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.

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Katie Miranda · Accepted Answer

Final Answer : D, Explanation :  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 = 2MR = P = 22 = C H (H, A)/HH=C H (H, A)/2For apple orchard:MC = C A (H, A)/A = 7MR = P = 77 = C A (H, A)/AA = C A (H, A)/7If the firms operate independently, we have:A 1  = C A (H, A)/7 = (250/100)H = 2.5HIf the firms are owned by a single profit-maximizing owner, we have:A 2  = C A (H, A)/7 = (350/100)H = 3.5HTherefore, A 1     = 350 and A 2     = 500.Hence, the answer is D.

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