 Prentice Hall Business Publishing
© 2003 Prentice Hall Business Publishing
Macroeconomics, 3/e
Olivier Blanchard
Properties of the AS curve
1. The AS curve is upward sloping. As explained earlier, an increase in output leads to an increase in the price level. 2. The AS curve goes through point A, where Y = Yn and P = Pe. This property has two implications:
Ch07_Pindyck生产成本
©2005 Pearson Education, Inc.
Chapter 7
9
Prospective Sunk Cost
Example (cont.) The first building should be purchased The $500,000 is a sunk cost and should
Chapter 7
13
边际成本
Marginal Cost (MC):
The cost of expanding output by one unit Fixed costs have no impact on marginal cost,
so it can be written as:
MC ΔVC ΔTC Δq Δq
100 50
Fixed cost does not vary with output
FC
0 1 2 3 4 5 6 7 8 9 10 11 12 13
©2005 Pearson Education, Inc.
Chapter 7
Output
21
Cost Curves
Cost ($/unit)
120
100
©2005 Pearson Education, Inc.
Chapter 7
14
平均成本
Average Total Cost (ATC)
Cost per unit of output Also equals average fixed cost (AFC) plus
average variable cost (AVC)
中级财务会计英文ch07
Learning Objectives
1. Describe the characteristics of intangible assets. 2. Identify the costs to include in the initial valuation of intangible assets. 3. Explain the procedure for amortizing intangible assets. 4. Describe the types of intangible assets. 5. Explain the conceptual issues related to goodwill. 6. Describe the accounting procedures for recording goodwill. 7. Explain the accounting issues related to intangible-asset
5. Expected actions of competitors, regulatory bodies, and others.
Chapter 7-12
Intangible Assets Amortization of Cost
Intangible Assets With a Finite Life Are Amortized.
Chapter Patents
7-3
Copyrights
Franchises
Intangible Assets
Intangible assets are those noncurrent economic resources that are used in the operations of the business but have no physical existence.
范里安-微观经济分析(第3版)中文完美翻译版-第5章-东南大学曹干
c( w, y, x f ) = wv xv ( w, y, x f ) + w f x f .
其中， wv xv ( w, y, x f ) 称为短期可变成本（short-run variable cost, SVC） ； w f x f 是固定成本 （fixed cost, FC） 。使用这些基本的单元，我们可以定义各种衍生成本概念： 短期总成本= STC = wv xv ( w, y, x f ) + w f x f 短期平均成本= SAC =
曹乾东南大学caoqianseu163com经济学译丛精品系列经济学译丛精品系列经济学译丛精品系列经济学译丛精品系列microeconomicsanalysistheditionvarianuniversitymichiganannarbor完美中文翻译版完美中文翻译版完美中文翻译版完美中文翻译版东南大学caoqianseu163com曹乾东南大学caoqianseu163com成本函数成本函数衡量在要素价格固定不变的情形下生产既定产量的最小成本
c( y ) = Ky + F .
因此，
1 a
AC ( y ) =
c( y ) = Ky y
1− a a
+
F . y
6
曹乾（东南大学 caoqianseu@）
5.3 长期成本曲线和短期成本曲线
下面我们分析长期成本曲线和短期成本曲线的关系。显然，长期成本曲线绝不会位于 任何短期成本曲线的上方， 这是因为短期成本最小化问题只是长期成本最小化问题带有约束 条件的版本。 我们将长期成本函数写为 c( y ) = c ( y , z ( y )). 此处我们删去了要素价格变量，因为根据 假设它们是固定不变的，令 z ( y ) 表示对于某个固定要素的成本最小化的需求。令 y 表示某 个既定的产量水平，z * = z ( y * ) 表示在该产量水平下对该固定要素的长期需求。 对于所有产 量 y 来说，短期成本 c( y , z ) 必定不会小于长期成本 c( y , z ( y )) ；对于产量 y ，短期成本和 长期成本是相等的，因此 c( y , z ) = c ( y , z ( y )) 。因此，长期成本曲线和短期成本曲线必
交通流
Network impacts of a road capacity reduction:Empirical analysisand model predictionsDavid Watling a ,⇑,David Milne a ,Stephen Clark baInstitute for Transport Studies,University of Leeds,Woodhouse Lane,Leeds LS29JT,UK b Leeds City Council,Leonardo Building,2Rossington Street,Leeds LS28HD,UKa r t i c l e i n f o Article history:Received 24May 2010Received in revised form 15July 2011Accepted 7September 2011Keywords:Traffic assignment Network models Equilibrium Route choice Day-to-day variabilitya b s t r a c tIn spite of their widespread use in policy design and evaluation,relatively little evidencehas been reported on how well traffic equilibrium models predict real network impacts.Here we present what we believe to be the first paper that together analyses the explicitimpacts on observed route choice of an actual network intervention and compares thiswith the before-and-after predictions of a network equilibrium model.The analysis isbased on the findings of an empirical study of the travel time and route choice impactsof a road capacity reduction.Time-stamped,partial licence plates were recorded across aseries of locations,over a period of days both with and without the capacity reduction,and the data were ‘matched’between locations using special-purpose statistical methods.Hypothesis tests were used to identify statistically significant changes in travel times androute choice,between the periods of days with and without the capacity reduction.A trafficnetwork equilibrium model was then independently applied to the same scenarios,and itspredictions compared with the empirical findings.From a comparison of route choice pat-terns,a particularly influential spatial effect was revealed of the parameter specifying therelative values of distance and travel time assumed in the generalised cost equations.When this parameter was ‘fitted’to the data without the capacity reduction,the networkmodel broadly predicted the route choice impacts of the capacity reduction,but with othervalues it was seen to perform poorly.The paper concludes by discussing the wider practicaland research implications of the study’s findings.Ó2011Elsevier Ltd.All rights reserved.1.IntroductionIt is well known that altering the localised characteristics of a road network,such as a planned change in road capacity,will tend to have both direct and indirect effects.The direct effects are imparted on the road itself,in terms of how it can deal with a given demand flow entering the link,with an impact on travel times to traverse the link at a given demand flow level.The indirect effects arise due to drivers changing their travel decisions,such as choice of route,in response to the altered travel times.There are many practical circumstances in which it is desirable to forecast these direct and indirect impacts in the context of a systematic change in road capacity.For example,in the case of proposed road widening or junction improvements,there is typically a need to justify econom-ically the required investment in terms of the benefits that will likely accrue.There are also several examples in which it is relevant to examine the impacts of road capacity reduction .For example,if one proposes to reallocate road space between alternative modes,such as increased bus and cycle lane provision or a pedestrianisation scheme,then typically a range of alternative designs exist which may differ in their ability to accommodate efficiently the new traffic and routing patterns.0965-8564/$-see front matter Ó2011Elsevier Ltd.All rights reserved.doi:10.1016/j.tra.2011.09.010⇑Corresponding author.Tel.:+441133436612;fax:+441133435334.E-mail address:d.p.watling@ (D.Watling).168 D.Watling et al./Transportation Research Part A46(2012)167–189Through mathematical modelling,the alternative designs may be tested in a simulated environment and the most efficient selected for implementation.Even after a particular design is selected,mathematical models may be used to adjust signal timings to optimise the use of the transport system.Road capacity may also be affected periodically by maintenance to essential services(e.g.water,electricity)or to the road itself,and often this can lead to restricted access over a period of days and weeks.In such cases,planning authorities may use modelling to devise suitable diversionary advice for drivers,and to plan any temporary changes to traffic signals or priorities.Berdica(2002)and Taylor et al.(2006)suggest more of a pro-ac-tive approach,proposing that models should be used to test networks for potential vulnerability,before any reduction mate-rialises,identifying links which if reduced in capacity over an extended period1would have a substantial impact on system performance.There are therefore practical requirements for a suitable network model of travel time and route choice impacts of capac-ity changes.The dominant method that has emerged for this purpose over the last decades is clearly the network equilibrium approach,as proposed by Beckmann et al.(1956)and developed in several directions since.The basis of using this approach is the proposition of what are believed to be‘rational’models of behaviour and other system components(e.g.link perfor-mance functions),with site-specific data used to tailor such models to particular case studies.Cross-sectional forecasts of network performance at specific road capacity states may then be made,such that at the time of any‘snapshot’forecast, drivers’route choices are in some kind of individually-optimum state.In this state,drivers cannot improve their route selec-tion by a unilateral change of route,at the snapshot travel time levels.The accepted practice is to‘validate’such models on a case-by-case basis,by ensuring that the model—when supplied with a particular set of parameters,input network data and input origin–destination demand data—reproduces current mea-sured mean link trafficflows and mean journey times,on a sample of links,to some degree of accuracy(see for example,the practical guidelines in TMIP(1997)and Highways Agency(2002)).This kind of aggregate level,cross-sectional validation to existing conditions persists across a range of network modelling paradigms,ranging from static and dynamic equilibrium (Florian and Nguyen,1976;Leonard and Tough,1979;Stephenson and Teply,1984;Matzoros et al.,1987;Janson et al., 1986;Janson,1991)to micro-simulation approaches(Laird et al.,1999;Ben-Akiva et al.,2000;Keenan,2005).While such an approach is plausible,it leaves many questions unanswered,and we would particularly highlight two: 1.The process of calibration and validation of a network equilibrium model may typically occur in a cycle.That is to say,having initially calibrated a model using the base data sources,if the subsequent validation reveals substantial discrep-ancies in some part of the network,it is then natural to adjust the model parameters(including perhaps even the OD matrix elements)until the model outputs better reflect the validation data.2In this process,then,we allow the adjustment of potentially a large number of network parameters and input data in order to replicate the validation data,yet these data themselves are highly aggregate,existing only at the link level.To be clear here,we are talking about a level of coarseness even greater than that in aggregate choice models,since we cannot even infer from link-level data the aggregate shares on alternative routes or OD movements.The question that arises is then:how many different combinations of parameters and input data values might lead to a similar link-level validation,and even if we knew the answer to this question,how might we choose between these alternative combinations?In practice,this issue is typically neglected,meaning that the‘valida-tion’is a rather weak test of the model.2.Since the data are cross-sectional in time(i.e.the aim is to reproduce current base conditions in equilibrium),then in spiteof the large efforts required in data collection,no empirical evidence is routinely collected regarding the model’s main purpose,namely its ability to predict changes in behaviour and network performance under changes to the network/ demand.This issue is exacerbated by the aggregation concerns in point1:the‘ambiguity’in choosing appropriate param-eter values to satisfy the aggregate,link-level,base validation strengthens the need to independently verify that,with the selected parameter values,the model responds reliably to changes.Although such problems–offitting equilibrium models to cross-sectional data–have long been recognised by practitioners and academics(see,e.g.,Goodwin,1998), the approach described above remains the state-of-practice.Having identified these two problems,how might we go about addressing them?One approach to thefirst problem would be to return to the underlying formulation of the network model,and instead require a model definition that permits analysis by statistical inference techniques(see for example,Nakayama et al.,2009).In this way,we may potentially exploit more information in the variability of the link-level data,with well-defined notions(such as maximum likelihood)allowing a systematic basis for selection between alternative parameter value combinations.However,this approach is still using rather limited data and it is natural not just to question the model but also the data that we use to calibrate and validate it.Yet this is not altogether straightforward to resolve.As Mahmassani and Jou(2000) remarked:‘A major difficulty...is obtaining observations of actual trip-maker behaviour,at the desired level of richness, simultaneously with measurements of prevailing conditions’.For this reason,several authors have turned to simulated gaming environments and/or stated preference techniques to elicit information on drivers’route choice behaviour(e.g. 1Clearly,more sporadic and less predictable reductions in capacity may also occur,such as in the case of breakdowns and accidents,and environmental factors such as severe weather,floods or landslides(see for example,Iida,1999),but the responses to such cases are outside the scope of the present paper. 2Some authors have suggested more systematic,bi-level type optimization processes for thisfitting process(e.g.Xu et al.,2004),but this has no material effect on the essential points above.D.Watling et al./Transportation Research Part A46(2012)167–189169 Mahmassani and Herman,1990;Iida et al.,1992;Khattak et al.,1993;Vaughn et al.,1995;Wardman et al.,1997;Jou,2001; Chen et al.,2001).This provides potentially rich information for calibrating complex behavioural models,but has the obvious limitation that it is based on imagined rather than real route choice situations.Aside from its common focus on hypothetical decision situations,this latter body of work also signifies a subtle change of emphasis in the treatment of the overall network calibration problem.Rather than viewing the network equilibrium calibra-tion process as a whole,the focus is on particular components of the model;in the cases above,the focus is on that compo-nent concerned with how drivers make route decisions.If we are prepared to make such a component-wise analysis,then certainly there exists abundant empirical evidence in the literature,with a history across a number of decades of research into issues such as the factors affecting drivers’route choice(e.g.Wachs,1967;Huchingson et al.,1977;Abu-Eisheh and Mannering,1987;Duffell and Kalombaris,1988;Antonisse et al.,1989;Bekhor et al.,2002;Liu et al.,2004),the nature of travel time variability(e.g.Smeed and Jeffcoate,1971;Montgomery and May,1987;May et al.,1989;McLeod et al., 1993),and the factors affecting trafficflow variability(Bonsall et al.,1984;Huff and Hanson,1986;Ribeiro,1994;Rakha and Van Aerde,1995;Fox et al.,1998).While these works provide useful evidence for the network equilibrium calibration problem,they do not provide a frame-work in which we can judge the overall‘fit’of a particular network model in the light of uncertainty,ambient variation and systematic changes in network attributes,be they related to the OD demand,the route choice process,travel times or the network data.Moreover,such data does nothing to address the second point made above,namely the question of how to validate the model forecasts under systematic changes to its inputs.The studies of Mannering et al.(1994)and Emmerink et al.(1996)are distinctive in this context in that they address some of the empirical concerns expressed in the context of travel information impacts,but their work stops at the stage of the empirical analysis,without a link being made to net-work prediction models.The focus of the present paper therefore is both to present thefindings of an empirical study and to link this empirical evidence to network forecasting models.More recently,Zhu et al.(2010)analysed several sources of data for evidence of the traffic and behavioural impacts of the I-35W bridge collapse in Minneapolis.Most pertinent to the present paper is their location-specific analysis of linkflows at 24locations;by computing the root mean square difference inflows between successive weeks,and comparing the trend for 2006with that for2007(the latter with the bridge collapse),they observed an apparent transient impact of the bridge col-lapse.They also showed there was no statistically-significant evidence of a difference in the pattern offlows in the period September–November2007(a period starting6weeks after the bridge collapse),when compared with the corresponding period in2006.They suggested that this was indicative of the length of a‘re-equilibration process’in a conceptual sense, though did not explicitly compare their empiricalfindings with those of a network equilibrium model.The structure of the remainder of the paper is as follows.In Section2we describe the process of selecting the real-life problem to analyse,together with the details and rationale behind the survey design.Following this,Section3describes the statistical techniques used to extract information on travel times and routing patterns from the survey data.Statistical inference is then considered in Section4,with the aim of detecting statistically significant explanatory factors.In Section5 comparisons are made between the observed network data and those predicted by a network equilibrium model.Finally,in Section6the conclusions of the study are highlighted,and recommendations made for both practice and future research.2.Experimental designThe ultimate objective of the study was to compare actual data with the output of a traffic network equilibrium model, specifically in terms of how well the equilibrium model was able to correctly forecast the impact of a systematic change ap-plied to the network.While a wealth of surveillance data on linkflows and travel times is routinely collected by many local and national agencies,we did not believe that such data would be sufficiently informative for our purposes.The reason is that while such data can often be disaggregated down to small time step resolutions,the data remains aggregate in terms of what it informs about driver response,since it does not provide the opportunity to explicitly trace vehicles(even in aggre-gate form)across more than one location.This has the effect that observed differences in linkflows might be attributed to many potential causes:it is especially difficult to separate out,say,ambient daily variation in the trip demand matrix from systematic changes in route choice,since both may give rise to similar impacts on observed linkflow patterns across re-corded sites.While methods do exist for reconstructing OD and network route patterns from observed link data(e.g.Yang et al.,1994),these are typically based on the premise of a valid network equilibrium model:in this case then,the data would not be able to give independent information on the validity of the network equilibrium approach.For these reasons it was decided to design and implement a purpose-built survey.However,it would not be efficient to extensively monitor a network in order to wait for something to happen,and therefore we required advance notification of some planned intervention.For this reason we chose to study the impact of urban maintenance work affecting the roads,which UK local government authorities organise on an annual basis as part of their‘Local Transport Plan’.The city council of York,a historic city in the north of England,agreed to inform us of their plans and to assist in the subsequent data collection exercise.Based on the interventions planned by York CC,the list of candidate studies was narrowed by considering factors such as its propensity to induce significant re-routing and its impact on the peak periods.Effectively the motivation here was to identify interventions that were likely to have a large impact on delays,since route choice impacts would then likely be more significant and more easily distinguished from ambient variability.This was notably at odds with the objectives of York CC,170 D.Watling et al./Transportation Research Part A46(2012)167–189in that they wished to minimise disruption,and so where possible York CC planned interventions to take place at times of day and of the year where impacts were minimised;therefore our own requirement greatly reduced the candidate set of studies to monitor.A further consideration in study selection was its timing in the year for scheduling before/after surveys so to avoid confounding effects of known significant‘seasonal’demand changes,e.g.the impact of the change between school semesters and holidays.A further consideration was York’s role as a major tourist attraction,which is also known to have a seasonal trend.However,the impact on car traffic is relatively small due to the strong promotion of public trans-port and restrictions on car travel and parking in the historic centre.We felt that we further mitigated such impacts by sub-sequently choosing to survey in the morning peak,at a time before most tourist attractions are open.Aside from the question of which intervention to survey was the issue of what data to collect.Within the resources of the project,we considered several options.We rejected stated preference survey methods as,although they provide a link to personal/socio-economic drivers,we wanted to compare actual behaviour with a network model;if the stated preference data conflicted with the network model,it would not be clear which we should question most.For revealed preference data, options considered included(i)self-completion diaries(Mahmassani and Jou,2000),(ii)automatic tracking through GPS(Jan et al.,2000;Quiroga et al.,2000;Taylor et al.,2000),and(iii)licence plate surveys(Schaefer,1988).Regarding self-comple-tion surveys,from our own interview experiments with self-completion questionnaires it was evident that travellersfind it relatively difficult to recall and describe complex choice options such as a route through an urban network,giving the po-tential for significant errors to be introduced.The automatic tracking option was believed to be the most attractive in this respect,in its potential to accurately map a given individual’s journey,but the negative side would be the potential sample size,as we would need to purchase/hire and distribute the devices;even with a large budget,it is not straightforward to identify in advance the target users,nor to guarantee their cooperation.Licence plate surveys,it was believed,offered the potential for compromise between sample size and data resolution: while we could not track routes to the same resolution as GPS,by judicious location of surveyors we had the opportunity to track vehicles across more than one location,thus providing route-like information.With time-stamped licence plates, the matched data would also provide journey time information.The negative side of this approach is the well-known poten-tial for significant recording errors if large sample rates are required.Our aim was to avoid this by recording only partial licence plates,and employing statistical methods to remove the impact of‘spurious matches’,i.e.where two different vehi-cles with the same partial licence plate occur at different locations.Moreover,extensive simulation experiments(Watling,1994)had previously shown that these latter statistical methods were effective in recovering the underlying movements and travel times,even if only a relatively small part of the licence plate were recorded,in spite of giving a large potential for spurious matching.We believed that such an approach reduced the opportunity for recorder error to such a level to suggest that a100%sample rate of vehicles passing may be feasible.This was tested in a pilot study conducted by the project team,with dictaphones used to record a100%sample of time-stamped, partial licence plates.Independent,duplicate observers were employed at the same location to compare error rates;the same study was also conducted with full licence plates.The study indicated that100%surveys with dictaphones would be feasible in moderate trafficflow,but only if partial licence plate data were used in order to control observation errors; for higherflow rates or to obtain full number plate data,video surveys should be considered.Other important practical les-sons learned from the pilot included the need for clarity in terms of vehicle types to survey(e.g.whether to include motor-cycles and taxis),and of the phonetic alphabet used by surveyors to avoid transcription ambiguities.Based on the twin considerations above of planned interventions and survey approach,several candidate studies were identified.For a candidate study,detailed design issues involved identifying:likely affected movements and alternative routes(using local knowledge of York CC,together with an existing network model of the city),in order to determine the number and location of survey sites;feasible viewpoints,based on site visits;the timing of surveys,e.g.visibility issues in the dark,winter evening peak period;the peak duration from automatic trafficflow data;and specific survey days,in view of public/school holidays.Our budget led us to survey the majority of licence plate sites manually(partial plates by audio-tape or,in lowflows,pen and paper),with video surveys limited to a small number of high-flow sites.From this combination of techniques,100%sampling rate was feasible at each site.Surveys took place in the morning peak due both to visibility considerations and to minimise conflicts with tourist/special event traffic.From automatic traffic count data it was decided to survey the period7:45–9:15as the main morning peak period.This design process led to the identification of two studies:2.1.Lendal Bridge study(Fig.1)Lendal Bridge,a critical part of York’s inner ring road,was scheduled to be closed for maintenance from September2000 for a duration of several weeks.To avoid school holidays,the‘before’surveys were scheduled for June and early September.It was decided to focus on investigating a significant southwest-to-northeast movement of traffic,the river providing a natural barrier which suggested surveying the six river crossing points(C,J,H,K,L,M in Fig.1).In total,13locations were identified for survey,in an attempt to capture traffic on both sides of the river as well as a crossing.2.2.Fishergate study(Fig.2)The partial closure(capacity reduction)of the street known as Fishergate,again part of York’s inner ring road,was scheduled for July2001to allow repairs to a collapsed sewer.Survey locations were chosen in order to intercept clockwiseFig.1.Intervention and survey locations for Lendal Bridge study.around the inner ring road,this being the direction of the partial closure.A particular aim wasFulford Road(site E in Fig.2),the main radial affected,with F and K monitoring local diversion I,J to capture wider-area diversion.studies,the plan was to survey the selected locations in the morning peak over a period of approximately covering the three periods before,during and after the intervention,with the days selected so holidays or special events.Fig.2.Intervention and survey locations for Fishergate study.In the Lendal Bridge study,while the‘before’surveys proceeded as planned,the bridge’s actualfirst day of closure on Sep-tember11th2000also marked the beginning of the UK fuel protests(BBC,2000a;Lyons and Chaterjee,2002).Trafficflows were considerably affected by the scarcity of fuel,with congestion extremely low in thefirst week of closure,to the extent that any changes could not be attributed to the bridge closure;neither had our design anticipated how to survey the impacts of the fuel shortages.We thus re-arranged our surveys to monitor more closely the planned re-opening of the bridge.Unfor-tunately these surveys were hampered by a second unanticipated event,namely the wettest autumn in the UK for270years and the highest level offlooding in York since records began(BBC,2000b).Theflooding closed much of the centre of York to road traffic,including our study area,as the roads were impassable,and therefore we abandoned the planned‘after’surveys. As a result of these events,the useable data we had(not affected by the fuel protests orflooding)consisted offive‘before’days and one‘during’day.In the Fishergate study,fortunately no extreme events occurred,allowing six‘before’and seven‘during’days to be sur-veyed,together with one additional day in the‘during’period when the works were temporarily removed.However,the works over-ran into the long summer school holidays,when it is well-known that there is a substantial seasonal effect of much lowerflows and congestion levels.We did not believe it possible to meaningfully isolate the impact of the link fully re-opening while controlling for such an effect,and so our plans for‘after re-opening’surveys were abandoned.3.Estimation of vehicle movements and travel timesThe data resulting from the surveys described in Section2is in the form of(for each day and each study)a set of time-stamped,partial licence plates,observed at a number of locations across the network.Since the data include only partial plates,they cannot simply be matched across observation points to yield reliable estimates of vehicle movements,since there is ambiguity in whether the same partial plate observed at different locations was truly caused by the same vehicle. Indeed,since the observed system is‘open’—in the sense that not all points of entry,exit,generation and attraction are mon-itored—the question is not just which of several potential matches to accept,but also whether there is any match at all.That is to say,an apparent match between data at two observation points could be caused by two separate vehicles that passed no other observation point.Thefirst stage of analysis therefore applied a series of specially-designed statistical techniques to reconstruct the vehicle movements and point-to-point travel time distributions from the observed data,allowing for all such ambiguities in the data.Although the detailed derivations of each method are not given here,since they may be found in the references provided,it is necessary to understand some of the characteristics of each method in order to interpret the results subsequently provided.Furthermore,since some of the basic techniques required modification relative to the published descriptions,then in order to explain these adaptations it is necessary to understand some of the theoretical basis.3.1.Graphical method for estimating point-to-point travel time distributionsThe preliminary technique applied to each data set was the graphical method described in Watling and Maher(1988).This method is derived for analysing partial registration plate data for unidirectional movement between a pair of observation stations(referred to as an‘origin’and a‘destination’).Thus in the data study here,it must be independently applied to given pairs of observation stations,without regard for the interdependencies between observation station pairs.On the other hand, it makes no assumption that the system is‘closed’;there may be vehicles that pass the origin that do not pass the destina-tion,and vice versa.While limited in considering only two-point surveys,the attraction of the graphical technique is that it is a non-parametric method,with no assumptions made about the arrival time distributions at the observation points(they may be non-uniform in particular),and no assumptions made about the journey time probability density.It is therefore very suitable as afirst means of investigative analysis for such data.The method begins by forming all pairs of possible matches in the data,of which some will be genuine matches(the pair of observations were due to a single vehicle)and the remainder spurious matches.Thus, for example,if there are three origin observations and two destination observations of a particular partial registration num-ber,then six possible matches may be formed,of which clearly no more than two can be genuine(and possibly only one or zero are genuine).A scatter plot may then be drawn for each possible match of the observation time at the origin versus that at the destination.The characteristic pattern of such a plot is as that shown in Fig.4a,with a dense‘line’of points(which will primarily be the genuine matches)superimposed upon a scatter of points over the whole region(which will primarily be the spurious matches).If we were to assume uniform arrival rates at the observation stations,then the spurious matches would be uniformly distributed over this plot;however,we shall avoid making such a restrictive assumption.The method begins by making a coarse estimate of the total number of genuine matches across the whole of this plot.As part of this analysis we then assume knowledge of,for any randomly selected vehicle,the probabilities:h k¼Prðvehicle is of the k th type of partial registration plateÞðk¼1;2;...;mÞwhereX m k¼1h k¼1172 D.Watling et al./Transportation Research Part A46(2012)167–189。
国际财务管理(原书第8版)教学手册ER8eSM_Ch07
CHAPTER 7 FUTURES AND OPTIONS ON FOREIGN EXCHANGE ANSWERS & SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMSQUESTIONS1. Explain the basic differences between the operation of a currency forward market and a futures market.Answer: The forward market is an OTC market where the forward contract for purchase or sale of foreign currency is tailor-made between the client and its international bank. No money changes hands until the maturity date of the contract when delivery and receipt are typically made. A futures contract is an exchange-traded instrument with standardized features specifying contract size and delivery date. Futures contracts are marked-to-market daily to reflect changes in the settlement price. Delivery is seldom made in a futures market. Rather a reversing trade is made to close out a long or short position.2. In order for a derivatives market to function most efficiently, two types of economic agents are needed: hedgers and speculators. Explain.Answer: Two types of market participants are necessary for the efficient operation of a derivatives market: speculators and hedgers. A speculator attempts to profit from a change in the futures price. To do this, the speculator will take a long or short position in a futures contract depending upon his expectations of future price movement. A hedger, on-the-other-hand, desires to avoid price variation by locking in a purchase price of the underlying asset through a long position in a futures contract or a sales price through a short position. In effect, the hedger passes off the risk of price variation to the speculator who is better able, or at least more willing, to bear this risk.3. Why are most futures positions closed out through a reversing trade rather than held to delivery?Answer: In forward markets, approximately 90 percent of all contracts that are initially established result in the short making delivery to the long of the asset underlying the contract. This is natural because the terms of forward contracts are tailor-made between the long and short. By contrast,only about one percent of currency futures contracts result in delivery. While futures contracts are useful for speculation and hedging, their standardized delivery dates make them unlikely to correspond to the actual future dates when foreign exchange transactions will occur. Thus, they are generally closed out in a reversing trade. In fact, the commission that buyers and sellers pay to transact in the futures market is a single amount that covers the round-trip transactions of initiating and closing out the position.4. How can the FX futures market be used for price discovery?Answer: To the extent that FX forward prices are an unbiased predictor of future spot exchange rates, the market anticipates whether one currency will appreciate or depreciate versus another. Because FX futures contracts trade in an expiration cycle, different contracts expire at different periodic dates into the future. The pattern of the prices of these contracts provides information as to the market’s current belief about the relative future value of one currency versus another at the scheduled expiration dates of the contracts. One will generally see a steadily appreciating or depreciating pattern; however, it may be mixed at times. Thus, the futures market is useful for price discovery, i.e., obtaining the market’s forecast of the spot exchange rate at different future dates.5. What is the major difference in the obligation of one with a long position in a futures (or forward) contract in comparison to an options contract?Answer: A futures (or forward) contract is a vehicle for buying or selling a stated amount of foreign exchange at a stated price per unit at a specified time in the future. If the long holds the contract to the delivery date, he pays the effective contractual futures (or forward) price, regardless of whether it is an advantageous price in comparison to the spot price at the delivery date. By contrast, an option is a contract giving the long the right to buy or sell a given quantity of an asset at a specified price at some time in the future, but not enforcing any obligation on him if the spot price is more favorable than the exercise price. Because the option owner does not have to exercise the option if it is to his disadvantage, the option has a price, or premium, whereas no price is paid at inception to enter into a futures (or forward) contract.6. What is meant by the terminology that an option is in-, at-, or out-of-the-money?Answer: A call (put) option with S t > E (E > S t) is referred to as trading in-the-money. If S t≅ E the option is trading at-the-money. If S t< E (E < S t) the call (put) option is trading out-of-the-money.7. List the arguments (variables) of which an FX call or put option model price is a function. How does the call and put premium change with respect to a change in the arguments?Answer: Both call and put options are functions of only six variables: S t, E, r i, r$, T andσ. When all else remains the same, the price of a European FX call (put) option will increase:1. the larger (smaller) is S,2. the smaller (larger) is E,3. the smaller (larger) is r i,4. the larger (smaller) is r$,5. the larger (smaller) r$ is relative to r i, and6. the greater is σ.When r$ and r i are not too much different in size, a European FX call and put will increase in price when the option term-to-maturity increases. However, when r$ is very much larger than r i, a European FX call will increase in price, but the put premium will decrease, when the option term-to-maturity increases. The opposite is true when r i is very much greater than r$. For American FX options the analysis is less complicated. Since a longer term American option can be exercised on any date that a shorter term option can be exercised, or a some later date, it follows that the all else remaining the same, the longer term American option will sell at a price at least as large as the shorter term option.PROBLEMS1. Assume today’s settlement price on a CM E EUR futures contract is $1.3140/EUR. You havea short position in one contract. Your performance bond account currently has a balance of $1,700. The next three days’ settlement prices are $1.3126, $1.3133, and $1.3049. Calculate the changes in the performance bond account from daily marking-to-market and the balance of the performance bond account after the third day.Solution: $1,700 + [($1.3140 - $1.3126) + ($1.3126 - $1.3133)+ ($1.3133 - $1.3049)] x EUR125,000 = $2,837.50, where EUR125,000 is the contract size of one EUR contract.2. Do problem 1 again assuming you have a long position in the futures contract.Solution: $1,700 + [($1.3126 - $1.3140) + ($1.3133 - $1.3126) + ($1.3049 - $1.3133)] x EUR125,000 = $562.50, where EUR125,000 is the contract size of one EUR contract.With only $562.50 in your performance bond account, you would experience a margin call requesting that additional funds be added to your performance bond account to bring the balance back up to the initial performance bond level.3. Using the quotations in Exhibit 7.3, calculate the face value of the open interest in the September 2016 Swiss franc futures contract.Solution: 178 contracts x SF125,000 = SF22,250,000, where SF125,000 is the contract size of one SF contract. Note: By comparison the face value of the open interest in the 43,970 June 2016 contracts is SF5,496,250,000.4. Using the quotations in Exhibit 7.3, note that the September 2016 Mexican peso futures contract has a price of $0.05481 per MXN. You believe the spot price in September will be $0.06133 per MXN. What speculative position would you enter into to attempt to profit from your beliefs? Calculate your anticipated profits, assuming you take a position in three contracts. What is the size of your profit (loss) if the futures price is indeed an unbiased predictor of the future spot price and this price materializes?Solution: If you expect the Mexican peso to rise from $0.05481 to $0.06133 per MXN, you would take a long position in futures since the futures price of $0.05481 is less than your expected spot price.Your anticipated profit from a long position in three contracts is: 3 x ($0.06133 - $0.05481) x MXN500,000 = $9,780 where MXN500,000 is the contract size of one MXN contract.If the futures price is an unbiased predictor of the expected spot price, the expected spot price is the futures price of $0.05481 per MXN. If this spot price materializes, you will not have any profits or losses from your short position in three futures contracts: 3 x ($0.05481 - $0.05481) x MXN500,000 = 0.5. Do problem 4 again assuming you believe the September 2016 spot price will be $0.04829 per MXN.Solution: If you expect the Mexican peso to depreciate from $0.05481 to $0.04829 per MXN, you would take a short position in futures since the futures price of $0.05481 is greater than your expected spot price.Your anticipated profit from a short position in three contracts is: 3 x ($0.05481 - $0.04829) x MXN500,000 = $9,780, where MXN500,000 is the contract size of one MXN contract.If the futures price is an unbiased predictor of the future spot price and this price materializes, you will not profit or lose from your long futures position.6. Using the market data in Exhibit7.6, show the net terminal value of a long position in one 90 Sep Japanese yen European call contract at the following terminal spot prices (stated in U.S. cents per 100 yen): 81, 85, 90, 95, and 99. Ignore any time value of money effect.Solution: The net terminal value of one call contract is:[Max[S T– E, 0]– C e] x JPY1,000,000/100 ÷ 100¢, where JPY1,000,000 is the contract size of one JPY contract.At 81: [Max[81 – 90, 0] – 2.60] x JPY1,000,000/100 ÷ 100¢ = -$260At 85: [Max[85 – 90, 0] – 2.60] x JPY1,000,000/100 ÷ 100¢ = -$260At 90: [Max[90 – 90, 0] – 2.60] x JPY1,000,000/100 ÷ 100¢ = -$260At 95: [Max[95 – 90, 0] – 2.60] x JPY1,000,000/100 ÷ 100¢ = $240At 99: [Max [99 – 90, 0] – 2.60] x JPY1,000,000/100 ÷ 100¢ = $6407. Using the market data in Exhibit 7.6, show the net terminal value of a long position in one 90 Sep Japanese yen European put contract at the following terminal spot prices (stated in U.S. cents per 100 yen): 81, 85, 90, 95, and 99. Ignore any time value of money effect.Solution: The net terminal value of one put contract is:[Max[E –S T, 0] –P e x JPY1,000,000/100 ÷ 100¢, where JPY1,000,000 is the contract size of one JPY contract.At 81: [Max[90 – 81, 0] – 1.80] x JPY1,000,000/100 ÷ 100¢ = $720At 85: [Max[90 – 85, 0] – 1.80] x JPY1,000,000/100 ÷ 100¢ = $320At 90: [Max[90 – 90, 0] – 1.80] x JPY1,000,000/100 ÷ 100¢ = -$180At 95: [Max[90 – 95, 0] – 1.80] x JPY1,000,000/100 ÷ 100¢ = -$180At 99: [Max[90 – 99, 0] – 1.80] x JPY1,000,000/100 ÷ 100¢ = -$1808. Assume that the Japanese yen is trading at a spot price of 92.04 cents per 100 yen. Further assume that the premium of an American call (put) option with a striking price of 93 is 2.10 (2.20) cents. Calculate the intrinsic value and the time value of the call and put options.Solution: Premium - Intrinsic Value = Time ValueCall: 2.10 - Max[92.04 – 93.00 = - .96, 0] = 2.10 cents per 100 yenPut: 2.20 - Max[93.00 – 92.04 = .96, 0] = 1.24 cents per 100 yen9. Assume spot Swiss franc is $0.7000 and the six-month forward rate is $0.6950. What is the minimum price that a six-month American call option with a striking price of $0.6800 should sell for in a rational market? Assume the annualized six-month Eurodollar rate is 3 ½ percent.Solution:Note to Instructor: A complete solution to this problem relies on the boundary expressions presented in footnote 3 of the text of Chapter 7.C a≥Max[(70 - 68), (69.50 - 68)/(1.0175), 0]≥Max[ 2, 1.47, 0] = 2 cents10. Do problem 9 again assuming an American put option instead of a call option.Solution: P a≥Max[(68 - 70), (68 - 69.50)/(1.0175), 0]≥Max[ -2, -1.47, 0] = 0 cents11. Use the European option-pricing models developed in the chapter to value the call of problem 9 and the put of problem 10. Assume the annualized volatility of the Swiss franc is 14.2 percent. This problem can be solved using the FXOPM.xls spreadsheet.Solution:d1 = [ln(69.50/68) + .5(.142)2(.50)]/(.142)√.50 = .2675d2 = d1 - .142√.50 = .2765 - .1004 = .1671N(d1) = .6055N(d2) = .5664N(-d1) = .3945N(-d2) = .4336C e = [69.50(.6055) - 68(.5664)]e-(.035)(.50) = 3.51 centsP e = [68(.4336) - 69.50(.3945)]e-(.035)(.50) = 2.03 cents12. Use the binomial option-pricing model developed in the chapter to value the call of problem 9. The volatility of the Swiss franc is 14.2 percent.Solution: The spot rate at T will be either 77.39¢ = 70.00¢(1.1056) or 63.32¢ = 70.00¢(.9045), where u = e.142√.50 = 1.1056 and d = 1/u = .9045. At the exercise price of E = 68, the option will only be exercised at time T if the Swiss franc appreciates; its exercise value would be C uT= 9.39¢= 77.39¢- 68. If the Swiss franc depreciates it would not be rational to exercise the option; its value would be C dT = 0.The hedge ratio is h = (9.39 – 0)/(77.39 – 63.32) = .6674.Thus, the call premium is:C0 = Max{[69.50(.6674) – 68((77.39/68)(.6674 – 1) +1)]/(1.0175), 70 – 68}= Max[4.05, 2] = 4.05 cents per SF.MINI CASE: THE OPTIONS SPECULATORA speculator is considering the purchase of five three-month Japanese yen call options with a striking price of 96 cents per 100 yen. The premium is 1.35 cents per 100 yen. The spot price is 95.28 cents per 100 yen and the 90-day forward rate is 95.71 cents. The speculator believes the yen will appre ciate to $1.00 per 100 yen over the next three months. As the speculator’s assistant, you have been asked to prepare the following:1. Graph the call option cash flow schedule.2. Determine the speculator’s profit if the yen appreciates to $1.00/100 yen.3. Determine the speculator’s profit if the yen only appreciates to the forward rate.4. Determine the future spot price at which the speculator will only break even.Suggested Solution to the Options Speculator:1.-2. (5 x ¥1,000,000) x [(100 - 96) - 1.35]/10000 = $1,325.00.3. Since the option expires out-of-the-money, the speculator will let the option expire worthless. He will only lose the option premium.4. S T = E + C = 96 + 1.35 = 97.35 cents per 100 yen.。
ch07风险资产与无风险资产之间的组合
举例 Example
rf = 7% E(rp) = 15% y = % in p σrf = 0% σp = 22% (1-y) = % in rf
7-6
投资组合预期收益
Expected Returns for Combinations
E(rc) = yE(rp) + (1 - y)rf rc = 全部或组合收益 全部或组合收益complete or combined portfolio For example, y = .75 E(rc) = .75(.15) + .25(.07) = .13 or 13%
7-15
杠杆头寸 leveraged position
Suppose the investment budget is $300,000 and our investor borrows an additional $120,000, investing the total available funds in the risky asset. This is a leveraged position in the risky asset; it is financed in part by borrowing. In that case Y = 420,000 / 300,000= 1.4 and 1 – y =1 -1.4 = 0.4 =1 reflecting a short position in the risk-free asset, which is a borrowing riskposition. Rather than lending at a 7% interest rate, the investor borrows at 7%. The distribution of the portfolio rate of return still exhibits the same reward-toreward-to-variability ratio: E (r C ) = 7% + (1.4 X 8%) = 18.2% σC = 1.4 X 22% = 30.8% S= E(rC ) - rf / σC = 18.2 – 7/30.8 = 0.36 E(
现金流量表英文版ch07statementofcashflows
11 Examples of cash flows from operating activities are:
(a) cash receipts from the sale of goods and the rendering of services;
(b) cash receipts from royalties, fees, commissions and other revenue;
(f) cash receipts from the repayment of advances and loans made to other parties (other than advances and loans of a financial institution);
Examples of cash flows arising from
Guidance notes indicate that an investment normally meets the definition of a cash equivalent when it has a maturity of three months or less from the date of acquisition.
Taxes on Income
11
cash flows arising from taxes on income are normally classified as operating, unless they can be specifically identified with financing or investing activities
现金流量表英文版ch07 statement of cash flows.ppt
13
The operating cash flows section of the statement of cash flows under the indirect method would appear something like this:
11
financing activities are:
(a) cash proceeds from issuing shares or other equity instruments;
(b) cash payments to owners to acquire or redeem the enterprise's shares;
Bank overdrafts which are repayable on demand and which form an integral part of an enterprise's cash management are also included as a component of cash and cash equivalents.
Guidance notes indicate that an investment normally meets the definition of a cash equivalent when it has a maturity of three months or less from the date of acquisition.
现金流量表英文版ch07 statement of cash flows
(a) cash payments to acquire property, plant and equipment, intangibles and other long-term assets. These payments include those relating to capitalised development costs and self-constructed property, plant and equipment;
(c) cash payments to suppliers for goods and services;
(d) cash payments to and on behalf of employees;
5
Examples of cash flows arising from
11
investing activities are:
8
Taxes on Income
11
cash flows arising from taxes on income are normally classified as operating, unless they can be specifically identified with financing or investing activities
Cash receipts from customers
short-run fluctuations 笔记
Short-run Fluctuations 短期波动I. 概念介绍A. 短期波动的定义B. 短期波动的成因1. 总供给和总需求的变化2. 外部冲击3. 生产率的变化II. 短期波动与经济周期的关系A. 短期波动导致的经济周期B. 经济周期对短期波动的影响1. 短期波动对应的经济周期阶段2. 经济周期的变化对短期波动的影响III. 短期波动的影响A. 对商品价格的影响B. 对产出和就业的影响C. 对货币政策的影响D. 对财政政策的影响IV. 应对短期波动的政策A. 货币政策的调控B. 财政政策的调整C. 结构性政策的实施V. 短期波动的经济学理论A. 经济波动的解释B. 有效市场假说与短期波动C. 钱币数量论与短期波动VI. 短期波动的实证研究A. 实证研究方法B. 研究发现及结论VII. 结语A. 短期波动对经济的重要性B. 如何有效管理短期波动以上是对短期波动这一宏观经济学概念的一些简要介绍。
短期波动是经济运行中不可避免的现象，了解其影响因素和应对政策对于维护经济稳定和促进经济增长至关重要。
希望本文能为对短期波动感兴趣的读者提供一些参考和启发。
短期波动是指经济运行中短期内产出、就业、价格水平等变动的现象。
在宏观经济学中，短期波动通常指的是几个月或者几年的时间段内，经济活动的波动。
短期波动可能是周期性的、一次性的或者随机的，其成因包括总供给和总需求的变化、外部冲击，以及生产率的变化。
短期波动与经济周期密切相关，短期波动可能导致经济周期的变化，经济周期的变化也会对短期波动产生影响。
经济周期一般包括繁荣期、衰退期、萧条期和复苏期，不同阶段的经济周期对应着不同的短期波动情况。
经济周期的变化也会对短期波动产生深远的影响，因为经济周期的变化会引起总供给和总需求的变化，从而影响短期波动的发展。
短期波动对经济的影响主要表现在商品价格、产出和就业、货币政策以及财政政策等方面。
在短期波动下，由于供求关系的变化，商品价格可能会出现波动；产出和就业水平也会随着经济波动而波动；货币政策和财政政策也会因为短期波动而作出相应的调整。
princ-ch07市场效率
消费者剩余与需求曲线
P
$350 $300 $250 $200
Flea的支付 意愿
P = $260 Flea的消费者剩余 = $300 – 260 = $40 总消费者剩余 =$40
$150
$100
$50
$0
Q
01234
消费者、生产者与市场效率
10
消费者剩余与需求曲线
P
$350 $300 $250
John, Chad, Anthony, Flea
消费者、生产者与市场效率
Qd 0 1 2 3 4
5
支付意愿与需求曲线
P
$350 $300 $250
P
$301及以 上
$200
251 – 300
$150 $100
$50 $0
176 – 250
126 – 175
Q
0 – 125
01234
消费者、生产者与市场效率
亚当.斯密与看不见的手
引自《国富论》,1776
亚当.斯密， 1723-1790
“人类几乎随时随地都需要同胞 的协助，仅仅指望他们的慷慨是 徒劳的。如果他能够唤起他们的 利己心，并向他们证明，他要他 们做的事情也对他们有利，那他 更有可能成功…… 我们想要的食品，不是出自屠户、 酿酒人或面包师的仁慈，而是出 于他们对自身利益的关心……”
Chrissy 的成本
Janet的 成本
Jack的成本
在每个数量，供 给曲线的高度是 边际卖者的成本
边际卖者：如果 价格再低一点就 首先离开市场的 卖者
$0
Q
0123
消费者、生产者与市场效率
19
P $40
$30
CH7运输决策
起讫点不同的单一问题 P171
解决方法：最短路径法（Shortest Route Method）
最短路径法描述：已知一个由链和节点组成的网 络，其中节点代表由链（运输路径）连接的点， 链代表节点之间的成本（距离、时间或距离和时 间的加权平均）。
例 某制造商与不同三个地点的供应商签订合同，由它供货给 三个工厂，约束条件是不超过合同所定的数量，但必须满足 生产要求。 是单一路径确定后的运量分配后续问题
供应商 A 《400 供应商 B 《700 工厂1 需求 =600 工厂2 需求 =500
4 7 6 5 5 5 9
供应商 C 《500
5 8
工厂3 需求 =300
图 阿马里洛和沃思堡之间高速公路网示意图，附行车时间
表 最短路径法的计算步骤表
步 骤 直接连接到未 解节点的已解 节点 A A B A B C A C E A C E F 与其直接连接 相关总成本 的最近未解结 点—候选节点 B C C D E F D F I D D I H 90 138 90+66=156 348 90+84=174 138+90=228 348 138+90=228 174+84=258 348 138+153=291 174+84=258 228+60=288 第n个最近 最小总成 已解节点 本 最新连接
14 —
12 — 10 — B
8—
(0,6.8)
6— 4— 2— 0
最优解 (3,6)
4x1 + 6x2 48 (挤压工时限制)
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
Fixed Costs
• Firms have no control over fixed costs in the short run. For this reason, fixed costs are sometimes called sunk costs. costs. • Average fixed cost (AFC) is the (AFC) total fixed cost (TFC) divided by the (TFC) number of units of output (q): (,000 1,000 1,000 1,000 1,000 (3) AFC (TFC/q) $ −− 1,000 500 333 250 200
• AFC falls as output rises; a phenomenon sometimes called spreading overhead. overhead.
TFC AFC = q
© 2002 Prentice Hall Business Publishing Principles of Economics, 6/e Karl Case, Ray Fair
ShortShort-Run Fixed Cost (Total and Average) of a Hypothetical Firm
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
The Shape of the Marginal Cost Curve in the Short Run
• The fact that in the short run every firm is constrained by some fixed input means that:
2. Firms can neither enter nor exit an
industry.
•
In the short run, all firms have costs that they must bear regardless of their output. These kinds of costs are called fixed costs. costs.
2. Techniques of production available*
3. The price of inputs*
*Determines production costs
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
PRODUCT 1 Units of output 2 Units of output 3 Units of output
USING TECHNIQUE A B A B A B
• The total variable cost curve shows the cost of production using the best available technique at each output level, given current factor prices.
Principles of Economics, 6/e Karl Case, Ray Fair
© 2002 Prentice Hall Business Publishing
The Shape of the Marginal Cost Curve in the Short Run
• Marginal costs ultimately increase with output in the short run.
Decisions Facing Firms
DECISIONS
1. The quantity of output to supply
are based on
INFORMATION
1. The price of output
2. How to produce that output (which technique to use) 3. The quantity of each input to demand
Principles of Economics, 6/e Karl Case, Ray Fair
© 2002 Prentice Hall Business Publishing
Costs in the Short Run
• Fixed cost is any cost that does not depend on the firm’s level of output. These costs are incurred even if the firm is producing nothing. • Variable cost is a cost that depends on the level of production chosen.
Total Cost = Total Fixed + Total Variable Cost Cost
© 2002 Prentice Hall Business Publishing Principles of Economics, 6/e Karl Case, Ray Fair
TC = TFC + TVC
UNITS OF INPUT REQUIRED (PRODUCTION FUNCTION) K 4 2 7 4 9 6 4 6 6 10 6 14 L TOTAL VARIABLE COST ASSUMING PK = $2, PL = $1 TVC = (K x PK) + (L x PL) (K (L (4 x $2) + (4 x $1) = $12 (2 x $2) + (6 x $1) = $10 (7 x $2) + (6 x $1) = $20 (4 x $2) + (10 x $1) = $18 (9 x $2) + (6 x $1) = $24 (6 x $2) + (14 x $1) = $26
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Graphing Total Variable Costs and Marginal Costs
• Total variable costs always increase with output. The marginal cost curve shows how total variable cost changes with single unit increases in total output. • Below 100 units of output, TVC increases at a decreasing rate. Beyond rate. 100 units of output, TVC increases at an increasing rate.
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Derivation of Total Variable Cost Schedule from Technology and Factor Prices
Karl Case, Ray Fair
Costs in the Short Run
• The short run is a period of time for which two conditions hold:
1. The firm is operating under a fixed
scale (fixed factor) of production, and
© 2002 Prentice Hall Business Publishing Principles of Economics, 6/e Karl Case, Ray Fair
Average Variable Cost
• Average variable cost (AVC) is the total variable cost divided by the number of units of output. • Marginal cost is the cost of one additional unit. Average variable unit. cost is the average variable cost per unit of all the units being produced. • Average variable cost follows marginal cost, but lags behind.
∆ TC ∆ TFC ∆ TVC MC = = + ∆Q ∆Q ∆Q
© 2002 Prentice Hall Business Publishing
Principles of Economics, 6/e
Karl Case, Ray Fair
Derivation of Marginal Cost from Total Variable Cost
© 2002 Prentice Hall Business Publishing Principles of Economics, 6/e Karl Case, Ray Fair
Variable Costs
• The total variable cost curve is a graph that shows the relationship between total variable cost and the level of a firm’s output. • The total variable cost is derived from production requirements and input prices.