How Is Demand Related to Revenue?

I have been getting a number of questions about going from the demand function to the revenue function. This was discussed in Question 2 of Section 10.1 at the beginning of the class.

There is also a handout in the Tech 4 folder that describes the process of getting the revenue function. In Tech 4, you start by finding a line that passes through your data to get D(Q). Even though the handout in the folder uses x, I highly suggest using Q instead of x so that your mind focuses on the fact that the input represents a quantity of product. So this function takes in the quantity and outputs the corresponding price. That is what demand functions do….they relate the price of an item with the corresponding quantity that consumers demand.

To find the revenue function R(Q), you need to take advantage of the fact that

revenue = price * quantity

If the price is given by the demand function D(Q) and the quantity by Q, this gives us

R(Q) = D(Q) * Q

What will the units be on the revenue function? That depends on the units for Q and D(Q). Once you have your revenue function, figure that out…it has a huge impact on what you do next to find the cost function C(Q).