Slide 1Basic Concepts of Production TheoryShort-Run versus Long-Run DecisionsThe Law of Diminishing ReturnsThe Law of Diminishing ReturnsThe Law of Diminishing ReturnsSlide 7MC and Marginal ProductRelations Between Short-Run Costs & ProductionAverage & Marginal Cost SchedulesSlide 11Short Run Linear Cost FunctionShort Run Cubic Cost FunctionProperties of a Short-Run Cubic Cost FunctionProperties of a Short-Run Cubic Cost FunctionProperties of a Short-Run Cubic Cost FunctionProperties of a Short-Run Cubic Cost FunctionSummary of Short-Run Empirical Cost FunctionsRegression Estimation for Production FunctionExamples of Cost EstimationPotential Estimation IssueEstimation of a Short-Run Production FunctionShort Run Average & Marginal Cost CurvesShort Run Cost Curve RelationsShort Run Cost Curve Relations10-1Chapter 10:Production and Cost Estimation10-2Basic Concepts of Production TheoryInputs are considered variable or fixed depending on how readily their usage can be changedVariable input~An input for which the level of usage may be varied to increase or decrease outputFixed input~An input for which the level of usage cannot be changed and which must be paid even if no output is producedQuasi-fixed input~A “lumpy” or indivisible input for which a fixed amount must be used for any positive level of output~None is purchased when output is zero10-3Short-Run versus Long-Run DecisionsShort run~A time period during which at least one of the firm’s inputs is fixed~Fixed inputs - cannot be adjusted as output changes in the short runLong run~A time horizon long enough for a firm to vary all of its inputs~Variable inputs - can be adjusted up or down as the quantity of output changes10-4The Law of Diminishing ReturnsLO2Total, Marginal, and Average Product: The Law of Diminishing Returns(1)Units of the Variable Resource (Labor)(2)Total Product (TP)(3)Marginal Product (MP)Change in (2)/ Change in (1)(4)Average Product (AP),(2)/(1)0 0 -1 10 10 Increasingmarginalreturns10.002 25 15 12.503 45 20 15.004 60 15Diminishingmarginalreturns15.005 70 10 14.006 75 5 12.507 75 0 10.718 70 -5Negativemarginalreturns8.757-4The Law of Diminishing Returns10-5The Law of Diminishing ReturnsLO2TPMPAPIncreasingMarginalReturnsDiminishingMarginalReturnsNegativeMarginalReturns1 2 3 4 5 6 7 8 90102030Total Product, TP1 2 3 4 5 6 7 8 92010Marginal Product, MP7-5The Law of Diminishing Returns10-6The Law of Diminishing ReturnsLO2TPMPAPIncreasingMarginalReturnsDiminishingMarginalReturnsNegativeMarginalReturns1 2 3 4 5 6 7 8 90102030Total Product, TP1 2 3 4 5 6 7 8 92010Marginal Product, MP7-6When AP is increasing, MP is greater than APWhen AP is decreasing, MP is less than APWhen AP reaches its maximum, AP = MPLaw of diminishing marginal product~As usage of a variable input increases, a point is reached beyond which its marginal product decreasesThe Law of Diminishing Returns10-7Labor Units (L)Total Product (Q)0 01 32 103 214 245 256 247 14AP when 3 units of labor are employed =_________________________________.MP of the 6th laborer =_________________________________.Diminishing marginal returns begin with the_____________ unit of labor.MP is negative when more than_____________ units of labor are employed. Average Product and Marginal Product10-8MC and Marginal ProductLO3Average Product andMarginal ProductCost (Dollars)MPAPMCAVCQuantity of OutputQuantity of Labor Production CurvesCost Curves7-8Relations Between Short-Run Costs & Production10-9Relations Between Short-Run Costs & ProductionWhen marginal product (average product) is increasing, marginal cost (average cost) is decreasingWhen marginal product (average product) is decreasing, marginal cost (average variable cost) is increasingWhen marginal product = average product at maximum AP, marginal cost = average variable cost at minimum AVC10-10Average & Marginal Cost Schedules10-11A firm’s fixed costs for 0 units of output and its average total cost of producing different output levels are summarized in the table below. Complete the table to find the fixed cost, variable cost, total cost, average fixed cost, average variable cost, and marginal cost at all relevant levels of output.Q FC VC TC AFC AVC ATC MC0 $15,000 $0 $15,000 - - - -100 $15,000 $30,000 $150 $150 $300 $150200 $15,000 $25,000 $40,000 $200 $100300 $15,000 $37,500 $52,500 $50 $125 $175400 $37.50 $187.50 $225 $375500 $15,000 $147,500 $162,500 $30 $295 $325 $725600 $15,000 $225,000 $25 $375 $775Average & Marginal Cost Schedules10-12Short Run Linear Cost Function10-13Short Run Cubic Cost Function10-14Average variable cost & marginal cost functions are, respectively:Properties of a Short-Run Cubic Cost Function2 3TVC aQ bQ cQ= + +2AVC a bQ cQ= + +22 3SMC a bQ cQ= + +10-15Average variable cost reaches its minimum value at:Properties of a Short-Run Cubic Cost Function2mQ b c=-2 3TVC aQ bQ cQ= + +10-16To conform to theoretical properties, parameters must satisfy the following restrictions: a > 0, b < 0, and c > 0Cubic specification produces S-shaped TVC curve & U-shaped AVC & SMC curvesProperties of a Short-Run Cubic Cost Function2 3TVC aQ bQ cQ= + +10-17All three cost curves employ the same parameters~Only necessary to estimate one of these functions to obtain estimates of all threeIn the short-run cubic specification, input prices are assumed constant~Not explicitly included in cost equationProperties of a Short-Run Cubic Cost Function10-18Summary of Short-Run Empirical Cost FunctionsShort-run cubic cost equationsTotal variable costAverage variable costMarginal costAverage variable cost reaches minimum atRestrictions on parametersa > 0, b < 0, and c > 02 3TVC aQ bQ cQ= + +2AVC a bQ cQ= + +22 3SMC a bQ cQ= + +2mbQc=-10-19Regression Estimation for Production Function10-20Examples of Cost Estimation10-21Potential Estimation Issue10-22Data collection may be complicated by the fact that accounting data do not include firm’s opportunity costs~Capital costs should reflect not only acquisition cost but any foregone rental income, depreciation, & capital gains/lossesNominal cost data~Data that have not been corrected for the effects of inflationMust eliminate effects of inflation~Correct for the influence of inflation by dividing nominal cost data by an appropriate price index (or implicit price deflator)Estimation of a Short-Run Production Function10-23Short Run Average & Marginal Cost Curves10-24Short Run Cost Curve