The inverse demand function for soybeans is p = 30,000

Question

The inverse demand function for soybeans is p = 30,000 - 6q. Total revenue in this market will be maximized when the quantity of soybeans produced is

Quizplus · Accepted Answer

To find the quantity that maximizes total revenue, we need to find the quantity where marginal revenue (MR) is equal to zero.

The inverse demand function is:

p = 30,000 - 6q

To find the MR function, we need to take the derivative of the inverse demand function with respect to q:

MR = dp/dq = -6

Setting MR = 0, we get:

-6 = 0

This is not possible, so there is no quantity where MR = 0. However, we do know that when MR is positive, total revenue is increasing, and when MR is negative, total revenue is decreasing.

Since the MR function is constant and negative (-6), we can say that total revenue is increasing at a decreasing rate as quantity increases. Therefore, to maximize total revenue, we need to produce the quantity where MR = p, which is at the midpoint of the demand curve.

The midpoint of the demand curve is:

(30,000 - 0) / 2 = 15,000

So, the quantity that maximizes total revenue is:

q = (30,000 - 15,000) / 6 = 2,500

Therefore, the correct answer is D) 2,500 bushels.