1. AEB 6184 – Simulation and Estimation of the Primal Elluminate - 6

2. Cobb-Douglas Parameters

3. Fuel Use (Field Operations)Fertilizer Dry Spread0.15Nitrogen91.80 Disk-Chisel1.70Phosphorous36.58 Field Cultivate0.70Potash23.50 Planting0.40 Spraying0.10 Combine1.45 Total Diesel4.50 Diesel Price2.64 Total Fuel11.88Total Fertilizer151.88 Field Data for Corn

4. Total Costs and RevenuesParameters Total Fuel11.88α0.0195 Total Fertilizer151.88β0.2500 Total Labor33.06γ0.0544 Total Variable Cost196.82Diesel (gal.)4.50 Corn Yield135.0Fertilizer (tons)0.4116 Corn Price4.50Labor (hours)4.15 Total Revenue607.50 Profit per Acre410.68 Revenues

5. Prices 20072008 Corn Price (FL)4.004.50 Corn Price (GA)4.504.60 Fertilizer Price367614 Fuel Price (Diesel)2.6393.393 Labor Price7.978.91

6. Cobb-Douglas Function

7.  We need to think about three four prices  Corn Price  Diesel Price  Fertilizer Price  Labor Price  We could assume normality  How to choose Ω?  Possible negative prices? Drawing Prices

8.  We could choose a uniform distribution.  For our purpose here, let’s assume that the standard deviation is 1/3 of the value of each price.  In addition, let’s assume that the input prices have a correlation coefficient of 0.35 and the output price is uncorrelated.  The variance matrix then becomes

9.  In the univariate form, given a mean of  and a standard deviation of  we would create the random sample by drawing a z from a standard normal distribution  In the multivariate world, we use the Cholesky decomposition of the variance matrix and use the vector of the means Drawing Random Samples

10. CornFuelFertilizerLabor 4.0317966-7.1139459207.2647413.085498 6.28399293.7932016376.3440315.001602 7.42396973.1434042371.200998.1599310 4.552542311.179552505.757597.6772579 4.37305283.9382136370.574377.5128182 5.6384301-9.1074158153.624406.2727747 1.64777215.5279925445.250537.2384782 1.828461810.856964522.646697.9042016 2.52325672.0854507351.8415512.358072 Price Draws

11. Production Levels

12. FuelFertilizerLaborOutput 4.77812600.617424543.3704676147.90853 7.83053550.850135128.4152978170.02817 0.92299980.261570663.7495936116.23514 2.85929250.389572124.1813763132.05003 0.44626930.071033870.950783376.77729 0.24323530.064778720.932054874.06527 2.38792630.181459251.1241763101.21032 5.25334490.3158794013.261536135.01835 Input Demands and Output Levels

13.  First stage estimation – Ordinary Least Squares  Second stage – System Ordinary Least Squares using the first-order conditions.  From the first-order conditions Estimation

14.  Each of the observations in the system can then be expressed as Estimation (Continued)

15.  Imposing the cross equation restrictions Estimation (Continued)

16.  First estimation (without heteroscedasticity) Estimation (Continued)

17.  With heteroscedasticity Estimation (Continued)

18. Parameter123True Alpha 02.19262.18372.18342.1804 Alpha 10.00690.01940.01930.0195 Alpha 20.25870.25030.24990.2500 Alpha 30.05190.05110.05410.0544 Kappa 10.38270.4233 Kappa 2-0.00030.0003 Results