Suppose a farmer is a price taker (MR = P = 6)in soybeans with cost functions given by The level of profits is

Question

Suppose a farmer is a price taker (MR = P = 6)in soybeans with cost functions given by  The level of profits is

Quizplus · Accepted Answer

To maximize profits, the farmer should produce where MC=MR. From the cost function, we can derive the MC function by taking the derivative of TC with respect to q: MC=4+0.02q. Setting this equal to MR=6, we get 4+0.02q=6, which gives q=100. Therefore, the farmer should produce 100 units of soybeans to maximize profits.

To calculate the level of profits, we need to subtract the total cost from the total revenue. Total revenue is given by q*P, which is 100*6=600. Total cost is given by TC=q(4+0.01q^2), which is 100(4+0.01*100^2)=500. Therefore, the level of profits is 600-500=100.

However, this question has a typo in the cost function provided, as the cost function given is missing the coefficient for the q term. Assuming the correct function is TC=4q+0.01q^2, the MC function becomes MC=4+0.02q, and the level of profits would be different. The correct answer would then be:

Answer: B)
 
Following the same approach as before, we find that the farmer should produce 150 units of soybeans to maximize profits. Total revenue is given by q*P, which is 150*6=900. Total cost is given by TC=q(4+0.01q^2), which is 150(4+0.01*150^2)=600. Therefore, the level of profits is 900-600=300.

Suppose a Farmer Is a Price Taker (MR = P