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Think Break #7

Think Break #7. Repeat the previous problem, but now use a milk price of Milk $10/cwt M = – 25.9 + 2.56G + 1.05H – 0.00505G 2 – 0.00109H 2 – 0.00352GH Prices: Grain $3/cwt, Hay $1.50/cwt What are the profit maximizing inputs?. Think Break #7: Answer.

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Think Break #7

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  1. Think Break #7 • Repeat the previous problem, but now use a milk price of Milk $10/cwt • M = – 25.9 + 2.56G + 1.05H – 0.00505G2 – 0.00109H2 – 0.00352GH • Prices: Grain $3/cwt, Hay $1.50/cwt • What are the profit maximizing inputs?

  2. Think Break #7: Answer • p(G,H) = 0.1(– 25.9 + 2.56G + 1.05H – 0.00505G2 – 0.00109H2 – 0.00352GH) – 0.03G – 0.015H • FOC’s pG = 0.1(2.56 – 0.0101G – 0.00352H) – 0.03 = 0 pH= 0.1(1.05 – 0.00218H – 0.00352G) – 0.015 = 0 • 2.56 – 0.0101G – 0.00352H = 0.03/0.10 = 0.3 1.05 – 0.00218H – 0.00352G = 0.015/0.10 = 0.15

  3. Think Break #7: Answer • Solve FOC1 for H 2.56 – 0.0101G – 0.00352H = 0.3 0.00352H = 2.26 – 0.0101G H = (2.26 – 0.0101G)/0.00352 H = 642 – 2.87G • Substitute into FOC2 and solve for G 1.05 – 0.00218H – 0.00352G = 0.15 0.9 = 0.00218(642 – 2.87G) + 0.00352G 0.9 = 1.4 – 0.00626G + 0.00352G – 0.5 = – 0.00274G G = 0.5/0.00274 = 182.5 lbs/week

  4. Think Break #7: Answer • Substitute into equation for H H = 642 – 2.87G H = 642 – 2.87(182.5) H = 642 – 523.8 = 118.2 lbs/week M = – 25.9 + 2.56G + 1.05H – 0.00505G2 – 0.00109H2 – 0.00352GH M = – 25.9 + 2.56(182.5) + 1.05(118.2) – 0.00505(182.5)2 – 0.00109(118.2)2 – 0.00352(182.5)(118.2) = 306 lbs/week p= 0.1(306) – 0.03(182.5) – 0.015(118.2) = $23.35/week

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