Question

Suppose that 3 brothers, Brian, Jimmy, and Michael have demand for books of Q=10-P, Q=20-2P, and Q = 30-0.5P respectively. If they are the only buyers of books, what is total consumer surplus at a price of 12?

Answer 1

Answer.) Lets first analyze individual demand curves.

Brian demand curve is

Q=10-P

Brian demand is simply indicating that if price level is higher or equal to 10 then Brian would not demand any book. Similarly, Jimmy's demand curve Q=20-2P also indicating that  if price level is higher or equal to 10 then Jimmy would not demand any book. Since price is already at 12,therefore, Brian and Jimmy both are out of book market. Now, Micheal's demand ,

Q = 30-0.5P

Put P = 12, we have

Q = 24

So,Michael would demand 24 books. Therefore, only Micheal's consumer surplus would also be same as total consumer surplus.

total consumer surplus= (1/2)(30-24)(12) = 36