Organize each of the following to express P as a function of Q

Question

Q=20-P

Q=20-5P

8Q=18-2P

Answer 1

This is known as finding the inverse demand function. All you have to do is use algebra to rearrange the functions so that price is isolated like this:

Q=20-P

P= 20 - Q

Q=20-5P

5P = 20 - Q

P = 4 - 0.2Q

8Q=18-2P

2P = 18 - 8Q

P = 9 - 4Q

If you set any of these functions equal to a supply function, you can solve for equilibrium price and quantity. You can also graph these functions in a graphing calculator to see these demand curves visually.