1、AnnouncementProblem Set 2:Due on April 9Reducing RiskConsumers are generally risk averse and therefore want to reduce riskThree ways consumers attempt to reduce risk are:1.Diversification2.Insurance3.Obtaining more informationReducing RiskDiversification Reducing risk by allocating resources to a va
2、riety of activities whose outcomes are not closely relatedExample:Suppose a firm has a choice of selling air conditioners,heaters,or both The probability of it being hot or cold is 0.5 How does a firm decide what to sell?Income from Sales of AppliancesHot WeatherCold WeatherAir conditioner sales$30,
3、000$12,000Heater sales12,00030,000Diversification ExampleIf the firm sells only heaters or air conditioners their income will be either$12,000 or$30,000Their expected income would be:1/2($12,000)+1/2($30,000)=$21,000Diversification ExampleIf the firm divides their time evenly between appliances,thei
4、r air conditioning and heating sales would be half their original valuesIf it were hot,their expected income would be$15,000 from air conditioners and$6,000 from heaters,or$21,000If it were cold,their expected income would be$6,000 from air conditioners and$15,000 from heaters,or$21,000Diversificati
5、on ExampleWith diversification,expected income is$21,000 with no riskBetter off diversifying to minimize riskFirms can reduce risk by diversifying among a variety of activities that are not closely relatedReducing Risk The Stock MarketIf invest all money in one stock,then take on a lot of risk If th
6、at stock loses value,you lose all your investment valueCan spread risk out by investing in many different stocks or investments Ex:Mutual fundsReducing Risk InsuranceRisk averse are willing to pay to avoid riskIf the cost of insurance equals the expected loss,risk averse people will buy enough insur
7、ance to recover fully from a potential financial lossThe Decision to InsureReducing Risk InsuranceFor the risk averse consumer,guarantee of same income regardless of outcome has higher utility than facing the probability of riskExpected utility with insurance is higher than withoutThe Law of Large N
8、umbersInsurance companies know that although single events are random and largely unpredictable,the average outcome of many similar events can be predictedWhen insurance companies sell many policies,they face relatively little riskWhy insurance companies generally dont insure earthquake and war?Why
9、nationwide compulsory health insurance?The Law of Large Numbers:An ExampleWhy pooling individual and independent random outcomes will reduce risk substantially?Suppose N farmers and each faces a random yearly output;they agree to pool their outputs and each gets the meandi iareXNXii.),(2Risk Spreadi
10、ng01)(12_1_NXVarXXNXNNNiiNReducing Risk Actuarially FairInsurance companies can be sure total premiums paid will equal total money paid outCompanies set the premiums so money received will be enough to pay expectedlossesReducing Risk Actuarially FairSome events with very little probability of occurr
11、ence such as floods and earthquakes are no longer insured privately Cannot calculate true expected values and expected losses Governments have had to create insurance for these types of events Ex:National Flood Insurance ProgramChapter 6ProductionTopics to be DiscussedThe Technology of ProductionPro
12、duction with One Variable Input IsoquantsProduction with Two Variable InputsReturns to ScaleIntroductionOur study of consumer behavior was broken down into 3 steps:Describing consumer preferences Consumers face budget constraints Consumers choose to maximize utilityProduction decisions of a firm are
13、 similar to consumer decisions Can also be broken down into three stepsProduction Decisions of a Firm1.Production Technology Describe how inputs can be transformed into outputsInputs:land,labor,capital and raw materialsOutputs:cars,desks,books,etc.Firms can produce different amounts of outputs using
14、 different combinations of inputsProduction Decisions of a Firm2.Cost Constraints Firms must consider prices of labor,capital and other inputs Firms want to minimize total production costs partly determined by input prices As consumers must consider budget constraints,firms must be concerned about c
15、osts of productionProduction Decisions of a Firm3.Input ChoicesGiven input prices and production technology,the firm must choose how much of each input to use in producing outputGiven prices of different inputs,the firm may choose different combinations of inputs to minimize costsIf labor is cheap,f
16、irm may choose to produce with more labor and less capitalProduction Decisions of a FirmIf a firm is a cost minimizer,we can also study How total costs of production vary with output How the firm chooses the quantity to maximize its profitsWe can represent the firms production technology in the form
17、 of a productionfunctionThe Technology of ProductionProduction Function:Indicates the highest output(q)that a firm can produce for every specified combination of inputs For simplicity,we will consider only labor(L)and capital(K)Physical vs.financial capital Shows what is technically feasible when th
18、e firm operates efficientlyThe Technology of ProductionThe production function for two inputs:q=F(K,L)Output(q)is a function of capital(K)and labor(L)The production function is true for a given technology If technology increases,more output can be produced for a given level of inputsProduction Funct
19、ionsy denotes the output level.The technologys production functionstates the maximum amount of output possible from an input bundle(assuming technical efficiency)yf xxn (,)1Technology SetsA production plan is an input bundle and an output level;(x1,xn,y).A production plan is feasible ifThe collectio
20、n of all feasible production plans is the technology set.yf xxn (,)1The Technology of ProductionShort Run versus Long Run It takes time for a firm to adjust production from one set of inputs to another Firms must consider not only what inputs can be varied but over what period of time that can occur
21、 We must distinguish between long run and short runThe Technology of ProductionShort Run Period of time in which quantities of one or more production factors cannot be changed These inputs are called fixed inputsLong Run Amount of time needed to make all production inputs variableShort run and long
22、run are not time specificProduction:One Variable InputWe will begin looking at the short run when only one input can be variedWe assume capital is fixed and labor is variable Output can only be increased by increasing labor Must know how output changes as the amount of labor is changed Production Fu
23、nctionsy=f(x)is theproductionfunction.xxInput LevelOutput Levelyy=f(x)is the maximal output level obtainable from x input units.One input,one outputProduction SetsxxInput LevelOutput LevelyOne input,one outputy”The technologysetTechnology SetsxxInput LevelOutput LevelyOne input,one outputy”The techn
24、ologysetTechnicallyinefficientplansTechnicallyefficient plansProduction:One Variable InputFirms make decisions based on the benefits and costs of productionSometimes useful to look at benefits and costs on an incremental basis How much more can be produced when at incremental units of an input?Somet
25、imes useful to make comparison on an average basisProduction:One Variable InputAverage product of Labor-Output per unit of a particular productMeasures the productivity of a firms labor in terms of how much,on average,each worker can produceLqInput LaborOutput APLProduction:One Variable InputMargina
26、l Product of Labor additional output produced when labor increases by one unitChange in output divided by the change in laborLqInput LaborOutput MPLAt point D,output is maximized.Labor per MonOutputper Month023456789101Total Product60112ABCDProduction:One Variable InputAverage ProductProduction:One
27、Variable Input1020Outputper Worker30802345679101Labor per MonthEMarginal ProductProduction:One Variable InputFrom the previous example,we can see that as we increase labor the additional output produced declinesLaw of Diminishing Marginal Returns:As the use of an input increases with other inputs fi
28、xed,the resulting additions to output will eventually decreaseNote that this law occurs when other inputs are fixedLaw of Diminishing Marginal ReturnsTypically applies only for the short run when one variable input is fixedCan be used for long-run decisions to evaluate the trade-offs of different pl
29、ant configurationsAssumes the quality of the variable input is constantLaw of Diminishing Marginal ReturnsAssumes a constant technology Changes in technology will cause shifts in the total product curve More output can be produced with same inputs Labor productivity can increase if there are improve
30、ments in technology,even though any given production process exhibits diminishing returns to laborThe Effect of Technological ImprovementOutput50100Labor pertime period023456789101AO1CO3O2BMoving from A to B to C,labor productivity is increasing over timeMalthus and the Food CrisisMalthus predicted
31、mass hunger and starvation as diminishing returns limited agricultural output and the population continued to growWhy did Malthus prediction fail?Did not take into account changes in technology Although he was right about diminishing marginal returns to laborProduction:Two Variable InputsFirm can pr
32、oduce output by combining different amounts of labor and capitalIn the long run,capital and labor are both variableWe can look at the output we can achieve with different combinations of capital and labor Production:Two Variable InputsThe information can be represented graphically using isoquants Cu
33、rves showing all possible combinations of inputs that yield the same outputCurves are smooth to allow for use of fractional inputs Curve 1 shows all possible combinations of labor and capital that will produce 55 units of outputIsoquant MapLabor per yea12345q1=55q2=75q3=9012345Capitalper yearDEABCPr
34、oduction:Two Variable InputsDiminishing Returns to Labor with IsoquantsHolding capital at 3 and increasing labor from 0 to 1 to 2 to 3 Output increases at a decreasing rate(0,55,20,15)illustrating diminishing marginal returns from labor in the short run and long runProduction:Two Variable InputsSubs
35、tituting Among Inputs Slope of the isoquant shows how one input can be substituted for the other and keep the level of output the same The negative of the slope is the marginal rate of technical substitution(MRTS)Amount by which the quantity of one input can be reduced when one extra unit of another
36、 input is used,so that output remains constantProduction:Two Variable InputsThe marginal rate of technical substitution equals:)(qLKMRTSInputLaborinChangeInputCapitalinChangeMRTS of level fixed a forMRTS and IsoquantsWe assume there is diminishing MRTS Increasing labor in one unit increments from 1
37、to 5 results in a decreasing MRTS from 1 to 1/2 Productivity of any one input is limitedDiminishing MRTS occurs because of diminishing returns and implies isoquants are convexThere is a relationship between MRTS and marginal products of inputsMRTS and Marginal ProductsIf we are holding output consta
38、nt,the net effect of increasing labor and decreasing capital must be zeroUsing changes in output from capital and labor we can see0 K)d)(MP L)d)(MPKLMRTS and Marginal ProductsRearranging equation,we can see the relationship between MRTS and MPsMRTSdLdKMPddLddK)()(LKLKL(MPK)(MP-(MP0 K)(MP L)(MPPerfec
39、t SubstitutesLaborper monthCapitalper monthQ1Q2Q3ABCFixed-ProportionsProduction FunctionLaborper monthCapitalpermonthL1K1Q1AQ2Q3BCWell-behaved TechnologyMonotonicity:if we increase the amount of at least one of the inputs,it should be possible to produce at least as much output as we producing origi
40、nallyThis is sometimes referred to as the property of free disposalWell-Behaved Technologies-Convexityx2x1x2x1x2x1yReturns to ScaleIn addition to discussing the tradeoff between inputs to keep production the sameHow does a firm decide,in the long run,the best way to increase output?Can change the sc
41、ale of production by increasing all inputs in proportion?If double inputs,output will most likely increase but by how much?Returns to ScaleRate at which output increases as inputs are increased proportionately Increasing returns to scale Constant returns to scale Decreasing returns to scaleConstant
42、Return to Scale0),.,(),.,(2121txxxfttxtxtxfnnDiminishing MP and CRTS0)1(0)()(),()10(12212121211112112121121xxxfxxxfytxxttxtxtxtxfxxyIncreasing Return to Scale1),.,(),.,(2121tanyforxxxfttxtxtxfnnDecreasing Return to Scale1),.,(),.,(2121tanyforxxxfttxtxtxfnnReturns-to-Scaley=f(x)xxInput LevelOutput Le
43、velyOne input,one output2x2yConstantreturns-to-scaleReturns-to-Scaley=f(x)xxInput LevelOutput Levelf(x)One input,one output2xf(2x)2f(x)Decreasingreturns-to-scaleReturns-to-Scaley=f(x)xxInput LevelOutput Levelf(x)One input,one output2xf(2x)2f(x)Increasingreturns-to-scaleReturns-to-Scaley=f(x)xInput L
44、evelOutput LevelOne input,one outputDecreasingreturns-to-scaleIncreasingreturns-to-scaleExamples of RTS:Cobb-Douglas FunctionDRSIRSCRSxAxy11121Examples of Returns-to-ScaleThe Cobb-Douglas production function isThe Cobb-Douglas technologys returns-to-scale isconstant if a1+an=1increasing if a1+an 1de
45、creasing if a1+an 1.nanaaxxxy2121ykkxkxkxnnaaanaa121)()()(21Chapter 7The Cost of ProductionTopics to be DiscussedCost MinimizationCosts in the Short Run and Long RunMeasuring Cost:Which Costs Matter?Long-Run Versus Short-Run Cost CurvesCost Minimizing Input ChoiceHow does a firm select inputs to pro
46、duce a given output at minimum cost?Assumptions Two Inputs:Labor(L)and capital(K)Price of labor:wage rate(w)The price of capital(r)r=depreciation rate+interest rate Or rental rate if not purchasing These are equal in a competitive capital marketThe Isocost LineThe Isocost Line A line showing all com
47、binations of L&K that can be purchased for the same cost Total cost of production is sum of firms labor cost,wL,and its capital cost,rK:C=wL+rK For each different level of cost,the equation shows another isocost lineThe Isocost LineRewriting C as an equation for a straight line:K=C/r-(w/r)L Slope of
48、 the isocost:-(w/r)is the ratio of the wage rate to rental cost of capital.This shows the rate at which capital can be substituted for labor with no change in costrwLKddChoosing Inputs We will address how to minimize cost for a given level of output by combining isocosts with isoquantsWe choose the
49、output we wish to produce and then determine how to do that at minimum cost Isoquant is the quantity we wish to produce Isocost is the combination of K and L that gives a set cost We assume that firms face no liquidity constraintsProducing a Given Output at Minimum CostLabor per yearCapitalperyearIs
50、ocost C2shows quantity Q1can be produced withcombination K2,L2 or K3,L3.However,both of theseare higher cost combinationsthan K1,L1.Q1Q1is an isoquant for output Q1.There are three isocost lines,of which 2 are possible choices in which to produce Q1.C0C1C2AK1L1K3L3K2L2Input Substitution When an Inpu
