suppose that the cost function of the honey farm is C_H(H, A)= H ²/100 - 3A and the cost function of the apple orchard is C_A(H, A)= A²/100, where H and A are the number of units of honey and apples produced respectively.The price of honey is $7 and the price of apples is $5 per unit.Let A₁ be the output of apples if the firms operate independently, and let A₂ be the output of apples if the firms are operated by a profit-maximizing single owner. A)A₁ = 125 and A₂ = 250. B)A₁ = A₂ = 250. C)A₁ = 200 and A₂ = 250. D)A₁ = 250 and A₂ = 400. E)A₁ = 350 and A₂ = 250.

Question

Quizplus · Accepted Answer

To find the output of apples for each scenario, we need to maximize the profit function of the honey farm and the apple orchard. For the honey farm: πH = revenue - cost πH = 7H - C_H(H, A)F1F1F1S1 Taking the derivative of πH with respect to H and setting it equal to 0 gives: 7 - ∂C_H(H, A)F1F1F1S1/∂H = 0 ∂C_H(H, A)F1F1F1S1/∂H = 7/3 Similarly, for the apple orchard: πA = 5A - C_A(H, A)F1F1F1S1 Taking the derivative of πA with respect to A and setting it equal to 0 gives: 5 - ∂C_A(H, A)F1F1F1S1/∂A = 0 ∂C_A(H, A)F1F1F1S1/∂A = 5/2 If the firms operate independently, then we have: ∂C_H(H, A₁)F1F1F1S1/∂H = 7/3 ∂C_A(A₁, H)F1F1F1S1/∂A = 5/2 Solving the above two equations simultaneously will give us A₁ = 250. If the firms are operated by a profit-maximizing single owner, then we have: Total profit = πH + πA Total profit = 7H + 5A - (C_H(H, A)F1F1F1S1 + C_A(H, A)F1F1F1S1) We need to maximize this function with respect to both H and A. By taking partial derivative with respect to H and A, we get: 7 - ∂C_H(H, A)F1F1F1S1/∂H = 0 5 - ∂C_A(H, A)F1F1F1S1/∂A = 0 Solving the above two equations simultaneously will give us A₂ = 400. Therefore, the answer is D) A₁ = 250 and A₂ = 400.

Suppose That the Cost Function of the Honey Farm Is