1、.Production Analysis and Compensation PolicyChapter 5.Chapter 5OVERVIEWProduction FunctionsTotal,Marginal,and Average ProductLaw of Diminishing Returns to a FactorInput Combination ChoiceMarginal Revenue Product and Optimal EmploymentOptimal Combination of Multiple InputsOptimal Levels of Multiple I
2、nputsReturns to ScaleProduction Function EstimationProductivity Measurement.Chapter 5 KEY CONCEPTSnproduction functionndiscrete production functionncontinuous production functionnreturns to scalenreturns to a factorntotal productnmarginal productnaverage productnlaw of diminishing returnsnisoquantnt
3、echnical efficiencyninput substitutionnmarginal rate of technicalnridge linesnmarginal revenue productneconomic efficiencynnet marginal revenuenisocost curve(or budget line)nconstant returns to scalenexpansion path nincreasing returns to scalendecreasing returns to scalenoutput elasticitynpower prod
4、uction functionnproductivity growthnlabor productivitynmultifactor productivity.Production FunctionsnProperties of Production FunctionsnProduction functions are determined by technology,equipment and input prices.nDiscrete production functions are lumpy.nContinuous production functions employ inputs
5、 in small increments.Returns to Scale and Returns to a FactornReturns to scale measure output effect of increasing all inputs.nReturns to a factor measure output effect of increasing one input.Total,Marginal,and Average ProductnTotal ProductTotal product is total output.Marginal ProductMarginal prod
6、uct is the change in output caused by increasing input use.If MPX=Q/X 0,total product is rising.If MPX=Q/X AP,AP is increasingWhen MP AP,AP is decreasingWhen MP=AP,AP is at its maximum.Law of Diminishing Returns to a FactornDiminishing Returns to a Factor ConceptThe law of diminishing returns(the la
7、w of diminishing marginal returns)states that the marginal product of a variable factor must eventually decline as more of the variable factor is combined with other fixed resources.Law of Diminishing Returns to a FactornIllustration of Diminishing Returns to a FactoroTypically,increased specializat
8、ion and better utilization of other factors in the production process allow factor productivity to grow.oIn practice it is very rare to see input combinations that exhibit increasing returns for any factor.With increasing returns to a factor,an industry would come to be dominated by one very large p
9、roducerand this is seldom the case.Input combinations in the range of diminishing returns are commonly observed.Input Combination ChoicenProduction IsoquantsIsoquant denotes a curve that represents the different combinations of inputs that can be efficiently used to produce a given level of output.T
10、echnical efficiency is least-cost production of a target level of output.Representative Isoquants for Table 5.1.Input Combination ChoicenInput Factor SubstitutionIsoquant shape shows input substitutability.C-shaped isoquants are common and imply imperfect substitutability.Isoquants for Inputs with V
11、arying Degrees of Substitutability:(A)Electric Power Generation;(B)Bicycle Production.Isoquants for Inputs with Varying Degrees of Substitution:(C)Dress Production.Marginal Rate of Technical SubstitutionnThe marginal rate of technical substitution(MRTS)is the amount of one input factor that must be
12、substituted for one unit of another input factor to maintain a constant level of output.MRTS=Y/X=Slope of an IsoquantnThe marginal rate of technical substitution usually diminishes as the amount of substitution increases.nAt the extremes,isoquants may even become positively sloped,indicating that th
13、e range over which input factors can be substituted for each other is limited.Marginal Rate of Technical SubstitutionnRational Limits of Input SubstitutionMPX0 or MPY 1 implies increasing returns.nQ=1 implies constant returns.nQ 1 implies decreasing returns.nReturns to Scale Estimation.Production Fu
14、nction EstimationnCubic Production FunctionsDisplay variable returns to scale.First increasing,then decreasing returns are common.nPower Production FunctionsAllow marginal productivity of each input to vary with employment of all inputs.Productivity MeasurementnHow Is Productivity Measured?Productiv
15、ity measurement is the responsibility of the Bureau of Labor Statistics(since 1800s).Productivity growth is the rate of change in output per unit of input.Labor productivity is the change in output per worker hour.nUses and Limitations of Productivity DataQuality changes make productivity measuremen
16、t difficult.Problems 1nDetermine whether the following production functions exhibit constant,increasing,or decreasing returns to scale.nQ=0.5X+2Y+40ZnQ=3L+10K+500nQ=4A+6B+8ABnQ=7L2+5LK+2K2A.Q=10L0.5K0.3.Problems 2n The Route 66 Truck Stop,Inc.,sells gasoline to both self-service and full-service cus
17、tomers.Those who pump their own gas benefit from the lower self-service price of$1.80 per gallon.Full-service customers enjoy the service of an attendant,but they pay a higher price of$1.90 per gallon.The company has observed the following relation between the number of attendants employed per day a
18、nd full-service output:.Number of Attendants per DayFull-Service Output(gallons)001200023800354004680058000Route 66 Truck Stop,Inc.nA.Construct a table showing the net marginal revenue product derived from attendant employment.nB.How many attendants would Route 66 employ at a daily wage rate of$160(
19、including wages and benefits)?nC.What is the highest daily wage rate Route 66 would pay to hire four attendants per day?.Problems 3 Will Truman&Associates,LLC is a successful Manhattan-based law firm.Worker productivity at the firm is measured in billable hours,which vary between partners and associ
20、ates.Partner time is billed to clients at a rate of$250 per hour,whereas associate time is billed at a rate of$125 per hour.On average,each partner generates 25 billable hours per 40hour workweek,with 15 hours spent on promotion,administrative,and supervisory responsibilities.Associates generate an
21、average of 35 billable hours per 40hour workweek and spend 5 hours per week in administrative and training meetings.Variable overhead costs average 50%of revenues generated by partners and,given supervisory requirements,60%of revenues generated by associates.nA.Calculate the annual(50 workweek)net m
22、arginal revenue product of partners and associates.nB.If partners earn$175,000 and associates earn$70,000 per year,does the company have an optimal combination of partners and associates?If not,why not?Make your answer explicit and support any recommendations for change.Problems 4 Ticket Services,In
23、c.,offers ticket promotion and handling services for concerts and sporting events.The Sherman Oaks,California,branch office makes heavy use of spot radio advertising on WHAMAM,with each 30-second ad costing$100.During the past year,the following relation between advertising and ticket sales per even
24、t has been observed:Sales(units)=5,000+100A-0.5A2 Sales(units)/Advertising=100-A Here,A represents a 30-second radio spot ad,and sales are measured in numbers of tickets.Rachel Green,manager for the Sherman Oaks office,has been asked to recommend an appropriate level of advertising.In thinking about
25、 this problem,Green noted its resemblance to the optimal resource employment problem studied in a managerial economics course.The advertising/sales relation could be thought of as a production function,with advertising as an input and sales as the output.The problem is to determine the profit-maximi
26、zing level of employment for the input,advertising,in this“production”system.Green recognized that a measure of output value was needed to solve the problem.After reflection,Green determined that the value of output is$2 per ticket,the net marginal revenue earned by Ticket Services(price minus all m
27、arginal costs except advertising).nA.Continuing with Greens production analogy,what is the marginal product of advertising?nB.What is the rule for determining the optimal amount of a resource to employ in a production system?Explain the logic underlying this rule.nC.Using the rule for optimal resource employment,determine the profit-maximizing number of radio ads.
