Assignment03-2003

# Assignment03-2003 - AEB 6533 Assignment 3 I Assuming a...

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AEB 6533 Assignment 3 I. Assuming a negative exponential utility function and a normal distribution, yields a Expected Value-Variance formulation of the expected utility problem. The objective function for this formulation is max 2 . . x x x x s t Ax b ρ μ - where μ is the expected return per acre, x is the choice vector containing the acres planted in each crop, ρ is the Arrow-Pratt risk aversion coefficient, is the variance matrix for returns per acre, and A is the constraint matrix. Assuming a risk aversion coefficient of 0.00002, 640 acres of cropland, \$44,000 of capital, and 100 hours of labor, is the crop combination 436.92 acres of corn, 55.38 acres of peanuts, and 147.69 acres of soybeans optimum? Remember each crop variable must be greater than or equal to zero. Table 1. Farm Portfolio Problem Cotton Corn Wheat Peanuts Soybeans Yield 1500 150 45 1.25 45 Price 0.49 2.23 3.46 678.00 6.20 Variable Cost 450 150 50 500 75 Capital 225.00

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