Midterm Exam Review AAE 575 Fall 2012

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Midterm Exam Review AAE 575 Fall 2012. Goal Today. Quickly review topics covered so far Explain what to focus on for midterm Review content/main points as we review it. Technical Aspects of Production. - PowerPoint PPT Presentation

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<p>PowerPoint Presentation</p> <p>Midterm Exam ReviewAAE 575Fall 2012Goal TodayQuickly review topics covered so farExplain what to focus on for midtermReview content/main points as we review itTechnical Aspects of ProductionWhat is a production function? What do we mean when we write y = f(x), y = f(x1, x2), etc.?What properties do we want for a production functionLevel, Slope, Curvature(Dont worry about quasi-concave)(Dont worry about input elasticity)Marginal product and average productDefinition/How to calculateWhats the difference?</p> <p>Technical Aspects of ProductionMultiple InputsThree relationships discussedFactor-Output (1 input production function)Factor-Factor (isoquants)Scale relationship (proportional increase inputs)(Dont worry about scale relationship)How do marginal products and average products work with multiple inputs?MPs and APs depend on all inputs</p> <p>Factor-Factor Relationships: IsoquantsWhat is an isoquant?Input combinations that give same output (level surface production function)Graphics for special cases: imperfect substitution, perfect substitution, no substitutionHow to find isoquant for a production function? Solve y = f(x1, x2) as x2 = g(x1, y) Factor-Factor Relationships: IsoquantsIsoquant slope dx2/dx1 = Marginal rate of technological substitution (MRTS)How calculate MRTS? Ratio of Marginal production MRTS = dx2/dx1 = f1/f2Dont worry about elasticity of factor substitutionDont worry about isoclines and ridgelines</p> <p>Factor Interdependence: Technical Substitution/ComplementarityWhats the difference between input substitutability and technical substitution/complementarity?Input SubstitutabilityConcerns substitution of inputs when output is held fixed along an isoquantMeasured by MRTSInputs must be substitutable along a well-behaved isoquantTechnical Substitution/Complementarity Concerns interdependence of input useDoes not hold output constantMeasured by changes in marginal products</p> <p>Factor Interdependence: Technical Substitution/ComplementarityIndicates how increasing one input affects marginal product (productivity) of another inputTechnically Competitive: increasing x1 decreases marginal product of x2 Technically Complementary: increasing x1 increases marginal product of x2 Technically Independent: increasing x1 does not affect marginal product of x2Factor Interdependence: Technical Substitution/ComplementarityTechnically Competitivef12 &lt; 0SubstitutesTechnically Complementaryf12 &gt; 0ComplementsTechnically Independentf12 = 0Independent</p> <p>What to SkipReturns to scale, partial input elasticity, elasticity of scale, homogeneityQuasi-concavityInput elasticityElasticity of factor substitutionIsoclines and ridgelines</p> <p>Problem Set #1What parameter restriction on a standard production function ensure desired properties for level, slope and curvature?How to derive formula for MP and AP for single &amp; multiple input production functions?Deriving isoquant equation and/or slope of isoquantCalculate cross partial derivative f12 and interpret meaning: Factor InterdependenceProduction FunctionsLinear, Quadratic, CubicLRP, QRPNegative ExponentialHyperbolicCobb-DouglasSquare rootIntercept = ?Economics of Optimal Input UseBasic model (1 input): p(x) = pf(x) rx K First Order Condition (FOC)p(x) = 0 and solve for xGet pMP = r or MP = r/pSecond Order Condition (SOC)p(x) &lt; 0 (concavity)Get pf(x) &lt; 0 (concave production function)Be able to implement this model for standard production functionsRead discussion in notes: what it all means</p> <p>xyMPOutput max is where MP = 0, x = xymax</p> <p>Profit Max is where MP = r/p, x = xoptr/pxxoptxymax15Economics of Optimal Input UseMultiple Inputsp(x1,x2) = pf(x1,x2) r1x1 r2x2 KFOCs: dp/dx1 = 0 and dp/dx2 = 0 and solve for pair (x1,x2)dp/dx = pf1(x1,x2) r1 = 0dp/dy = pf2(x1,x2) r2 = 0SOCs: more complexf11 &lt; 0, f22 &lt; 0, plus f11f22 (f12)2 &gt; 0Be able to implement this model for simple production functionRead discussion in notes: what it all means</p> <p>Graphicsx1x2Isoquant y = y0-r1/r2x1*x2*= -MP1/MP217Special Cases: Discrete InputsTillage system, hybrid maturity, seed treatment or notHierarchical Models: production function parameters depend on other inputs: can be a mix of discrete and continuous inputsProblem set #2: ymax and b1 of negative exponential depending on tillage and hybrid maturityp(x,T,M) = pf(x,T,M) rx C(T) C(M) K Be able to determine optimal input use for x, T and MCalculate optimal continuous input (X) for each discrete input level (T and M) and associated profit, then choose discrete option with highest profit</p> <p>Special Cases: ThresholdsWhen to use herbicide, insecticide, fungicide, etc. Input used at some fixed recommended rate, not a continuous variablepno = PY(1 lno) Gptrt = PY(1 ltrt) Ctrt G </p> <p>pno = PYno(1 aN) Gptrt = PYtrt(1 aN(1 k)) Ctrt GSet pno = ptrt and solve for NEIL = Ctrt/(PYak)Treat if N &gt; NEIL, otherwise, dont treatFinal CommentsExpect a problem oriented examGiven production functionFind MP; AP; parameter restrictions to ensure level, slope, and curvature; isoquant equationInput Substitution vs Factor InterdependenceMRTS = f1/f2 vs f12Economic optimal input useSingle and multiple inputs (continuous)Discrete, mixed inputs, and thresholdsChart308001700300050007500102001280015100171001840019200195001960019400</p> <p>Milk</p> <p>milkFeed TDN (lbs/yr)Milk (lbs/yr)TDNTDN2MilkFitSUMMARY OUTPUTTDNMilkAPMPTDNMilkMPVMPprice TDNprofit00000-2261.470588235300000$0$150-$4001,0008001,0001,000,000800211.3025210084Regression Statistics18008008001800800$96$150-$4542,0001,7002,0004,000,0001,7002560.0775694893Multiple R0.984331214221,70085090021,700900$108$150-$4963,0003,0003,0009,000,0003,0004784.8545572075R Square0.968907939233,0001000130033,0001300$156$150-$4904,0005,0004,00016,000,0005,0006885.6334841629Adjusted R Square0.963725929145,0001250200045,0002000$240$150-$4005,0007,5005,00025,000,0007,5008862.4143503555Standard Error1456.91326494857,5001500250057,5002500$300$150-$2506,00010,2006,00036,000,00010,20010715.1971557854Observations15610,20017002700610,2002700$324$150-$767,00012,8007,00049,000,00012,80012443.9819004525712,80018292600712,8002600$312$150$868,00015,1008,00064,000,00015,10014048.7685843568ANOVA815,10018882300815,1002300$276$150$2129,00017,1009,00081,000,00017,10015529.5572074984dfSSMSFSignificance F917,10019002000917,1002000$240$150$30210,00018,40010,000100,000,00018,40016886.3477698772Regression2793746178.194355396873089.097177186.97530768360.00000000091018,400184013001018,4001300$156$150$30811,00019,20011,000121,000,00019,20018119.1402714932Residual1225471155.13897872122596.261581561119,20017458001119,200800$96$150$25412,00019,50012,000144,000,00019,50019227.9347123465Total14819217333.3333331219,50016253001219,500300$36$150$14013,00019,60013,000169,000,00019,60020212.7310924371319,60015081001319,600100$12$150$214,00019,40014,000196,000,00019,40021073.5294117647CoefficientsStandard Errort StatP-valueLower 95%Upper 95%1419,4001386-2001419,400-200-$24$150-$172Intercept-2261.4705882353993.1681472023-2.27702690080.0419027798-4425.3980523722-97.5431240984TDN2.53477213960.32928412457.69782674370.00000556411.81732367693.2522206024TDN2-0.0000619990.0000226832-2.73325859840.0181566126-0.0001114215-0.0000125766</p> <p>milk</p> <p>Milk (lbs/yr)TDN (lbs/yr)Milk (lbs/yr)</p> <p>figure ap mp</p> <p>MilkFit</p> <p>Sheet3</p> <p>Milk</p> <p>MP</p> <p>InputTPMPAP001666.0216108.0329139.74441511.05551111.0660510.076228.986207.8961-16.81059-25.9</p> <p>0006661610829139.6666666667441511551111605106228.85714285716207.7561-16.777777777859-25.9</p> <p>TPMPAP</p> <p>1</p> <p>#REF!</p> <p>11</p> <p>#REF!#REF!Labor</p> <p>Chart4080090013002000250027002600230020001300800300100-200</p> <p>MP</p> <p>milkFeed TDN (lbs/yr)Milk (lbs/yr)TDNTDN2MilkFitSUMMARY OUTPUTTDNMilkAPMPTDNMilkMPVMPprice TDNprofit00000-2261.470588235300000$0$150-$4001,0008001,0001,000,000800211.3025210084Regression Statistics18008008001800800$96$150-$4542,0001,7002,0004,000,0001,7002560.0775694893Multiple R0.984331214221,70085090021,700900$108$150-$4963,0003,0003,0009,000,0003,0004784.8545572075R Square0.968907939233,0001000130033,0001300$156$150-$4904,0005,0004,00016,000,0005,0006885.6334841629Adjusted R Square0.963725929145,0001250200045,0002000$240$150-$4005,0007,5005,00025,000,0007,5008862.4143503555Standard Error1456.91326494857,5001500250057,5002500$300$150-$2506,00010,2006,00036,000,00010,20010715.1971557854Observations15610,20017002700610,2002700$324$150-$767,00012,8007,00049,000,00012,80012443.9819004525712,80018292600712,8002600$312$150$868,00015,1008,00064,000,00015,10014048.7685843568ANOVA815,10018882300815,1002300$276$150$2129,00017,1009,00081,000,00017,10015529.5572074984dfSSMSFSignificance F917,10019002000917,1002000$240$150$30210,00018,40010,000100,000,00018,40016886.3477698772Regression2793746178.194355396873089.097177186.97530768360.00000000091018,400184013001018,4001300$156$150$30811,00019,20011,000121,000,00019,20018119.1402714932Residual1225471155.13897872122596.261581561119,20017458001119,200800$96$150$25412,00019,50012,000144,000,00019,50019227.9347123465Total14819217333.3333331219,50016253001219,500300$36$150$14013,00019,60013,000169,000,00019,60020212.7310924371319,60015081001319,600100$12$150$214,00019,40014,000196,000,00019,40021073.5294117647CoefficientsStandard Errort StatP-valueLower 95%Upper 95%1419,4001386-2001419,400-200-$24$150-$172Intercept-2261.4705882353993.1681472023-2.27702690080.0419027798-4425.3980523722-97.5431240984TDN2.53477213960.32928412457.69782674370.00000556411.81732367693.2522206024TDN2-0.0000619990.0000226832-2.73325859840.0181566126-0.0001114215-0.0000125766</p> <p>milk</p> <p>Milk (lbs/yr)TDN (lbs/yr)Milk (lbs/yr)</p> <p>figure ap mp</p> <p>MilkFit</p> <p>Sheet3</p> <p>Milk</p> <p>MP</p> <p>InputTPMPAP001666.0216108.0329139.74441511.05551111.0660510.076228.986207.8961-16.81059-25.9</p> <p>0006661610829139.6666666667441511551111605106228.85714285716207.7561-16.777777777859-25.9</p> <p>TPMPAP</p> <p>1</p> <p>#REF!</p> <p>11</p> <p>#REF!#REF!Labor</p>