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 $2 and the price of apples is $7 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 = 250 and A₂ = 350. B)A₁ = A₂ = 350. C)A₁ = 175 and A₂ = 350. D)A₁ = 350 and A₂ = 500. E)A₁ = 100 and A₂ = 350.

Question

Quizplus · Accepted Answer

For each farm, the profit-maximizing level of output is where marginal cost equals marginal revenue: For honey farm: MC = C_H(H, A)/H = 2 MR = P = 2 2 = C_H(H, A)/H H=C_H(H, A)/2 For apple orchard: MC = C_A(H, A)/A = 7 MR = P = 7 7 = C_A(H, A)/A A = C_A(H, A)/7 If the firms operate independently, we have: A₁ = C_A(H, A)/7 = (250/100)H = 2.5H If the firms are owned by a single profit-maximizing owner, we have: A₂ = C_A(H, A)/7 = (350/100)H = 3.5H Therefore, A₁ F1F1F1S1F1F1F10 = 350 and A₂ F1F1F1S1F1F1F10 = 500. Hence, the answer is D.

Suppose That the Cost Function of the Honey Farm Is