Chapter 3THEORY OF FIRMS BEHAVIORMicroeconomics II

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Topics to be DiscussedPart 1: ProductionThe Technology of ProductionProduction with Two Variable InputsReturns to Scale

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IntroductionOur study of consumer behavior was broken down into 3 steps Describing consumer preferencesConsumers face budget constraintsConsumers choose to maximize utilityProduction decisions of a firm are similar to consumer decisionsCan also be broken down into three steps

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Production Decisions of a FirmProduction TechnologyDescribe how inputs can be transformed into outputsInputs: land, labor, capital & raw materialsOutputs: cars, desks, books, etc.Firms can produce different amounts of outputs using different combinations of inputs

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Production Decisions of a FirmCost ConstraintsFirms must consider prices of labor, capital and other inputsFirms want to minimize total production costs partly determined by input pricesAs consumers must consider budget constraints, firms must be concerned about costs of production

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Production Decisions of a FirmInput 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, may choose to produce with more labor and less capital

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Production Decisions of a FirmIf a firm is a cost minimize, we can also studyHow total costs of production varies with outputHow does the firm choose the quantity to maximize its profitsWe can represent the firms production technology in for form of a production function

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The 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) Shows what is technically feasible when the firm operates efficiently

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The 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 technologyIf technology increases, more output can be produced for a given level of inputs

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The Technology of ProductionShort RunPeriod of time in which quantities of one or more production factors cannot be changed.These inputs are called fixed inputs.Long-runAmount of time needed to make all production inputs variable.Short run and long run are not time specific

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Production: Two Variable InputsFirm can produce output by combining different amounts of labor and capitalIn the long-run, capital and labor are both variable.We can look at the output we can achieve with different combinations of capital and labor Table 6.4

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Production: Two Variable Inputs

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Production: Two Variable InputsThe information can be represented graphically using isoquantsCurves showing all possible combinations of inputs that yield the same outputCurves are smooth to allow for use of fractional inputsCurve 1 shows all possible combinations of labor and capital that will produce 55 units of output

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Isoquant MapEx: 55 units of output can be produced with 3K & 1L (pt. A) OR 1K & 3L (pt. D)

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Production: 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-run.

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Production: Two Variable InputsDiminishing Returns to Capital with IsoquantsHolding labor constant at 3 increasing capital from 0 to 1 to 2 to 3.Output increases at a decreasing rate (0, 55, 20, 15) due to diminishing returns from capital in short-run and long-run.

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Diminishing ReturnsIncreasing labor holding capital constant (A, B, C) ORIncreasing capital holding labor constant (E, D, C

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Production: Two Variable InputsSubstituting Among InputsCompanies must decide what combination of inputs to use to produce a certain quantity of output There is a trade-off between inputs allowing them to use more of one input and less of another for the same level of output.

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Production: Two Variable InputsSubstituting Among Inputs Slope of the isoquant shows how one input can be substituted for the other and keep the level of output the same.Positive 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 input is used, so that output remains constant.

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Production: Two Variable InputsThe marginal rate of technical substitution equals:

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Production: Two Variable InputsAs increase labor to replace capitalLabor becomes relatively less productiveCapital becomes relatively more productiveNeed less capital to keep output constantIsoquant becomes flatter

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Marginal Rate ofTechnical SubstitutionLabor per month1234123455Capital per yearSlope measures MRTSMRTS decreases as move down the indifference curve

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MRTS and Marginal ProductsIf we are holding output constant

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MRTS and IsoquantsWe assume there is diminishing MRTSIncreasing labor in one unit increments from 1 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 convex.There is a relationship between MRTS and marginal products of inputs

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Isoquants: Special CasesTwo extreme cases show the possible range of input substitution in productionPerfect substitutesMRTS is constant at all points on isoquantSame output can be produced with a lot of capital or a lot of labor or a balanced mix

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Perfect SubstitutesLaborper monthCapitalper monthSame output can be reached with mostly capital or mostly labor (A or C) or with equal amount of both (B)

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Isoquants: Special CasesExtreme cases (cont.)Perfect ComplementsFixed proportions production functionThere is no substitution available between inputsThe output can be made with only a specific proportion of capital and laborCannot increase output unless increase both capital and labor in that specific proportion

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Fixed-ProportionsProduction FunctionLabor per monthCapitalpermonthSame output can only be produced with one set of inputs.

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Returns 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 outputCan change the scale of production by increasing all inputs in proportionIf double inputs, output will most likely increase but by how much?

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Returns to ScaleRate at which output increases as inputs are increased proportionatelyIncreasing returns to scaleConstant returns to scaleDecreasing returns to scale

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Returns to ScaleIncreasing returns to scale: output more than doubles when all inputs are doubledLarger output associated with lower cost (cars)One firm is more efficient than many (utilities)The isoquants get closer together

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Increasing Returns to ScaleThe isoquants move closer togetherA

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Returns to ScaleConstant returns to scale: output doubles when all inputs are doubledSize does not affect productivityMay have a large number of producersIsoquants are equidistant apart

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Returns to ScaleConstant Returns: Isoquants are equally spaced

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Returns to ScaleDecreasing returns to scale: output less than doubles when all inputs are doubledDecreasing efficiency with large sizeReduction of entrepreneurial abilitiesIsoquants become farther apart

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Returns to Scale: Carpet IndustryThe carpet industry has grown from a small industry to a large industry with some very large firms.There are four relatively large manufactures along with a number of smaller onesGrowth has come fromIncreased consumer demandMore efficient production reducing costsInnovation and competition have reduced real prices

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The U.S. Carpet Industry

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Returns to Scale: Carpet IndustrySome growth can be explained by returns to scaleCarpet production is highly capital intensiveHeavy upfront investment in machines for carpet productionIncreases in scale of operating have occurred by putting in larger and more efficient machines into larger plants

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Returns to Scale: Carpet Industry ResultsLarge ManufacturersIncreased in machinery & laborDoubling inputs has more than doubled outputEconomies of scale exist for large producers

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Returns to Scale: Carpet Industry ResultsSmall ManufacturersSmall increases in scale have little or no impact on outputProportional increases in inputs increase output proportionallyConstant returns to scale for small producers

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Returns to Scale: Carpet IndustryFrom this we can see that the carpet industry is one where:There are constant returns to scale for relatively small plantsThere are increasing returns to scale for relatively larger plantsThese are however limitedEventually reach decreasing returns

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Chapter 3 (cont)Part 2: The Cost of Production

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Topics to be DiscussedMeasuring Cost: Which Costs Matter?Cost in the Long RunLong-Run Versus Short-Run Cost CurvesProduction with Two Outputs--Economies of Scope

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Measuring Cost:Which Costs Matter?Accountants tend to take a retrospective view of firms costs, where as economists tend to take a forward-looking viewAccounting CostActual expenses plus depreciation charges for capital equipmentEconomic CostCost to a firm of utilizing economic resources in production, including opportunity cost

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Measuring Cost:Which Costs Matter?Economic costs distinguish between costs the firm can control and those it cannotConcept of opportunity cost plays an important roleOpportunity costCost associated with opportunities that are foregone when a firms resources are not put to their highest-value use.

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Opportunity CostAn ExampleA firm owns its own building and pays no rent for office spaceDoes this mean the cost of office space is zero?The building could have been rented insteadForegone rent is the opportunity cost of using the building for production and should be included in economic costs of doing business

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Opportunity CostA person starting their own business must take into account the opportunity cost of their timeCould have worked elsewhere making a competitive salary Accountants and economists often treat depreciation differently as well

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Measuring Cost:Which Costs Matter?Although opportunity costs are hidden and should be taken into account, sunk costs should notSunk CostExpenditure that has been made and cannot be recoveredShould not influence a firms future economic decisions.

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Sunk CostFirm buys a piece of equipment that cannot be converted to another useExpenditure on the equipment is a sunk costHas no alternative use so cost cannot be recovered opportunity cost is zeroDecision to buy the equipment might have been good or bad, but now does not matter

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Prospective Sunk CostAn ExampleFirm is considering moving its headquartersA firm paid $500,000 for an option to buy a building.The cost of the building is $5 million or a total of $5.5 million.The firm finds another building for $5.25 million.Which building should the firm buy?

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Prospective Sunk CostExample (cont.)The first building should be purchased.The $500,000 is a sunk cost and should not be considered in the decision to buyWhat should be considered isSpending an additional $5,250,000 orSpending an additional $5,000,000

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Measuring Cost:Which Costs Matter?Some costs vary with output, while some remain the same no matter amount of outputTotal cost can be divided into:Fixed CostDoes not vary with the level of outputVariable Cost Cost that varies as output varies

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Fixed and Variable CostsTotal output is a function of variable inputs and fixed inputs. Therefore, the total cost of production equals the fixed cost (the cost of the fixed inputs) plus the variable cost (the cost of the variable inputs), or

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Fixed and Variable CostsWhich costs are variable and which are fixed depends on the time horizonShort time horizon most costs are fixedLong time horizon many costs become variableIn determining how changes in production will affect costs, must consider if affects fixed or variable costs

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Fixed Cost Versus Sunk CostFixed cost and sunk cost are often confusedFixed CostCost paid by a firm that is in business regardless of the level of outputSunk Cost Cost that have been incurred and cannot be recovered

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Measuring Cost:Which Costs Matter?Personal ComputersMost costs are variable Largest component: laborSoftwareMost costs are sunkInitial cost of developing the software

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Marginal and Average CostIn completing a discussion of costs, must also distinguish betweenAverage CostMarginal CostAfter definition of costs is complete, one can consider the analysis between short-run and long-run costs

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Measuring CostsMarginal Cost (MC):The cost of expanding output by one unit.Fixed cost have no impact on marginal cost, so it can be written as:

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Measuring CostsAverage Total Cost (ATC)Cost per unit of outputAlso equals average fixed cost (AFC) plus average variable cost (AVC).

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Measuring CostsAll the types of costs relevant to production have now been discussedCan now discuss how they differ in the long and short runCosts that are fixed in the short run may not be fixed in the long runTypically in the long run, most if not all costs are variable

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Cost in the Long RunIn the long run a firm can change all of its inputsIn making cost minimizing choices, must look at the cost of using capital and labor in production decisions

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Cost in the Long RunCapital is either rented/leased or purchasedWe will consider capital rented as if it were purchasedAssume Delta is considering purchasing an airplane for $150 millionPlane lasts for 30 years$5 per year economic depreciation for the plane

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Cost in the Long RunDelta needs to compare its revenues and costs on an annual basisIf the firm had not purchased the plane, it would have earned interest on the $150 millionForgone interest is an opportunity cost that must be consideredAssume the interest rate 10 percent

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User Cost of CapitalThe user cost of capital must be consideredThe annual cost of owning and using the airplane instead of selling or never buying itSum of the economic depreciation and the interest (the financial return) that could have been earned had the money been invested elsewhere

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Cost in the Long RunUser Cost of Capital = Economic Depreciation + (Interest Rate)*(Value of Capital)= $5 mil + (.10)($150 million)Year 1 = $5 million + (.10)($150 million) = $20 millionYear 10 = $5 million +(.10)($100 million) = $15 million

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Cost in the Long RunUser cost can also be described as;Rate per dollar of capital, rr = Depreciation Rate + Interest RateIn our example, depreciation rate was 3.33% and interest was 10% so r = 3.33% + 10% = 13.33%

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Cost Minimizing Input ChoiceHow do we put all this together to select inputs to produce a given output at minimum cost?AssumptionsTwo Inputs: Labor (L) & capital (K)Price of labor: wage rate (w)The price of capital r = depreciation rate + interest rateOr rental rate if not purchasingThese are equal in a competitive capital market

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Cost in the Long RunThe Isocost LineA line showing all combinations of L & K that can be purchased for the same costTotal cost of production is sum of firms labor cost, wL and its capital cost rKC = wL + rKFor each different level of cost, the equation shows another isocost line

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Cost in the Long RunRewriting C as an equation for a straight line:K = C/r - (w/r)LSlope of 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 cost.

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Choosing Inputs We will address how to minimize cost for a given level of output by combining isocosts with isoquantsWe choose the output we wish to produce and then determine how to do that at minimum costIsoquant is the quantity we wish to produceIsocost is the combination of K and L that gives a set cost

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Producing a Given Output at Minimum CostIsocost C2 shows quantity Q1 can be produced withcombination K2L2 or K3L3.However, both of theseare higher cost combinationsthan K1L1.Q1 is an isoquant for output Q1.There are three isocost lines, of which 2 are possible choices in which to produce Q1

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Input Substitution When an Input Price ChangeIf the price of labor changes, then the slope of the isocost line change, w/rIt now takes a new quantity of labor and capital to produce the outputIf price of labor increases relative to price of capital, and capital is substituted for labor

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Input Substitution When an Input Price ChangeThe new combination of K and L is used to produce Q1.Combination B is used in place of combination A.If the price of laborrises, the isocost curvebecomes steeper due to the change in the slope -(w/L).Labor per yearCapitalperyear

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Cost in the Long RunHow does the isocost line relate to the firms production process?

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Cost in the Long RunThe minimum cost combination can then be written as:Minimum cost for a given output will occur when each dollar of input added to the production process will add an equivalent amount of output.

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Cost in the Long RunIf w = $10, r = $20, and MPL = MPK, which input would be used more of?Labor because it is cheaperIncreasing labor lowers MPLDecreasing capital raises MPKSubstitute labor for capital until

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Cost in the Long RunCost minimization with Varying Output LevelsFor each level of output, there is an isocost curve showing minimum cost for that output levelA firms expansion path shows the minimum cost combinations of labor and capital at each level of output.Slope equals K/L

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A Firms Expansion PathThe expansion path illustratesthe least-cost combinations oflabor and capital that can be used to produce each level ofoutput in the long-run.50

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Expansion Path & Long-run CostsFirms expansion path has same information as long-run total cost curveTo move from expansion path to LR cost curveFind tangency with isoquant and isocostDetermine min cost of producing the output level selectedGraph output-cost combination

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A Firms Long-Run Total Cost Curve

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Long-Run Versus Short-Run Cost CurvesIn the short run some costs are fixedIn the long run firm can change anything including plant sizeCan produce at a lower average cost in long run than in short runCapital and labor are both flexibleWe can show this by holding capital fixed in the short run and flexible in long run

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The Inflexibility of Short-Run ProductionCapital is fixed at K1To produce q1, min cost at K1,L1If increase output to Q2, min costis K1 and L3 in short runLabor per yearCapitalperyearIn LR, can change capital and min costs falls to K2 and L2

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Long-Run VersusShort-Run Cost CurvesLong-Run Average Cost (LAC)Most important determinant of the shape of the LR AC and MC curves is relationship between scale of the firms operation and inputs required to min costConstant Returns to ScaleIf input is doubled, output will doubleAC cost is constant at all levels of output.

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Long-Run Versus Short-Run Cost CurvesIncreasing Returns to ScaleIf input is doubled, output will more than doubleAC decreases at all levels of output.Decreasing Returns to ScaleIf input is doubled, output will less than doubleAC increases at all levels of output

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Long-Run Versus Short-Run Cost CurvesIn the long-run:Firms experience increasing and decreasing returns to scale and therefore long-run average cost is U shaped.Source of U-shape is due to returns to scale rather than diminishing marginal returns to a factor of productionLong-run marginal cost curve measures the change in long-run total costs as output is increased by 1 unit

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Long-Run Versus Short-Run Cost CurvesLong-run marginal cost leads long-run average cost:If LMC < LAC, LAC will fallIf LMC > LAC, LAC will riseTherefore, LMC = LAC at the minimum of LACIn special case where LAC if constant, LAC and LMC are equal

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Long-Run Average and Marginal CostOutputCost($ per unitof output

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Long Run CostsAs output increases, firms AC of producing is likely to decline to a pointOn a larger scale, workers can better specializeScale can provide flexibility managers can organize production more effectivelyFirm may be able to get inputs at lower cost if it can get quantity discounts. Lower prices might lead to different input mix

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Long Run CostsAt some point, AC will begin to increaseFactory space and machinery may make it more difficult for workers to do their job efficientlyManaging a larger firm may become more complex and inefficient as the number of tasks increaseBulk discounts can no longer be utilized. Limited availability of inputs may cause price to rise

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Long Run CostsWhen input proportions change, the firms expansion path is no longer a straight lineConcept of return to scale no longer appliesEconomies of scale reflects input proportions that change as the firm change its level of productionUnlike returns to scale, economies of scale allows inputs proportions vary

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Economies and Diseconomies of ScaleEconomies of ScaleIncrease in output is greater than the increase in inputs.Diseconomies of ScaleIncrease in output is less than the increase in inputs.U-shaped LAC shows economies of scale for relatively low output levels and diseconomies of scale for higher levels

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Long Run CostsIncreasing Returns to ScaleOutput more than doubles when the quantities of all inputs are doubledEconomies of ScaleDoubling of output requires less than a doubling of cost

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Long Run CostsEconomies of scale are measured in terms of cost-output elasticity, ECEC is the percentage change in the cost of production resulting from a 1-percent increase in output

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Long Run CostsEC is equal to 1, MC = ACCosts increase proportionately with outputNeither economies nor diseconomies of scaleEC < 1 when MC < ACEconomies of scaleBoth MC and AC are decliningEC > 1 when MC > ACDiseconomies of scaleBoth MC and AC are rising

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Long-Run Versus Short-Run Cost CurvesWe will use short and long-run cost to determine the optimal plant sizeWe can show the short run average costs for 3 different plant sizesThis decision is important because once built, the firm may not be able to change plant size for a while

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Long-Run Cost withConstant Returns to ScaleThe optimal plant size will depend on the anticipated outputIf expect to produce q0, then should build smallest plant: AC = $8If produce more, like q1, AC risesIf expect to produce q2, middle plant is least costIf expect to produce q3, largest plant is best

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Long-Run Cost with Economiesand Diseconomies of Scale

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Long-Run Cost withConstant Returns to ScaleWhat is the firms long-run cost curve?Firms can change scale to change output in the long-run.The long-run cost curve is the dark blue portion of the SAC curve which represents the minimum cost for any level of output.Firm will always choose plant that minimizes the average cost of production

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Long-Run Cost withConstant Returns to ScaleThe long-run average cost curve envelopes the short-run average cost curvesThe LAC curve exhibits economies of scale initially but exhibits diseconomies at higher output levels

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Production with Two Outputs Economies of ScopeMany firms produce more than one product and those product are closely linkedExamples:Chicken farm--poultry and eggsAutomobile company--cars and trucksUniversity--Teaching and research

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Production with Two Outputs Economies of ScopeAdvantagesBoth use capital and labor.The firms share management resources.Both use the same labor skills and type of machinery.

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Production with Two Outputs Economies of ScopeFirms must choose how much of each to produce.The alternative quantities can be illustrated using product transformation curvesCurves showing the various combinations of two different outputs (products) that can be produced with a given set of inputs

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Product Transformation CurveNumber of carsNumberof tractorsO1 illustrates a low levelof output. O2 illustratesa higher level of output withtwo times as much labor and capital.Each curve showscombinations of output with a given combination of L & K.

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Product Transformation CurveProduct transformation curves are negatively slopeTo get more of one output, must give up some of the other outputConstant returns exist in this exampleSecond curve lies twice as far from origin as the first curveCurve is concaveJoint production has its advantages

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Production with Two Outputs Economies of ScopeThere is no direct relationship between economies of scope and economies of scale.May experience economies of scope and diseconomies of scaleMay have economies of scale and not have economies of scope

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Production with Two Outputs Economies of ScopeThe degree of economies of scope (SC) can be measured by percentage of cost saved producing two or more products jointly:

C(q1) is the cost of producing q1C(q2) is the cost of producing q2C(q1,q2) is the joint cost of producing both products

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Production with Two Outputs Economies of ScopeWith economies of scope, the joint cost is less than the sum of the individual costsInterpretation:If SC > 0 Economies of scopeIf SC < 0 Diseconomies of scopeThe greater the value of SC, the greater the economies of scope

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