Production and cost

14 de Mar de 2015
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Production and cost

• 1. Ram Kumar Phuyal, Ph.D.Ram Kumar Phuyal, Ph.D. MicroeconomicsMicroeconomics Kathmandu UniversityKathmandu University Theory of Production and CostsTheory of Production and Costs
• 2. Contents: This presentation includes about production function with one and two variable input(s), returns to scale, and short run and long run costs functions.
• 3. The Production FunctionThe Production Function  TheThe production functionproduction function refers to the physical relationshiprefers to the physical relationship between the inputs or resources of a firm and theirbetween the inputs or resources of a firm and their output of goods and services at a given period of time,output of goods and services at a given period of time, ceteris paribus.ceteris paribus.  The production function isThe production function is dependentdependent on differenton different time frames. Firms can produce for a brief or lengthytime frames. Firms can produce for a brief or lengthy period of time.period of time.
• 4. Firm’s InputsFirm’s Inputs  Inputs - are resources that contribute in theInputs - are resources that contribute in the production of a commodity.production of a commodity.  Most resources are lumped into three categories:Most resources are lumped into three categories:  Land,Land,  Labor,Labor,  CapitalCapital  OrganizationOrganization  Raw materials and etc.Raw materials and etc.
• 5. Fixed vs. Variable InputsFixed vs. Variable Inputs  Fixed inputs -resources used at a constant amount inFixed inputs -resources used at a constant amount in the production of a commodity.the production of a commodity.  Variable inputs - resources that can change in quantityVariable inputs - resources that can change in quantity depending on the level of output being produced.depending on the level of output being produced.  The longer planning the period, the distinction betweenThe longer planning the period, the distinction between fixed and variable inputs disappears, i.e., all inputs arefixed and variable inputs disappears, i.e., all inputs are variable in the long run.variable in the long run.
• 6. Production Analysis with One Variable InputProduction Analysis with One Variable Input  Total product (Q)Total product (Q) refers to the total amount of outputrefers to the total amount of output produced in physical units (may refer to, kilogramsproduced in physical units (may refer to, kilograms of sugar, sacks of rice produced, etc)of sugar, sacks of rice produced, etc)  TheThe marginal product (MP)marginal product (MP) refers to the rate of changerefers to the rate of change in output as an input is changed by one unit, holdingin output as an input is changed by one unit, holding all other inputs constant.all other inputs constant. L L TP MP L ∆ = ∆
• 7. Total vs. Marginal ProductTotal vs. Marginal Product  Total Product (TPx) = total amount of outputTotal Product (TPx) = total amount of output produced at different levels of inputsproduced at different levels of inputs  Marginal Product (MPx) = rate of change in output asMarginal Product (MPx) = rate of change in output as input X is increased by one unit,input X is increased by one unit, ceteris paribusceteris paribus.. X X TP MP X ∆ = ∆
• 8. Production Function of a Rice FarmerProduction Function of a Rice Farmer Table 1.Table 1. Units of LUnits of L Total ProductTotal Product (Q(QLL or TPor TPLL)) Marginal ProductMarginal Product (MP(MPL)L) 00 00 -- 11 22 22 22 66 44 33 1212 66 44 2020 88 55 2626 66 66 3030 44 77 3232 22 88 3232 00 99 3030 -2-2 1010 2626 -4-4
• 9. FIGURE 1. Total product curve. The total product curve shows the behavior of total product with an input (e.g., labor) used in production assuming a certain technological level. L QL QL 2 6 12 20 26 30 32 Labor Totalproduct 0 2 4 6 8 1097531
• 10. Marginal ProductMarginal Product  TheThe marginal productmarginal product refers to the rate of change in outputrefers to the rate of change in output as an input is changed by one unit, holding all other inputsas an input is changed by one unit, holding all other inputs constant.constant.  Observe that the marginal productObserve that the marginal product initially increases, reaches ainitially increases, reaches a maximum level, and beyond this point, the marginal product declines,maximum level, and beyond this point, the marginal product declines, reaches zero, and subsequently becomes negative.reaches zero, and subsequently becomes negative.  TheThe law of diminishing returnslaw of diminishing returns states that "as the use ofstates that "as the use of an input increases (with other inputs fixed), a point willan input increases (with other inputs fixed), a point will eventually be reached at which the resulting additions toeventually be reached at which the resulting additions to output decrease"output decrease"
• 11. Total and Marginal ProductTotal and Marginal Product -10 -5 0 5 10 15 20 25 30 35 0 1 2 3 4 5 6 7 8 9 TPL MPL FIGURE 2.
• 12. Law of Diminishing MarginalLaw of Diminishing Marginal ReturnsReturns  As more and more of an input is addedAs more and more of an input is added (given a fixed amount of other inputs)(given a fixed amount of other inputs), total, total output may increase; however, as theoutput may increase; however, as the additions to total output will tend toadditions to total output will tend to diminish.diminish.  Counter-intuitive proof: if the law ofCounter-intuitive proof: if the law of diminishing returns does not hold, thediminishing returns does not hold, the world’s supply of food can be produced inworld’s supply of food can be produced in a hectare of land.a hectare of land.
• 13. Average Product (AP)Average Product (AP)  Average product is a concept commonlyAverage product is a concept commonly associated with efficiency.associated with efficiency.  TheThe average productaverage product measures the total output permeasures the total output per unit of input used.unit of input used.  The "productivity" of an input is usuallyThe "productivity" of an input is usually expressed in terms of its average product.expressed in terms of its average product.  The greater the value of average product, theThe greater the value of average product, the higher the efficiency in physical terms.higher the efficiency in physical terms.  Formula:Formula: L L TP AP L =
• 14. TABLE 2. Average product of labor. Labor (L) Total product of labor (TPL) Average product of labor (APL) 0 0 0 1 2 2 2 6 3 3 12 4 4 20 5 5 26 5.2 6 30 5 7 32 4.5 8 32 4 9 30 3.3 10 26 2.6
• 15. Rise = Y Run = L0 L Y The slope of the line from the origin is a measure of the AVERAGE Y L1 L2 a b rise Slope = run Y L = FIGURE 3.
• 16. Labor Q QL 0 Total Product a b c d The average product at b is highest. AP at c is less than at a. AP at d is less than at c. FIGURE 4. L
• 17. L Q TPL Highest Slope of Line from Origin Max APL Inflection point Max MPL 0 L1 L2 L3 FIGURE 5.
• 18. Relationship between Average andRelationship between Average and Marginal CurvesMarginal Curves  When the marginal is less than the average, theWhen the marginal is less than the average, the average decreases.average decreases.  When the marginal is equal to the average, theWhen the marginal is equal to the average, the average does not change (it is either at maximumaverage does not change (it is either at maximum or minimum)or minimum)  When the marginal is greater than the average,When the marginal is greater than the average, the average increasesthe average increases
• 19. Relationship between Average and MarginalRelationship between Average and Marginal Curves: Example of Econ 11 ScoresCurves: Example of Econ 11 Scores  When the marginal score (new exam) is lessWhen the marginal score (new exam) is less than your average score, the averagethan your average score, the average decreases.decreases.  When the marginal score (new exam) is equalWhen the marginal score (new exam) is equal to the average score, the average does notto the average score, the average does not change.change.  When the marginal score (new exam) isWhen the marginal score (new exam) is greater than your average score, the averagegreater than your average score, the average increases.increases.
• 20. L Q Max APL Max MPL 0 L1 L2 L3 MPL APL At Max AP, MP=AP FIGURE 5. AP, MP
• 21. L AP,MP 0 L1 L2 L3 MPL APL Stage I MP>AP AP increasing Stage II MP<AP AP decreasing MP still positive Stage III MP<0 AP decreasing L TP 0 L1 L2 L3 TPL FIGURE 6.
• 22. Three Stages of ProductionThree Stages of Production  In Stage IIn Stage I  APAPLL is increasing so MP>AP.is increasing so MP>AP.  All the product curves are increasingAll the product curves are increasing  Stage I stops whereStage I stops where APAPLL reaches its maximum atreaches its maximum at pointpoint A.A.  MP peaks and then declines at pointMP peaks and then declines at point CC and beyond,and beyond, so the law of diminishing returns begins to manifestso the law of diminishing returns begins to manifest at this stageat this stage
• 23. Three Stages of ProductionThree Stages of Production  Stage IIStage II  starts where thestarts where the APAPLL of the input begins to decline.of the input begins to decline.  QQLL still continues to increase, although at astill continues to increase, although at a decreasing rate, and in fact reaches a maximumdecreasing rate, and in fact reaches a maximum  Marginal product is continuously declining andMarginal product is continuously declining and reaches zero at pointreaches zero at point D,D, as additional labor inputsas additional labor inputs are employed.are employed.
• 24. Three Stages of ProductionThree Stages of Production  Stage III starts where theStage III starts where the MPLMPL has turnedhas turned negative.negative.  all product curves are decreasing.all product curves are decreasing.  total output starts falling even as the input istotal output starts falling even as the input is increasedincreased
• 25. Cost of ProductionCost of Production  Opportunity Cost Principle -Opportunity Cost Principle - the economic cost of an inputthe economic cost of an input used in a production process is the value of outputused in a production process is the value of output sacrificed elsewhere. The opportunity cost of an inputsacrificed elsewhere. The opportunity cost of an input is the value of foregone income in best alternativeis the value of foregone income in best alternative employment.employment.  Implicit vs. Explicit CostsImplicit vs. Explicit Costs  Explicit costsExplicit costs – costs paid in cash– costs paid in cash  Implicit costImplicit cost – imputed cost of self-owned or self employed– imputed cost of self-owned or self employed resources based on their opportunity costs.resources based on their opportunity costs.
• 26. Costs on Short-RunCosts on Short-Run 1.1. Total Fixed CostTotal Fixed Cost (TFC)(TFC) 2.2. Total Variable CostTotal Variable Cost (TVC)(TVC) 3.3. Total CostTotal Cost (TC=TVC+TFC)(TC=TVC+TFC) 4.4. Average Fixed CostAverage Fixed Cost (AFC=TFC/Q)(AFC=TFC/Q) 5.5. Average Variable CostAverage Variable Cost (AVC=TVC/Q)(AVC=TVC/Q) 6.6. Average Total CostAverage Total Cost (AC=AFC+AVC)(AC=AFC+AVC) 7.7. Marginal CostMarginal Cost (MC= ∆AVC/∆Q(MC= ∆AVC/∆Q
• 27. Short Run AnalysisShort Run Analysis  Total fixed cost (TFC)Total fixed cost (TFC) is more commonly referredis more commonly referred to as "sunk cost" or "overhead cost."to as "sunk cost" or "overhead cost."  Examples: include the payment or rent for land,Examples: include the payment or rent for land, buildings and machinery.buildings and machinery.  The fixed cost is independent of the level ofThe fixed cost is independent of the level of output produced.output produced.  Graphically, depicted as a horizontal lineGraphically, depicted as a horizontal line
• 28. Short Run AnalysisShort Run Analysis  Total variable cost (TVC)Total variable cost (TVC) refers to the cost thatrefers to the cost that changes as the amount of output produced ischanges as the amount of output produced is changed.changed.  Examples - purchases of raw materials, payments toExamples - purchases of raw materials, payments to workers, electricity bills, fuel and power costs.workers, electricity bills, fuel and power costs.  Total variable cost increases as the amount of outputTotal variable cost increases as the amount of output increases.increases.  If no output is produced, then total variable costIf no output is produced, then total variable cost is zero;is zero;  the larger the output, the greater the total variablethe larger the output, the greater the total variable cost.cost.
• 29. Short Run AnalysisShort Run Analysis  Total costTotal cost (TC)(TC) is the sum of total fixed costis the sum of total fixed cost and total variable costand total variable cost  TC=TFC+TVCTC=TFC+TVC  As the level of output increases, total cost of theAs the level of output increases, total cost of the firm also increases.firm also increases.
• 30. Table 3Table 3-Costs-Costs Units of Labor Total Product Total Fixed Cost Total Variable Cost Total Cost Marginal Cost Average Cost L TPL TFC TVC TC MC AC 0 0 100 0 100 - - 1 6 100 30 130 30 130 2 10 100 50 150 20 75 3 12 100 60 160 10 53.3 4 13 100 65 165 5 41.25 5 15 100 75 175 10 35 6 19 100 95 195 20 32.5 7 25 100 125 225 30 32.14 8 33 100 165 265 40 33.12 9 43 100 215 315 50 35 10 55 100 275 375 60 37.5
• 31. Q0 TFC (Total Fixed Cost) Costs TVC (Total Variable Cost) TC (Total Cost) “TOTAL” COST CURVES FIGURE 7.
• 32. Q0 AFC (Average Fixed Cost) Costs AFC=TFC/Q. As more output is produced, the Average Fixed Cost decreases. FIGURE 8.
• 33. Q0 Costs TVC (Total Variable Cost) q1 The Average Variable Cost at a point on the TVC curve is measured by the slope of the line from the origin to that point. AVC=TVC/Q Minimum AVC FIGURE 9.
• 35. Q0 Costs AVC (Average Variable Cost) q1 The Average Variable Cost is U shaped. First it decreases, reaches a minimum and then increases. Minimum AVC FIGURE 11.
• 36. Q0 Costs AVC (Average Variable Cost) q1 The Marginal Cost curve passes through the minimum point of the AVC curve. It is also U-shaped. First it decreases, reaches a minimum and then increases. Minimum AVC MC (Marginal Cost) FIGURE 12.
• 38. Table 4-Average CostsTable 4-Average Costs (Q) (TC) (AC) 0 100 - 1 130 130.00 2 150 75.00 3 160 53.33 4 165 41.25 5 175 35.00 6 195 32.50 7 225 32.14 8 265 33.13 9 315 35.00 10 375 37.50
• 39. Total Product (Q) Total Variable Cost (AVC) Average Variable Cost (AVC) 0 0 0 1 30 30.0 2 50 25.0 3 60 20.0 4 65 16.3 5 75 15.0 6 95 15.8 7 125 17.9 8 165 20.6 9 215 23.9 10 275 27.5 Table 5-Average Variable Costs
• 40. LongRunTotalCostLTC LTC Q Total Product All inputs are variable in the long run. There are no fixed costs. LONG-RUN TOTAL COST CURVE FIGURE 14.
• 41. Long Run ACLong Run AC  The LAC curve is an envelop curve of allThe LAC curve is an envelop curve of all possible plant sizes. Also known as “planningpossible plant sizes. Also known as “planning curve”curve”  It traces the lowest average cost of producingIt traces the lowest average cost of producing each level of output.each level of output.  It is U-shaped because ofIt is U-shaped because of  Economies of ScaleEconomies of Scale  Diseconomies of ScaleDiseconomies of Scale
• 42. LAC SAC1 Q0 COSTS SAC3 LONG-RUN AVERAGE COST CURVE SAC4 SAC5 SAC6 SAC7 SAC8 SAC9 SAC2 FIGURE 15.
• 44. LAC Q0 COST SAC1 q0 SAC2 Building a larger sized plant (size 2) will result in a lower average cost of producing q0 FIGURE 17.
• 45. LAC Q0 COST SAC1 q0 SAC2 Likewise, a larger sized plant (size 3) will result to a lower average cost of producing q1 q1 SAC3 FIGURE 18.
• 46. Economies and Diseconomies of ScaleEconomies and Diseconomies of Scale  Economies of ScaleEconomies of Scale- long run average cost- long run average cost decreases as output increases.decreases as output increases.  Technological factorsTechnological factors  SpecializationSpecialization  Diseconomies of ScaleDiseconomies of Scale: - long run average cost: - long run average cost increases as output increases.increases as output increases.  Problems with management – becomes costly,Problems with management – becomes costly, unwieldyunwieldy
• 47. LAC SAC1 Q0 COST SAC2 LONG-RUN AVERAGE COST CURVE Q1 Economies of Scale Diseconomies of Scale FIGURE 19.
• 48. LAC SAC1 Q0 COST LONG-RUN AVERAGE and MARGINAL COST CURVES Q1 LMC SMC1 SMC2 SAC2 FIGURE 20.
• 49. LAC and LMCLAC and LMC  Long-run Average Cost (LAC) curveLong-run Average Cost (LAC) curve  is U-shaped.is U-shaped.  the envelope of all the short-run average costthe envelope of all the short-run average cost curves; driven by economies and diseconomiescurves; driven by economies and diseconomies of size.of size.  Long-run Marginal Cost (LMC) curveLong-run Marginal Cost (LMC) curve  Also U-shaped;Also U-shaped;  intersects LAC at LAC’s minimum point.intersects LAC at LAC’s minimum point.