Question

If the following is the demand equation for an item, where Q and P are the quantity demanded (lbs) and current price ($/unit) of an item, then what is its inverse demand equation?

Answer 1

The inverse demand equation is found by rearranging the original demand equation to solve for P as a function of Q. For example, if the demand equation is P = 8 - 0.5Qd, the inverse demand equation would be Qd = 16 - 2P.

Step-by-step explanation:

To determine the inverse demand equation, we must manipulate the original demand equation so that it solves for P as a function of Q. The original question did not specify the demand equation, but assuming a general linear demand equation of the form Q = a - bP, we rearrange terms to solve for P. Here's how to do it step-by-step:

1. Start with the demand equation: Q = a - bP.
2. Add bP to both sides: Q + bP = a.
3. Subtract Q from both sides: bP = a - Q.
4. Finally, divide by b to isolate P: P = (a - Q) / b.

This is the inverse demand equation, where P is now expressed as a function of Q.

If we take an example from the provided information where the demand equation is P = 8 - 0.5Qd, to find its inverse, we rearrange it as follows:

1. Start with the demand equation: P = 8 - 0.5Qd.
2. Add 0.5Qd to both sides: P + 0.5Qd = 8.
3. Subtract P from both sides: 0.5Qd = 8 - P.
4. Finally, divide by 0.5 to isolate Qd: Qd = (8 - P) / 0.5.

The inverse demand equation would be Qd = (8 - P) / 0.5, which can be simplified to Qd = 16 - 2P.