A demand curve for a product has the equation , where p is price and q is quantity. What is the marginal revenue as a function of the quantity sold?

Question

A demand curve for a product has the equation  , where p is price and q is quantity. What is the marginal revenue as a function of the quantity sold?

Quizplus · Accepted Answer

The marginal revenue is the derivative of the revenue function with respect to quantity. The revenue function is given by:

R(q) = pq

We can substitute the demand equation into the revenue function to eliminate price:

R(q) = q(100 - 4q)

Taking the derivative with respect to q, we get:

MR(q) = 100 - 8q

Thus, the marginal revenue as a function of quantity sold is 100 - 8q. The answer choice that matches this function is B.

A Demand Curve for a Product Has the Equation