Math 1100
Extra Credit 3
2 December, 2011
• This assignment is worth 10 extra points, to be added to your exam
score.
• You should turn it in by Friday, 9 December, 2011.
• Show all your work clearly. In particular, set up your integrals neatly
and in an obvious place. Better yet, circle them.
Name:
Extra Credit 1:Consumer and Producer Surplus
(That’s right! A business application!)
Read pages 904 − 908 in the textbook. If you have questions feel free to ask, but the book
explains it as well as I could, so try that first.
1. The demand function for a product is p = 34 − x2 . If the equilibrium price is $9, what
is the consumers’ surplus?
12
2. If the supply function for a product is p = x−1
and the supply function is p = 1 + 0.2x,
find the consumer’s surplus at the equilibrium point.
3. A monopoly has a total cost function of C(x) = 120x + 6x2 for its product, and the
demand function for this product is p = 360 − 3x − 2x2 . Find the consumers’ surplus at
the point where the monopoly has maximum profit.
x
4. If the supply function for a commodity is p = 10e 3 , what is the producers’ surplus when
15 units are sold?
5. The demand function for a certain product is p = 144 − 2x2 and the supply function is
p = x2 + 33x + 48. Find the producers’ surplus at the equilibrium point.